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Thermal Engineering

What is Typical Pressure in Engineering – Examples – Definition

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Typical pressures in engineering and few examples are summarized here. For most engineering problems pascal (Pa) is fairly small unit, so kPa and MPa are used. Thermal Engineering

Typical Pressures in Engineering – Examples

The pascal (Pa) as a unit of pressure measurement is widely used throughout the world and has largely replaced the pounds per square inch (psi) unit, except in some countries that still use the Imperial measurement system, including the United States. For most engineering problems pascal (Pa) is fairly small unit, so it is convenient to work with multiples of the pascal: the kPa, the MPa, or the bar. Following list summarizes a few examples:

  • Typically most of nuclear power plants operates multi-stage condensing steam turbines. These turbines exhaust steam at a pressure well below atmospheric (e.g. at 0.08 bar or 8 kPa or 1.16 psia) and in a partially condensed state. In relative units it is a negative gauge pressure of about – 0.92 bar, – 92 kPa, or – 13.54 psig.
  • The Standard Atmospheric Pressure approximates to the average pressure at sea-level at the latitude 45° N.  The Standard Atmospheric Pressure is defined at sea-level at 273oK (0oC) and is:
    • 101325 Pa
    • 1.01325 bar
    • 14.696 psi
    • 760 mmHg
    • 760 torr
  • Car tire overpressure is about 2.5 bar, 0.25 MPa, or 36 psig.
  • Steam locomotive fire tube boiler: 150–250 psig
  • A high-pressure stage of condensing steam turbine at nuclear power plant operates at steady state with inlet conditions of  6 MPa (60 bar, or 870 psig), t = 275.6°C, x = 1
  • A boiling water reactor is cooled and moderated by water like a PWR, but at a lower pressure (e.g. 7MPa, 70 bar, or 1015 psig), which allows the water to boil inside the pressure vessel producing the steam that runs the turbines.
  • Pressurized water reactors are cooled and moderated by high-pressure liquid water (e.g. 16MPa, 160 bar, or 2320 psig). At this pressure water boils at approximately 350°C (662°F), which provides subcooling margin of about 25°C.
  • The supercritical water reactor (SCWR) is operated at supercritical pressure. The term supercritical in this context refers to the thermodynamic critical point of water (TCR = 374 °C;  pCR = 22.1 MPa)
  • Common rail direct fuel injection: On diesel engines, it features a high-pressure (over 1 000 bar or 100 MPa or 14500 psi) fuel rail.
 
Pressure in Pressurized Water Reactor
pressurizer
A pressurizer is a key component of PWRs.

Pressurized water reactors use a reactor pressure vessel (RPV) to contain the nuclear fuel, moderator, control rods and coolant. They are cooled and moderated by high-pressure liquid water (e.g. 16MPa). At this pressure water boils at approximately 350°C (662°F).  This high pressure is maintained by pressurizer. Inlet temperature of the water is about 290°C (554°F). The water (coolant) is heated in the reactor core to approximately 325°C (617°F) as the water flows through the core. As it can be seen, the reactor has approximately 25°C subcooled coolant (distance from the saturation).

A pressurizer is a component of a pressurized water reactor. Pressure in the primary circuit of PWRs is maintained by a pressurizer, a separate vessel that is connected to the primary circuit (hot leg) and partially filled with water which is heated to the saturation temperature (boiling point) for the desired pressure by submerged electrical heaters.

On the other hand there are spray lines to decrease pressure inside the pressurizer, which in turn causes decrease in pressure in reactor coolant system. These spray lines sprays reactor coolant from the cold leg of a loop into the steam space and condenses a portion of the steam. The quenching action reduces pressure and limits the pressure increases.

Pressures in Condensing Steam Turbines
engineering thermodynamics
Rankine Cycle – Thermodynamics as Energy Conversion Science

Typically most of nuclear power plants operates multi-stage condensing steam turbines. In these turbines the high-pressure stage receives steam (this steam is nearly saturated steam – x = 0.995 – point C at the figure; 6 MPa; 275.6°C) from a steam generator and exhaust it to moisture separator-reheater (point D). The steam must be reheated in order to avoid damages that could be caused to blades of steam turbine by low quality steam. The reheater heats the steam (point D) and then the steam is directed to the low-pressure stage of steam turbine, where expands (point E to F). The exhausted steam is at a pressure well below atmospheric (absolute pressure of 0.008 MPa), and is in a partially condensed state (point F), typically of a quality near 90%.

See also: Wet Steam

See also: Steam Tables

Pressure coefficient - How pressure influences reactivity
The pressure coefficient (or the moderator density coefficient) is defined as the change in reactivity per unit change in pressure.

αP = dρ⁄dP

It is expressed in units of pcm/MPa. The magnitude and sign (+ or -) of the pressure coefficient is primarily a function of the moderator-to-fuel ratio. That means it primarily depends on certain reactor design.

Although water is considered to be incompressible, in reality, it is slightly compressible (especially at 325°C (617°F)). It is obvious, the effect of pressure in the primary circuit have similar consequences as the moderator temperature. In comparison with effects of moderator temperature changes, changes in pressure have of lower order impact on reactivity and the causes are only in the density of moderator, not in the change of microscopic cross-sections.

 
References:
Reactor Physics and Thermal Hydraulics:
  1. J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).
  2. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
  3. W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.
  4. Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317
  5. Todreas Neil E., Kazimi Mujid S. Nuclear Systems Volume I: Thermal Hydraulic Fundamentals, Second Edition. CRC Press; 2 edition, 2012, ISBN: 978-0415802871
  6. Zohuri B., McDaniel P. Thermodynamics in Nuclear Power Plant Systems. Springer; 2015, ISBN: 978-3-319-13419-2
  7. Moran Michal J., Shapiro Howard N. Fundamentals of Engineering Thermodynamics, Fifth Edition, John Wiley & Sons, 2006, ISBN: 978-0-470-03037-0
  8. Kleinstreuer C. Modern Fluid Dynamics. Springer, 2010, ISBN 978-1-4020-8670-0.
  9. U.S. Department of Energy, THERMODYNAMICS, HEAT TRANSFER, AND FLUID FLOW. DOE Fundamentals Handbook, Volume 1, 2 and 3. June 1992.

See also:

Pressure

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What is Characteristics of SCWRs – Definition

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Characteristics of SCWRs. SCWRs operate at pressures above the critical pressure, properties of water in the reactor change gradually and continuously. Thermal Engineering

Characteristics of SCWRs

Properties of Supercritical WaterSCWRs operate at pressures above the critical pressure,  properties of water in the reactor change gradually and continuously from those we ordinarily associate with a liquid (high density, small compressibility) to those of a gas (low density, large compressibility) without a phase change. There is no change in the phase of water in the core. On the other hand, physical properties such as density, specific heat, specific enthalpy undergo significant changes, especially in the temperature range of the pseudocritical region (for 25 MPa between 372°C and 392°C). For example,

  • the density of supercritical water at the inlet and at the outlet is about 777 kg/m3  (for 25MPa and 280°C) and 90 kg/m3 (for 25MPa and 500°C),
  • the specific enthalpy of supercritical water at the inlet and at the outlet is about 1230 kJ/kg (for 25MPa and 280°C) and 3165 kJ/kg (for 25MPa and 500°C)

From a neutronics point of view, the density of water is the most important factor. There is a significant change of neutron spectrum, which changes with the axial coordinate of the core. It is caused by the greater moderation in places with greater density. For this reason, a coupled neutronics – thermal hydraulics calculation is inevitable to obtain neutron flux distribution within the core. In each nuclear reactor, there is a direct proportionality between the neutron flux and the reactor thermal power.

