Joule’s Second Law states: The internal energy of a fixed mass of an ideal gas depends only on its temperature (not pressure or volume). Thermal Engineering

## Joule’s Second Law

For any gas whose equation of state is given exactly by **pV = nRT** (or **pv = RT**), the **specific internal energy** depends on temperature only. This rule was originally found in 1843 by an English physicist **James Prescott Joule** experimentally for real gases and is known as **Joule’s second law**:

*The internal energy of a fixed mass of an ideal gas depends only on its temperature (not pressure or volume).*

The specific enthalpy of a gas described by **pV = nRT** also depends on temperature only. Note that, the **enthalpy** is the thermodynamic quantity equivalent to the** total heat content** of a system. It is equal to the internal energy of the system plus the product of pressure and volume. In intensive variables the **Joule’s second law **is therefore given by *h = h(T) = u(T) + pv = u(T) + RT.*

These three equations constitute the ideal gas model, summarized as follows:

**pv = RT**

**u = u(T)**

**h = h(T) = u(T) + RT**

References:

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

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