## Adiabatic Process

An **adiabatic process** is a thermodynamic process, in which there is **no heat transfer** into or out of the system (Q = 0). The system can be considered to be **perfectly insulated**. In an adiabatic process, energy is transferred only as work. The assumption of no heat transfer is very important, since we can use the adiabatic approximation only in **very rapid processes**. In these rapid processes, there is not enough time for the transfer of energy as heat to take place to or from the system.

In real devices (such as turbines, pumps, and compressors) **heat losses** and losses in the combustion process occur, but these losses are usually low in comparison to overall energy flow and we can approximate some thermodynamic processes by the adiabatic process.

## Adiabatic Expansion – Adiabatic Compression

See also: What is an Ideal Gas

In an ideal gas, molecules have no volume and do not interact. According to the ideal gas law, pressure varies linearly with temperature and quantity, and inversely with volume.

*pV = nRT*

where:

*p*is the absolute pressure of the gas*n*is the amount of substance*T*is the absolute temperature*V*is the volume*R*is the ideal, or universal, gas constant, equal to the product of the Boltzmann constant and the Avogadro constant,

In this equation the symbol R is a constant called the **universal gas constant** that has the same value for all gases—namely, R = 8.31 J/mol K.

The **adiabatic process** can be expressed with the **ideal gas law** as:

*pV ^{κ} = constant*

or

**p _{1}V_{1}^{κ} = p_{2}V_{2}^{κ}**

in which ** κ = c _{p}/c_{v}** is the ratio of the

**specific heats**(or

**heat capacities**) for the gas. One for

**constant pressure (c**

_{p}**)**and one for

**constant volume (c**

_{v}**)**. Note that, this ratio

**κ**

**= c**is a factor in determining the speed of sound in a gas and other adiabatic processes.

_{p}/c_{v}**Other p, V, T Relation**

On a **p-V diagram**, the process occurs along a line (called an **adiabat**) that has the equation **p = constant / V ^{κ}**.

**For an ideal gas and a polytropic process, the case**

*n = κ*

**corresponds to an adiabatic process.**

## Example of Adiabatic Expansion

Assume an **adiabatic expansion** of helium (**3 → 4**) in a **gas turbine**. Since helium behaves almost as an ideal gas, use the ideal gas law to calculate **outlet temperature** of the gas (**T _{4,real}**). In this turbines the high-pressure stage receives gas (point 3 at the figure; p

_{3 }=

**6.7 MPa**;

**T**(917°C)) from a heat exchanger and exhaust it to another heat exchanger, where the outlet pressure is p

_{3}= 1190 K_{4}=

**2.78 MPa**(point 4)

**.**

**Solution:**

The outlet temperature of the gas, T_{4,real}, can be calculated using **p, V, T Relation** for adiabatic process. Note that, it is the same relation as for the isentropic process, therefore results must be identical. It this case, we calculate the expansion for different gas turbine (less efficient) as in case of **Isentropic Expansion in Gas Turbine.**

In this equation the factor for helium is equal to **κ****=c _{p}/c_{v}=1.66**. From the previous equation follows that the outlet temperature of the gas,

**T**, is:

_{4,real}See also: **Mayer’s relation**

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