Since the coolant (moderator) undergo significant change in density, the SCWR can also be designed as a fast neutron reactor. This property depends on certain reactor design.

 
Critical Point of Water
Phase diagram of water
Phase diagram of water.
Source: wikipedia.org CC BY-SA

In thermodynamics, a critical point (or critical state) is the end point of a phase equilibrium curve. The phase diagram of water is a pressure-temperature diagram for water that shows how all three phases (solid, liquid, and vapor) may coexist together in thermal equilibrium. Along the vaporization line, the liquid and vapor phases are in equilibrium, along the fusion line, the solid and liquid phases are in equilibrium and along the sublimation line, the solid and vapor phases are in equilibrium. The only point at which all three phases may exist in equilibrium is the triple point. The vaporization line ends at the critical point because there is no distinct change from the liquid phase to the vapor phase above the critical point.

Above the critical point, there is no constant-temperature vaporization process. At the critical point the saturated-liquid and saturated-vapor states are identical. The temperature, pressure, and specific volume at the critical point are called the critical temperature, critical pressure, and critical volume. For water, these parameters are the following:

  • Pcr = 22.09 MPa
  • Tcr = 374.14 °C (or 647.3 K)
  • vcr = 0.003155 m3/kg
  • uf = ug = 2014 kJ/kg
  • hf = hg = 2084 kJ/kg
  • sf = sg =4.406 kJ/kg K

A supercritical phase (e.g. water at a pressure above the critical pressure) does not separate into two phases when it is cooled at constant pressure (along a horizontal line above the critical point in phase diagram). Instead, its properties change gradually and continuously from those we ordinarily associate with a gas (low density, large compressibility) to those of a liquid (high density, small compressibility) without a phase change.

As can be seen from steam tables, as we approach the critical point, the differences in physical properties (such as density and enthalpy) between the liquid and vapor phases become smaller. For example, just below the critical point at the pressure of 21.8 MPa and the temperature of 373°C the specific enthalpy of saturated liquid is 1970 kJ/kg, while the specific enthalpy of saturated vapor is 2230 kJ/kg. The specific heat of vaporization is only 260 kJ/kg. Exactly at the critical point these differences become zero, and at this point the distinction between liquid and vapor disappears. The heat of vaporization also becomes zero at the critical point.

Near the critical point, the physical properties of the liquid and the vapor change dramatically. For example, liquid water under normal conditions has a low thermal expansion coefficient, is nearly incompressible, is an excellent solvent for electrolytes, and has a high dielectric constant. But near the critical point, all these properties change into the exact opposite: water becomes compressible, has a significant thermal expansion coefficient, has a low dielectric constant, is a bad solvent for electrolytes. At pressures greater than the critical pressure the physical properties also undergo a fast transition, but without singularities. With further increase in pressure the transition becomes smoother. This transition region is called pseudocritical region, at a given pressure the temperature where the specific heat has its maximum is called pseudocritical point.

For nearly all familiar materials the critical pressures are much greater than atmospheric pressure, therefore we don’t observe this behavior in everyday life. But in energy engineering, there are many applications for supercritical water. One of ways to increase thermal efficiency of thermodynamic cycles (e.g. Rankine cycle) is to increase the peak temperature and pressure in the boiler. High-pressure steam boilers in thermal power plants regularly run at pressures and temperatures well above the critical point.

In nuclear engineering, the supercritical water reactor is considered a promising advancement for nuclear power plants because of its high thermal efficiency (~45 % vs. ~33 % for current LWRs). This concept of reactor operates at supercritical pressure (i.e. greater than 22.1 MPa) and belongs to Generation IV reactor designs.

Properties of Supercritical Water
Properties of Supercritical WaterA supercritical fluid is a fluid that is at pressures higher than its thermodynamic critical values. At the critical and supercritical pressures a fluid is considered as a single-phase substance in spite of the fact that all thermophysical properties undergo significant changes within the critical and pseudocritical regions.

____________________

Pseudocritical line – pseudocritical points. Pseudocritical line consist of pseudocritical points, which are points at a pressure above the critical pressure and at a temperature (Tpc > Tcr) corresponding to the maximum value of the specific heat at this particular pressure.

____________________

Pseudocritical line - Pseudocritical pointsAt pressures above the critical pressure,  properties of water in the reactor change gradually and continuously from those we ordinarily associate with a liquid (high density, small compressibility) to those of a gas (low density, large compressibility) without a phase change. There is no change in the phase of water in the core. On the other hand, physical properties such as density, specific heat, specific enthalpy undergo significant changes, especially in the temperature range of the pseudocritical region (for 25 MPa between 372°C and 392°C). For example,

  • the density of supercritical water at the inlet and at the outlet is about 777 kg/m3  (for 25MPa and 280°C) and 90 kg/m3 (for 25MPa and 500°C),
  • the specific enthalpy of supercritical water at the inlet and at the outlet is about 1230 kJ/kg (for 25MPa and 280°C) and 3165 kJ/kg (for 25MPa and 500°C)

supercritical-fluid-specific-heat-conductivityFollowing figures shows the behaviour of thermophysical properties of water near the critical (22.1MPa) and pseudocritical (25MPa) points. Near the critical point these property changes are dramatic. In the vicinity of the pseudocritical point at 25 MPa, these property changes become less significant. At 25 MPa the most significant property changes occur within ±25◦C around pseudocritical point (389.4◦C), this region is known as the pseudocritical region. For convenience, below the pseudocritical point fluid properties are considered to show liquid-like behaviour and above the pseudocritical point they are considered to show gas-like behaviour.

Steam Tables - Supercritical Water

Special Link:  Steam Tables – nist.gov

Characteristics of SCWRs
 
References:
Reactor Physics and Thermal Hydraulics:
  1. J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).
  2. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
  3. W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.
  4. Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317
  5. Todreas Neil E., Kazimi Mujid S. Nuclear Systems Volume I: Thermal Hydraulic Fundamentals, Second Edition. CRC Press; 2 edition, 2012, ISBN: 978-0415802871
  6. Zohuri B., McDaniel P. Thermodynamics in Nuclear Power Plant Systems. Springer; 2015, ISBN: 978-3-319-13419-2
  7. Moran Michal J., Shapiro Howard N. Fundamentals of Engineering Thermodynamics, Fifth Edition, John Wiley & Sons, 2006, ISBN: 978-0-470-03037-0
  8. Kleinstreuer C. Modern Fluid Dynamics. Springer, 2010, ISBN 978-1-4020-8670-0.
  9. U.S. Department of Energy, THERMODYNAMICS, HEAT TRANSFER, AND FLUID FLOW. DOE Fundamentals Handbook, Volume 1, 2 and 3. June 1992.

