Ideal Gas Model

The ideal gas model is used to predict the behavior of gases and is one of the most useful and commonly used substance models ever developed. It was found that if we confine 1 mol samples of various gases in identical volumes and hold the gases at the same temperature, then their measured pressures are almost the same.

Moreover, when we confine gases at lower densities, the differences tend to disappear. It was found, such gases tend to obey the following relation, which is known as the ideal gas law: 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. The power of the ideal gas law is in its simplicity. When any two thermodynamic variables, p, v, and T, are given, the third can easily be found.

The ideal gas model is based on the following assumptions:

1. The pressure, volume, and temperature of an ideal gas obey the ideal gas law.
2. The specific internal energy is only a function of the temperature: u = u(T).
3. The molar mass of an ideal gas is identical to the molar mass of the real substance.
4. The specific heatscp and cv — are independent of temperature, which means constants.

From the microscopic point of view, it is based on these assumptions:

1. The molecules of the gas are small, hard spheres.
2. The only forces between the gas molecules are those that determine the point-like collisions.
3. All collisions are elastic, and all motion is frictionless.
4. The average distance between molecules is much larger than the size of the molecules.
5. The molecules are moving in random directions.
6. There is no other attractive or repulsive force between these molecules.

Validity of Ideal Gas Law

Since ideal gas is defined as one in which all collisions between atoms or molecules are perfectly elastic. There are no intermolecular attractive forces, and there is no such thing in nature as a truly ideal gas. On the other hand, all real gases approach the ideal state at low pressures (densities). At low pressures, molecules are far enough apart that they do not interact with one another.

In other words, the Ideal Gas Law is accurate only at relatively low pressures (relative to the critical pressure pcr) and high temperatures (relative to the critical temperature Tcr). At these parameters, the compressibility factor, Z = pv / RT, is approximately 1. The compressibility factor is used to account for deviation from the ideal situation. This correction factor is dependent on pressure and temperature for each gas considered.

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.

Ideal Gas Law