See also:

SCWR

We hope, this article, Characteristics of SCWRs, helps you. If so, give us a like in the sidebar. Main purpose of this website is to help the public to learn some interesting and important information about thermal engineering.

What is Supercritical Fluid – Supercritical Water – Definition

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Supercritical Fluid – Supercritical Water. A supercritical fluid is a single-phase fluid that is at pressures higher than its thermodynamic critical values. Thermal Engineering

Supercritical Fluid – Supercritical Water

Phase diagram of water
Phase diagram of water.
Source: wikipedia.org CC BY-SA

The classification of steam on wet, dry and superheated has its limitation. Consider the behavior of the system which is heated at the pressure, that is higher than the critical pressure. In this case, there would be no change in phase from liquid to steam. At all states there would be only one phase. Vaporization and condensation can occur only when the pressure is less than the critical pressure. The terms liquid and vapor tend to lose their significance.

At pressure, that is higher than the critical pressure,  water is in special state, that is known as supercritical fluid state. A supercritical fluid is a fluid that is at pressures higher than its thermodynamic critical values. At the critical and supercritical pressures a fluid is considered as a single-phase substance in spite of the fact that all thermophysical properties undergo significant changes within the critical and pseudocritical regions.

See also: Critical Point of Water

 
What is Supercritical Steam
Supercritical “steam” is actually supercritical water, because at supercritical pressures fluid is considered as a single-phase substance. However, this term is widely (and incorrectly) used in the literature in relation to supercritical “steam” generators and turbines.
What is Pseudocritical Line
Pseudocritical line - Pseudocritical pointsPseudocritical line – pseudocritical points. Pseudocritical line consist of pseudocritical points, which are points at a pressure above the critical pressure and at a temperature (Tpc > Tcr) corresponding to the maximum value of the specific heat at this particular pressure.
 
Supercritical Water Reactor - SCWR
Characteristics of SCWRs

See also: Supercritical Water Reactor

The supercritical water reactor (SCWR) is a concept of Generation IV reactor, that is operated at supercritical pressure (i.e. greater than 22.1 MPa). The term supercritical in this context refers to the thermodynamic critical point of water (TCR = 374 °C;  pCR = 22.1 MPa), and must not be confused with the criticality of the reactor core, that describes changes in the neutron population in the reactor core.

The supercritical water reactor may be operated as a thermal reactor or as a fast-neutron reactor, depending on the core design. The concept of the supercritical water reactor may be based on classical pressure vessel as in commercial PWRs or on pressure tubes as in CANDU reactors. The pressure-vessel design of supercritical water reactors is developed largely in the EU, US, Japan, Korea, and China, while the pressure-channel design is developed largely in Canada and in Russia. The pressure-vessel design allows using a traditional high-pressure circuit layout. The pressure-channel design allows the key features of passive accident and decay heat removal by radiation and convection from the distributed channels even with no active cooling and fuel melting and use of multi-pass reactor flows making reheating and superheating possible.

For both pressure vessel and pressure-tube designs, a once through steam cycle has been envisaged, omitting any coolant recirculation inside the reactor. It is similar as in boiling water reactors, steam will be supplied directly to the steam turbine and the feed water from the steam cycle will be supplied back to the core.

As well as the supercritical water reactor may use light water or heavy water as neutron moderator. As can be seen, there are many SCWR designs, but all SCWRs have a key feature, that is the use of water beyond the thermodynamic critical point as primary coolant. Since this feature allows to increase the peak temperature, the supercritical water reactors are considered a promising advancement for nuclear power plants because of its high thermal efficiency (~45 % vs. ~33 % for current LWRs).

Properties of Supercritical WaterA supercritical fluid is a fluid that is at pressures higher than its thermodynamic critical values. At the critical and supercritical pressures a fluid is considered as a single-phase substance in spite of the fact that all thermophysical properties undergo significant changes within the critical and pseudocritical regions.

At pressures above the critical pressure,  properties of water in the reactor change gradually and continuously from those we ordinarily associate with a liquid (high density, small compressibility) to those of a gas (low density, large compressibility) without a phase change. There is no change in the phase of water in the core. On the other hand, physical properties such as density, specific heat, specific enthalpy undergo significant changes, especially in the temperature range of the pseudocritical region (for 25 MPa between 372°C and 392°C). For example, in a typical supercritical water reactor:

  • the density of supercritical water at the inlet and at the outlet is about 777 kg/m3  (for 25MPa and 280°C) and 90 kg/m3 (for 25MPa and 500°C),
  • the specific enthalpy of supercritical water at the inlet and at the outlet is about 1230 kJ/kg (for 25MPa and 280°C) and 3165 kJ/kg (for 25MPa and 500°C)

supercritical-fluid-specific-heat-conductivityFollowing figures shows the behaviour of thermophysical properties of water near the critical (22.1MPa) and pseudocritical (25MPa) points. Near the critical point these property changes are dramatic. In the vicinity of the pseudocritical point at 25 MPa, these property changes become less significant. At 25 MPa the most significant property changes occur within ±25◦C around pseudocritical point (389.4◦C), this region is known as the pseudocritical region. For convenience, below the pseudocritical point fluid properties are considered to show liquid-like behaviour and above the pseudocritical point they are considered to show gas-like behaviour.

 
Steam Tables
Special links:
 www.nist.gov – Steam Tables – Saturation (Temperature)
 www.nist.gov – Steam Tables – Saturation (Pressure)
 www.nist.gov – Steam Tables – Compressed Water – Superheated Steam
 
References:
Reactor Physics and Thermal Hydraulics:
  1. J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).
  2. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
  3. W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.
  4. Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317
  5. Todreas Neil E., Kazimi Mujid S. Nuclear Systems Volume I: Thermal Hydraulic Fundamentals, Second Edition. CRC Press; 2 edition, 2012, ISBN: 978-0415802871
  6. Zohuri B., McDaniel P. Thermodynamics in Nuclear Power Plant Systems. Springer; 2015, ISBN: 978-3-319-13419-2
  7. Moran Michal J., Shapiro Howard N. Fundamentals of Engineering Thermodynamics, Fifth Edition, John Wiley & Sons, 2006, ISBN: 978-0-470-03037-0
  8. Kleinstreuer C. Modern Fluid Dynamics. Springer, 2010, ISBN 978-1-4020-8670-0.
  9. U.S. Department of Energy, THERMODYNAMICS, HEAT TRANSFER, AND FLUID FLOW. DOE Fundamentals Handbook, Volume 1, 2 and 3. June 1992.

See also:

Steam

We hope, this article, Supercritical Fluid – Supercritical Water, helps you. If so, give us a like in the sidebar. Main purpose of this website is to help the public to learn some interesting and important information about thermal engineering.

What is Supercritical Steam – Definition

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What is Supercritical Steam. Supercritical steam is actually supercritical water, because at supercritical pressures fluid is considered as a single-phase substance. Thermal Engineering

What is Supercritical Steam

Supercritical “steam” is actually supercritical water, because at supercritical pressures fluid is considered as a single-phase substance. However, this term is widely (and incorrectly) used in the literature in relation to supercritical “steam” generators and turbines.

See also: Supercritical Water

Supercritical Water

Phase diagram of water
Phase diagram of water.
Source: wikipedia.org CC BY-SA

At pressure, that is higher than the critical pressure,  water is in special state, that is known as supercritical fluid state. A supercritical fluid is a fluid that is at pressures higher than its thermodynamic critical values. At the critical and supercritical pressures a fluid is considered as a single-phase substance in spite of the fact that all thermophysical properties undergo significant changes within the critical and pseudocritical regions.

See also: Critical Point of Water

 
References:
Reactor Physics and Thermal Hydraulics:
  1. J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).
  2. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
  3. W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.
  4. Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317
  5. Todreas Neil E., Kazimi Mujid S. Nuclear Systems Volume I: Thermal Hydraulic Fundamentals, Second Edition. CRC Press; 2 edition, 2012, ISBN: 978-0415802871
  6. Zohuri B., McDaniel P. Thermodynamics in Nuclear Power Plant Systems. Springer; 2015, ISBN: 978-3-319-13419-2
  7. Moran Michal J., Shapiro Howard N. Fundamentals of Engineering Thermodynamics, Fifth Edition, John Wiley & Sons, 2006, ISBN: 978-0-470-03037-0
  8. Kleinstreuer C. Modern Fluid Dynamics. Springer, 2010, ISBN 978-1-4020-8670-0.
  9. U.S. Department of Energy, THERMODYNAMICS, HEAT TRANSFER, AND FLUID FLOW. DOE Fundamentals Handbook, Volume 1, 2 and 3. June 1992.

See also:

Supercritical Water

We hope, this article, Supercritical Steam, helps you. If so, give us a like in the sidebar. Main purpose of this website is to help the public to learn some interesting and important information about thermal engineering.

What is Property of Supercritical Water – Definition

by
Properties of Supercritical Water. At pressures above the critical pressure, properties of water in the reactor change gradually and continuously. Thermal Engineering

Properties of Supercritical Water

Properties of Supercritical WaterA supercritical fluid is a fluid that is at pressures higher than its thermodynamic critical values. At the critical and supercritical pressures a fluid is considered as a single-phase substance in spite of the fact that all thermophysical properties undergo significant changes within the critical and pseudocritical regions.

At pressures above the critical pressure,  properties of water in the reactor change gradually and continuously from those we ordinarily associate with a liquid (high density, small compressibility) to those of a gas (low density, large compressibility) without a phase change. There is no change in the phase of water in the core. On the other hand, physical properties such as density, specific heat, specific enthalpy undergo significant changes, especially in the temperature range of the pseudocritical region (for 25 MPa between 372°C and 392°C). For example, in a typical supercritical water reactor:

  • the density of supercritical water at the inlet and at the outlet is about 777 kg/m3  (for 25MPa and 280°C) and 90 kg/m3 (for 25MPa and 500°C),
  • the specific enthalpy of supercritical water at the inlet and at the outlet is about 1230 kJ/kg (for 25MPa and 280°C) and 3165 kJ/kg (for 25MPa and 500°C)

supercritical-fluid-specific-heat-conductivityFollowing figures shows the behaviour of thermophysical properties of water near the critical (22.1MPa) and pseudocritical (25MPa) points. Near the critical point these property changes are dramatic. In the vicinity of the pseudocritical point at 25 MPa, these property changes become less significant. At 25 MPa the most significant property changes occur within ±25◦C around pseudocritical point (389.4◦C), this region is known as the pseudocritical region. For convenience, below the pseudocritical point fluid properties are considered to show liquid-like behaviour and above the pseudocritical point they are considered to show gas-like behaviour.

 
Steam Tables
Special links:
 www.nist.gov – Steam Tables – Saturation (Temperature)
 www.nist.gov – Steam Tables – Saturation (Pressure)
 www.nist.gov – Steam Tables – Compressed Water – Superheated Steam
 
What is Pseudocritical Line
Pseudocritical line - Pseudocritical pointsPseudocritical line – pseudocritical points. Pseudocritical line consist of pseudocritical points, which are points at a pressure above the critical pressure and at a temperature (Tpc > Tcr) corresponding to the maximum value of the specific heat at this particular pressure.
Characteristics of SCWRs
Typical properties of coolant in SCWR.
 
References:
Reactor Physics and Thermal Hydraulics:
  1. J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).
  2. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
  3. W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.
  4. Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317
  5. Todreas Neil E., Kazimi Mujid S. Nuclear Systems Volume I: Thermal Hydraulic Fundamentals, Second Edition. CRC Press; 2 edition, 2012, ISBN: 978-0415802871
  6. Zohuri B., McDaniel P. Thermodynamics in Nuclear Power Plant Systems. Springer; 2015, ISBN: 978-3-319-13419-2
  7. Moran Michal J., Shapiro Howard N. Fundamentals of Engineering Thermodynamics, Fifth Edition, John Wiley & Sons, 2006, ISBN: 978-0-470-03037-0
  8. Kleinstreuer C. Modern Fluid Dynamics. Springer, 2010, ISBN 978-1-4020-8670-0.
  9. U.S. Department of Energy, THERMODYNAMICS, HEAT TRANSFER, AND FLUID FLOW. DOE Fundamentals Handbook, Volume 1, 2 and 3. June 1992.

See also:

Supercritical Water

We hope, this article, Property of Supercritical Water, helps you. If so, give us a like in the sidebar. Main purpose of this website is to help the public to learn some interesting and important information about thermal engineering.

What is Pseudocritical line – Pseudocritical points – Definition

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Pseudocritical line consist of pseudocritical points, which are points at a pressure above the critical pressure and at a temperature (Tpc > Tcr).

Supercritical Fluid – Supercritical Water

Pseudocritical line - Pseudocritical pointsPseudocritical line – pseudocritical points. Pseudocritical line consist of pseudocritical points, which are points at a pressure above the critical pressure and at a temperature (Tpc > Tcr) corresponding to the maximum value of the specific heat at this particular pressure.

At pressures above the critical pressure,  properties of water in the reactor change gradually and continuously from those we ordinarily associate with a liquid (high density, small compressibility) to those of a gas (low density, large compressibility) without a phase change. There is no change in the phase of water in the core. On the other hand, physical properties such as density, specific heat, specific enthalpy undergo significant changes, especially in the temperature range of the pseudocritical region (for 25 MPa between 372°C and 392°C). For example, in a typical supercritical water reactor:

  • the density of supercritical water at the inlet and at the outlet is about 777 kg/m3  (for 25MPa and 280°C) and 90 kg/m3 (for 25MPa and 500°C),
  • the specific enthalpy of supercritical water at the inlet and at the outlet is about 1230 kJ/kg (for 25MPa and 280°C) and 3165 kJ/kg (for 25MPa and 500°C)

supercritical-fluid-specific-heat-conductivityFollowing figures shows the behaviour of thermophysical properties of water near the critical (22.1MPa) and pseudocritical (25MPa) points. Near the critical point these property changes are dramatic. In the vicinity of the pseudocritical point at 25 MPa, these property changes become less significant. At 25 MPa the most significant property changes occur within ±25◦C around pseudocritical point (389.4◦C), this region is known as the pseudocritical region. For convenience, below the pseudocritical point fluid properties are considered to show liquid-like behaviour and above the pseudocritical point they are considered to show gas-like behaviour.

 
References:
Reactor Physics and Thermal Hydraulics:
  1. J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).
  2. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
  3. W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.
  4. Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317
  5. Todreas Neil E., Kazimi Mujid S. Nuclear Systems Volume I: Thermal Hydraulic Fundamentals, Second Edition. CRC Press; 2 edition, 2012, ISBN: 978-0415802871
  6. Zohuri B., McDaniel P. Thermodynamics in Nuclear Power Plant Systems. Springer; 2015, ISBN: 978-3-319-13419-2
  7. Moran Michal J., Shapiro Howard N. Fundamentals of Engineering Thermodynamics, Fifth Edition, John Wiley & Sons, 2006, ISBN: 978-0-470-03037-0
  8. Kleinstreuer C. Modern Fluid Dynamics. Springer, 2010, ISBN 978-1-4020-8670-0.
  9. U.S. Department of Energy, THERMODYNAMICS, HEAT TRANSFER, AND FLUID FLOW. DOE Fundamentals Handbook, Volume 1, 2 and 3. June 1992.

See also:

Supercritical Water

We hope, this article, Pseudocritical line – Pseudocritical points, helps you. If so, give us a like in the sidebar. Main purpose of this website is to help the public to learn some interesting and important information about thermal engineering.

What is Mass and Weight – Properties – Definition

by
What is mass and weight. The terms mass and weight are physical quantities and are often confused with one another, but it is important to distinguish between them. Thermal Engineering

Mass and Weight

One of the most familiar forces is the weight of a body, which is the gravitational force that the earth exerts on the body. In general, gravitation is a natural phenomenon by which all things with mass are brought toward one another. The terms mass and weight are often confused with one another, but it is important to distinguish between them. It is absolutely essential to understand clearly the distinctions between these two physical quantities.

See also: Law of Conservation of Mass

 
What is Mass
The mass of an object is a fundamental property of the object. It is a numerical measure of its inertia and the measure of an object’s resistance to acceleration when a force is applied. It is also a fundamental measure of the amount of matter in the object. The greater the mass, the greater the force needed to cause a given acceleration. This is reflected in Newton’s second law (F=ma).

The mass of a certain body will remain constant even if the gravitational acceleration acting upon that body changes. For example, on earth an object has a certain mass and a certain weight. When the same object is placed in outer space, away from the earth’s gravitational field, its mass remains the same, but it is now in a “weightless” condition. This means in this condition it will weight zero, because gravitational acceleration and, thus, force will equal to zero.

Mass and weight are related: Bodies having large mass also have large weight. A large stone is hard to throw because of its large mass, and hard to lift off the ground because of its large weight. To understand the relationship between mass and weight, consider a freely falling stone, that has an acceleration of magnitude g (g = 9.81 m/s2 is the acceleration due to Earth’s gravitational field). Newton’s second law tells us that a force must act to produce this acceleration. If a 1 kilogram stone falls with an acceleration of the required force has magnitude:

F = ma = 1 [kg] x 9.81 [m/s2] = 9.8 [kg m/s2] = 9.8 N

The force that makes the body accelerate downward is its weight. Any body near the surface of the earth that has a mass of 1 kg must have a weight of 9.8 N to give it the acceleration we observe when it is in free fall.

Example: The weight of a stone on the Earth, on the Mars and on the Moon

Weight of a stone on the Earth

gravitational-field-earth-mars-moonThe acceleration due to Earth’s gravitational field is gEarth = 9.81 m/s2.The weight of a stone with mass 1 kg on the Earth can be calculated as:

FEarth = 1 [kg] x 9.81 [m/s2] = 9.8 [kg m/s2] = 9.8 N

Weight of a stone on the Mars

The acceleration of gravity on the Mars is approximately 38% of the acceleration of gravity on the earth. The acceleration due to Moon’s gravitational field is gMars = 3.71 m/s2.

Therefore the weight of the same stone with mass 1 kg on the Mars is:

FMoon = 1 [kg] x 3.71 [m/s2] = 3.71 [kg m/s2] = 3.71 N

Weight of a stone on the Moon

The acceleration of gravity on the Moon is approximately 1/6 of the acceleration of gravity on the earth. The acceleration due to Moon’s gravitational field is gMoon = 1.62 m/s2.

Therefore the weight of the same stone with mass 1 kg on the Moon is:

FMoon = 1 [kg] x 1.62 [m/s2] = 1.62 [kg m/s2] = 1.62 N

The Standard Kilogram

The usual symbol for mass is m and its SI unit is the kilogram. The SI standard of mass is a cylinder of platinum and iridium that is kept at the International Bureau of Weights and Measures near Paris and assigned, by international agreement, a mass of 1 kilogram.

Standard Kilogram
A computer-generated image of the International Prototype kilogram (IPK), which is made from an alloy of 90% platinum and 10% iridium (by weight) and machined into a right-circular cylinder (height = diameter) of 39.17 mm. Source: wikipedia.org; License: CC BY-SA

Relativistic Mass

While the mass is normally considered to be an unchanging property of an object, at speeds approaching the speed of light one must consider the increase in the relativistic mass. The relativistic definition of momentum is sometimes interpreted as an increase in the mass of an object. In this interpretation, a particle can have a relativistic mass, mrel. The increase in effective mass with speed is given by the expression:

relativistic-mass-min

In this “mass-increase” formula, m is referred to as the rest mass of the object. It follows from this formula, that an object with nonzero rest mass cannot travel at the speed of light. As the object approaches the speed of light, the object’s momentum increase without bound. On the other hand, when the relative velocity is zero, the Lorentz factor is simply equal to 1, and the relativistic mass is reduced to the rest mass. With this interpretation, the mass of an object appears to increase as its speed increases. In must be added, many physicists believe an object has only one mass (its rest mass), and that it is only the momentum that increases with speed.

What is Mass Defect
See also: Mass Defect

In special theory of relativity certain types of matter may be created or destroyed, but in all of these processes, the mass and energy associated with such matter remains unchanged in quantity. It was found the rest mass of an atomic nucleus is measurably smaller than the sum of the rest masses of its constituent protons, neutrons and electrons. Mass was no longer considered unchangeable in the closed system. The difference is a measure of the nuclear binding energy which holds the nucleus together. According to the Einstein relationship (E=mc2), this binding energy is proportional to this mass difference and it is known as the mass defect.

 
What is Weight
The terms  are often confused with one another, but it is important to distinguish between them. In science and engineering, the weight of an object is usually taken to be the force on the object due to gravity. In general, gravitation is a natural phenomenon by which all things with mass are brought toward one another.

The mass of an object is a fundamental property of the object. It is a numerical measure of its inertia and the measure of an object’s resistance to acceleration when a force is applied. It is also a fundamental measure of the amount of matter in the object. The greater the mass, the greater the force needed to cause a given acceleration. This is reflected in Newton’s second law (F=ma).

The mass of a certain body will remain constant even if the gravitational acceleration acting upon that body changes. For example, on earth an object has a certain mass and a certain weight. When the same object is placed in outer space, away from the earth’s gravitational field, its mass remains the same, but it is now in a “weightless” condition. This means in this condition it will weight zero, because gravitational acceleration and, thus, force will equal to zero.

Mass and weight are related:

Bodies having large mass also have large weight. A large stone is hard to throw because of its large mass, and hard to lift off the ground because of its large weight. To understand the relationship between mass and weight, consider a freely falling stone, that has an acceleration of magnitude g (g = 9.81 m/s2 is the acceleration due to Earth’s gravitational field). Newton’s second law tells us that a force must act to produce this acceleration. If a 1 kilogram stone falls with an acceleration of the required force has magnitude:

F = ma = 1 [kg] x 9.81 [m/s2] = 9.8 [kg m/s2] = 9.8 N

The force that makes the body accelerate downward is its weight. Any body near the surface of the earth that has a mass of 1 kg must have a weight of 9.8 N to give it the acceleration we observe when it is in free fall.

Example: The weight of a stone on the Earth, on the Mars and on the Moon

Weight of a stone on the Earth

gravitational-field-earth-mars-moonThe acceleration due to Earth’s gravitational field is gEarth = 9.81 m/s2.The weight of a stone with mass 1 kg on the Earth can be calculated as:

FEarth = 1 [kg] x 9.81 [m/s2] = 9.8 [kg m/s2] = 9.8 N

Weight of a stone on the Mars

The acceleration of gravity on the Mars is approximately 38% of the acceleration of gravity on the earth. The acceleration due to Moon’s gravitational field is gMars = 3.71 m/s2.

Therefore the weight of the same stone with mass 1 kg on the Mars is:

FMoon = 1 [kg] x 3.71 [m/s2] = 3.71 [kg m/s2] = 3.71 N

Weight of a stone on the Moon

The acceleration of gravity on the Moon is approximately 1/6 of the acceleration of gravity on the earth. The acceleration due to Moon’s gravitational field is gMoon = 1.62 m/s2.

Therefore the weight of the same stone with mass 1 kg on the Moon is:

FMoon = 1 [kg] x 1.62 [m/s2] = 1.62 [kg m/s2] = 1.62 N

Artificial Gravity
In the 20th century, Einstein’s principle of equivalence put all observers, moving or accelerating, on the same footing. Einstein summarised this notion in a postulate:

Principle of Equivalence:

An observer cannot determine, in any way whatsoever, whether the laboratory he occupies is in a uniform gravitational field or is in a reference frame that is accelerating relative to an inertial frame.

This led to an ambiguity as to what exactly is meant by the force of gravity and weight. A scale in an accelerating elevator cannot be distinguished from a scale in a gravitational field.  Gravitational force and weight thereby became essentially frame-dependent quantities. According to the general theory of relativity, gravitational and inertial mass are not different properties of matter but two aspects of a fundamental and single property of matter.

Artificial Gravity
An animation of a 50-meter diameter rotating space-station. Source: wikipedia.org (P.Fraundorf) License: CC BY-SA 4.0

In situations in which gravitation is absent but the chosen coordinate system is not inertial, but is accelerated with the observer, then g-forces and corresponding proper accelerations felt by observers in these coordinate systems are caused by the mechanical forces which resist their weight in such systems. The most realistic method of producing artificial gravity, for example aboard a space station, can be imitated in a rotating spaceship. Objects inside would be pushed toward the hull and they will have some weight. This weight is produced by fictitious forces or “inertial forces” which appear in all such accelerated coordinate systems. Unlike real gravity, which pulls towards a center of the planet, the centripetal force pushes towards the axis of rotation.

 
References:
Reactor Physics and Thermal Hydraulics:
  1. J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).
  2. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
  3. W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.
  4. Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317
  5. Todreas Neil E., Kazimi Mujid S. Nuclear Systems Volume I: Thermal Hydraulic Fundamentals, Second Edition. CRC Press; 2 edition, 2012, ISBN: 978-0415802871
  6. Zohuri B., McDaniel P. Thermodynamics in Nuclear Power Plant Systems. Springer; 2015, ISBN: 978-3-319-13419-2
  7. Moran Michal J., Shapiro Howard N. Fundamentals of Engineering Thermodynamics, Fifth Edition, John Wiley & Sons, 2006, ISBN: 978-0-470-03037-0
  8. Kleinstreuer C. Modern Fluid Dynamics. Springer, 2010, ISBN 978-1-4020-8670-0.
  9. U.S. Department of Energy, THERMODYNAMICS, HEAT TRANSFER, AND FLUID FLOW. DOE Fundamentals Handbook, Volume 1, 2 and 3. June 1992.

See also:

Thermodynamic Properties

We hope, this article, Mass and Weight – Properties, helps you. If so, give us a like in the sidebar. Main purpose of this website is to help the public to learn some interesting and important information about thermal engineering.

What is Mass vs Weight – Definition

by
Mass vs weight: Bodies having large mass also have large weight. But they are not the same physical quantity. But it depends on gravitational field. Thermal Engineering

Mass vs. Weight

One of the most familiar forces is the weight of a body, which is the gravitational force that the earth exerts on the body. In general, gravitation is a natural phenomenon by which all things with mass are brought toward one another. The terms mass and weight are often confused with one another, but it is important to distinguish between them. It is absolutely essential to understand clearly the distinctions between these two physical quantities.

 
What is Mass
The mass of an object is a fundamental property of the object. It is a numerical measure of its inertia and the measure of an object’s resistance to acceleration when a force is applied. It is also a fundamental measure of the amount of matter in the object. The greater the mass, the greater the force needed to cause a given acceleration. This is reflected in Newton’s second law (F=ma).

The mass of a certain body will remain constant even if the gravitational acceleration acting upon that body changes. For example, on earth an object has a certain mass and a certain weight. When the same object is placed in outer space, away from the earth’s gravitational field, its mass remains the same, but it is now in a “weightless” condition. This means in this condition it will weight zero, because gravitational acceleration and, thus, force will equal to zero.

Mass and weight are related: Bodies having large mass also have large weight. A large stone is hard to throw because of its large mass, and hard to lift off the ground because of its large weight. To understand the relationship between mass and weight, consider a freely falling stone, that has an acceleration of magnitude g (g = 9.81 m/s2 is the acceleration due to Earth’s gravitational field). Newton’s second law tells us that a force must act to produce this acceleration. If a 1 kilogram stone falls with an acceleration of the required force has magnitude:

F = ma = 1 [kg] x 9.81 [m/s2] = 9.8 [kg m/s2] = 9.8 N

The force that makes the body accelerate downward is its weight. Any body near the surface of the earth that has a mass of 1 kg must have a weight of 9.8 N to give it the acceleration we observe when it is in free fall.

Example: The weight of a stone on the Earth, on the Mars and on the Moon

Weight of a stone on the Earth

gravitational-field-earth-mars-moonThe acceleration due to Earth’s gravitational field is gEarth = 9.81 m/s2.The weight of a stone with mass 1 kg on the Earth can be calculated as:

FEarth = 1 [kg] x 9.81 [m/s2] = 9.8 [kg m/s2] = 9.8 N

Weight of a stone on the Mars

The acceleration of gravity on the Mars is approximately 38% of the acceleration of gravity on the earth. The acceleration due to Moon’s gravitational field is gMars = 3.71 m/s2.

Therefore the weight of the same stone with mass 1 kg on the Mars is:

FMoon = 1 [kg] x 3.71 [m/s2] = 3.71 [kg m/s2] = 3.71 N

Weight of a stone on the Moon

The acceleration of gravity on the Moon is approximately 1/6 of the acceleration of gravity on the earth. The acceleration due to Moon’s gravitational field is gMoon = 1.62 m/s2.

Therefore the weight of the same stone with mass 1 kg on the Moon is:

FMoon = 1 [kg] x 1.62 [m/s2] = 1.62 [kg m/s2] = 1.62 N

The Standard Kilogram

The usual symbol for mass is m and its SI unit is the kilogram. The SI standard of mass is a cylinder of platinum and iridium that is kept at the International Bureau of Weights and Measures near Paris and assigned, by international agreement, a mass of 1 kilogram.

Standard Kilogram
A computer-generated image of the International Prototype kilogram (IPK), which is made from an alloy of 90% platinum and 10% iridium (by weight) and machined into a right-circular cylinder (height = diameter) of 39.17 mm. Source: wikipedia.org; License: CC BY-SA

Relativistic Mass

While the mass is normally considered to be an unchanging property of an object, at speeds approaching the speed of light one must consider the increase in the relativistic mass. The relativistic definition of momentum is sometimes interpreted as an increase in the mass of an object. In this interpretation, a particle can have a relativistic mass, mrel. The increase in effective mass with speed is given by the expression:

relativistic-mass-min

In this “mass-increase” formula, m is referred to as the rest mass of the object. It follows from this formula, that an object with nonzero rest mass cannot travel at the speed of light. As the object approaches the speed of light, the object’s momentum increase without bound. On the other hand, when the relative velocity is zero, the Lorentz factor is simply equal to 1, and the relativistic mass is reduced to the rest mass. With this interpretation, the mass of an object appears to increase as its speed increases. In must be added, many physicists believe an object has only one mass (its rest mass), and that it is only the momentum that increases with speed.

 
What is Weight
The terms  are often confused with one another, but it is important to distinguish between them. In science and engineering, the weight of an object is usually taken to be the force on the object due to gravity. In general, gravitation is a natural phenomenon by which all things with mass are brought toward one another.

The mass of an object is a fundamental property of the object. It is a numerical measure of its inertia and the measure of an object’s resistance to acceleration when a force is applied. It is also a fundamental measure of the amount of matter in the object. The greater the mass, the greater the force needed to cause a given acceleration. This is reflected in Newton’s second law (F=ma).

The mass of a certain body will remain constant even if the gravitational acceleration acting upon that body changes. For example, on earth an object has a certain mass and a certain weight. When the same object is placed in outer space, away from the earth’s gravitational field, its mass remains the same, but it is now in a “weightless” condition. This means in this condition it will weight zero, because gravitational acceleration and, thus, force will equal to zero.

Mass and weight are related:

Bodies having large mass also have large weight. A large stone is hard to throw because of its large mass, and hard to lift off the ground because of its large weight. To understand the relationship between mass and weight, consider a freely falling stone, that has an acceleration of magnitude g (g = 9.81 m/s2 is the acceleration due to Earth’s gravitational field). Newton’s second law tells us that a force must act to produce this acceleration. If a 1 kilogram stone falls with an acceleration of the required force has magnitude:

F = ma = 1 [kg] x 9.81 [m/s2] = 9.8 [kg m/s2] = 9.8 N

The force that makes the body accelerate downward is its weight. Any body near the surface of the earth that has a mass of 1 kg must have a weight of 9.8 N to give it the acceleration we observe when it is in free fall.

 
References:
Reactor Physics and Thermal Hydraulics:
  1. J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).
  2. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
  3. W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.
  4. Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317
  5. Todreas Neil E., Kazimi Mujid S. Nuclear Systems Volume I: Thermal Hydraulic Fundamentals, Second Edition. CRC Press; 2 edition, 2012, ISBN: 978-0415802871
  6. Zohuri B., McDaniel P. Thermodynamics in Nuclear Power Plant Systems. Springer; 2015, ISBN: 978-3-319-13419-2
  7. Moran Michal J., Shapiro Howard N. Fundamentals of Engineering Thermodynamics, Fifth Edition, John Wiley & Sons, 2006, ISBN: 978-0-470-03037-0
  8. Kleinstreuer C. Modern Fluid Dynamics. Springer, 2010, ISBN 978-1-4020-8670-0.
  9. U.S. Department of Energy, THERMODYNAMICS, HEAT TRANSFER, AND FLUID FLOW. DOE Fundamentals Handbook, Volume 1, 2 and 3. June 1992.

See also:

Mass and Weight

We hope, this article, Mass vs Weight, helps you. If so, give us a like in the sidebar. Main purpose of this website is to help the public to learn some interesting and important information about thermal engineering.

What is Mass – Definition

by
What is Mass. The mass of an object is a fundamental property of the object. It is a numerical measure of its inertia and the measure of an object’s resistance to acceleration. Thermal Engineering

What is Mass

One of the most familiar forces is the weight of a body, which is the gravitational force that the earth exerts on the body. In general, gravitation is a natural phenomenon by which all things with mass are brought toward one another. The terms mass and weight are often confused with one another, but it is important to distinguish between them. It is absolutely essential to understand clearly the distinctions between these two physical quantities.

 
Law of Conservation of Matter
The law of conservation of matter or principle of matter conservation states that the mass of an object or collection of objects never changes over time, no matter how the constituent parts rearrange themselves.

The mass can neither be created nor destroyed.

The law requires that during any nuclear reaction, radioactive decay or chemical reaction in an isolated system, the total mass of the reactants or starting materials must be equal to the mass of the products.

The mass of an object is a fundamental property of the object. It is a numerical measure of its inertia and the measure of an object’s resistance to acceleration when a force is applied. It is also a fundamental measure of the amount of matter in the object. The greater the mass, the greater the force needed to cause a given acceleration. This is reflected in Newton’s second law (F=ma).

The mass of a certain body will remain constant even if the gravitational acceleration acting upon that body changes. For example, on earth an object has a certain mass and a certain weight. When the same object is placed in outer space, away from the earth’s gravitational field, its mass remains the same, but it is now in a “weightless” condition. This means in this condition it will weight zero, because gravitational acceleration and, thus, force will equal to zero.

Mass and weight are related: Bodies having large mass also have large weight. A large stone is hard to throw because of its large mass, and hard to lift off the ground because of its large weight. To understand the relationship between mass and weight, consider a freely falling stone, that has an acceleration of magnitude g (g = 9.81 m/s2 is the acceleration due to Earth’s gravitational field). Newton’s second law tells us that a force must act to produce this acceleration. If a 1 kilogram stone falls with an acceleration of the required force has magnitude:

F = ma = 1 [kg] x 9.81 [m/s2] = 9.8 [kg m/s2] = 9.8 N

The force that makes the body accelerate downward is its weight. Any body near the surface of the earth that has a mass of 1 kg must have a weight of 9.8 N to give it the acceleration we observe when it is in free fall.

Example: The weight of a stone on the Earth, on the Mars and on the Moon

Weight of a stone on the Earth

gravitational-field-earth-mars-moonThe acceleration due to Earth’s gravitational field is gEarth = 9.81 m/s2.The weight of a stone with mass 1 kg on the Earth can be calculated as:

FEarth = 1 [kg] x 9.81 [m/s2] = 9.8 [kg m/s2] = 9.8 N

Weight of a stone on the Mars

The acceleration of gravity on the Mars is approximately 38% of the acceleration of gravity on the earth. The acceleration due to Moon’s gravitational field is gMars = 3.71 m/s2.

Therefore the weight of the same stone with mass 1 kg on the Mars is:

FMoon = 1 [kg] x 3.71 [m/s2] = 3.71 [kg m/s2] = 3.71 N

Weight of a stone on the Moon

The acceleration of gravity on the Moon is approximately 1/6 of the acceleration of gravity on the earth. The acceleration due to Moon’s gravitational field is gMoon = 1.62 m/s2.

Therefore the weight of the same stone with mass 1 kg on the Moon is:

FMoon = 1 [kg] x 1.62 [m/s2] = 1.62 [kg m/s2] = 1.62 N

The Standard Kilogram

The usual symbol for mass is m and its SI unit is the kilogram. The SI standard of mass is a cylinder of platinum and iridium that is kept at the International Bureau of Weights and Measures near Paris and assigned, by international agreement, a mass of 1 kilogram.

Standard Kilogram
A computer-generated image of the International Prototype kilogram (IPK), which is made from an alloy of 90% platinum and 10% iridium (by weight) and machined into a right-circular cylinder (height = diameter) of 39.17 mm. Source: wikipedia.org; License: CC BY-SA
 
What is Mass Defect
See also: Mass Defect

In special theory of relativity certain types of matter may be created or destroyed, but in all of these processes, the mass and energy associated with such matter remains unchanged in quantity. It was found the rest mass of an atomic nucleus is measurably smaller than the sum of the rest masses of its constituent protons, neutrons and electrons. Mass was no longer considered unchangeable in the closed system. The difference is a measure of the nuclear binding energy which holds the nucleus together. According to the Einstein relationship (E=mc2), this binding energy is proportional to this mass difference and it is known as the mass defect.

Relativistic Mass
While the mass is normally considered to be an unchanging property of an object, at speeds approaching the speed of light one must consider the increase in the relativistic mass. The relativistic definition of momentum is sometimes interpreted as an increase in the mass of an object. In this interpretation, a particle can have a relativistic mass, mrel. The increase in effective mass with speed is given by the expression:

relativistic-mass-min

In this “mass-increase” formula, m is referred to as the rest mass of the object. It follows from this formula, that an object with nonzero rest mass cannot travel at the speed of light. As the object approaches the speed of light, the object’s momentum increase without bound. On the other hand, when the relative velocity is zero, the Lorentz factor is simply equal to 1, and the relativistic mass is reduced to the rest mass. With this interpretation, the mass of an object appears to increase as its speed increases. In must be added, many physicists believe an object has only one mass (its rest mass), and that it is only the momentum that increases with speed.

 
References:
Reactor Physics and Thermal Hydraulics:
  1. J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).
  2. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
  3. W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.
  4. Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317
  5. Todreas Neil E., Kazimi Mujid S. Nuclear Systems Volume I: Thermal Hydraulic Fundamentals, Second Edition. CRC Press; 2 edition, 2012, ISBN: 978-0415802871
  6. Zohuri B., McDaniel P. Thermodynamics in Nuclear Power Plant Systems. Springer; 2015, ISBN: 978-3-319-13419-2
  7. Moran Michal J., Shapiro Howard N. Fundamentals of Engineering Thermodynamics, Fifth Edition, John Wiley & Sons, 2006, ISBN: 978-0-470-03037-0
  8. Kleinstreuer C. Modern Fluid Dynamics. Springer, 2010, ISBN 978-1-4020-8670-0.
  9. U.S. Department of Energy, THERMODYNAMICS, HEAT TRANSFER, AND FLUID FLOW. DOE Fundamentals Handbook, Volume 1, 2 and 3. June 1992.

See also:

Mass and Weight

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What is Weight on Earth, Mars and Moon – Gravity – Definition

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The weight of a stone on the Earth, on the Mars and on the Moon. These weights depends on the gravitational fields of these planets. Thermal Engineering

Weight on Earth, Mars and Moon

Mass and weight are related: Bodies having large mass also have large weight. A large stone is hard to throw because of its large mass, and hard to lift off the ground because of its large weight. To understand the relationship between mass and weight, consider a freely falling stone, that has an acceleration of magnitude g (g = 9.81 m/s2 is the acceleration due to Earth’s gravitational field). Newton’s second law tells us that a force must act to produce this acceleration. If a 1 kilogram stone falls with an acceleration of the required force has magnitude:

F = ma = 1 [kg] x 9.81 [m/s2] = 9.8 [kg m/s2] = 9.8 N

The force that makes the body accelerate downward is its weight. Any body near the surface of the earth that has a mass of 1 kg must have a weight of 9.8 N to give it the acceleration we observe when it is in free fall.

Example: The weight of a stone on the Earth, on the Mars and on the Moon

Weight of a stone on the Earth

gravitational-field-earth-mars-moonThe acceleration due to Earth’s gravitational field is gEarth = 9.81 m/s2.The weight of a stone with mass 1 kg on the Earth can be calculated as:

FEarth = 1 [kg] x 9.81 [m/s2] = 9.8 [kg m/s2] = 9.8 N

Weight of a stone on the Mars

The acceleration of gravity on the Mars is approximately 38% of the acceleration of gravity on the earth. The acceleration due to Moon’s gravitational field is gMars = 3.71 m/s2.

Therefore the weight of the same stone with mass 1 kg on the Mars is:

FMoon = 1 [kg] x 3.71 [m/s2] = 3.71 [kg m/s2] = 3.71 N

Weight of a stone on the Moon

The acceleration of gravity on the Moon is approximately 1/6 of the acceleration of gravity on the earth. The acceleration due to Moon’s gravitational field is gMoon = 1.62 m/s2.

Therefore the weight of the same stone with mass 1 kg on the Moon is:

FMoon = 1 [kg] x 1.62 [m/s2] = 1.62 [kg m/s2] = 1.62 N

 
References:
Reactor Physics and Thermal Hydraulics:
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  4. Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317
  5. Todreas Neil E., Kazimi Mujid S. Nuclear Systems Volume I: Thermal Hydraulic Fundamentals, Second Edition. CRC Press; 2 edition, 2012, ISBN: 978-0415802871
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  8. Kleinstreuer C. Modern Fluid Dynamics. Springer, 2010, ISBN 978-1-4020-8670-0.
  9. U.S. Department of Energy, THERMODYNAMICS, HEAT TRANSFER, AND FLUID FLOW. DOE Fundamentals Handbook, Volume 1, 2 and 3. June 1992.

See also:

Mass and Weight

We hope, this article, Weight on Earth, Mars and Moon – Gravity, helps you. If so, give us a like in the sidebar. Main purpose of this website is to help the public to learn some interesting and important information about thermal engineering.