This document discusses ideal gases and how they differ from real gases. It provides an introduction to ideal gases, noting their key characteristics and assumptions. The document then covers the ideal gas law and how it combines Boyle's, Charles', and Gay-Lussac's laws. Real gases are described as deviating from ideal behavior, especially near their critical point. Equations for both ideal and real gases are presented. The concepts of reduced properties and the principle of corresponding states for comparing real gases are also summarized.

1. Thermodynamic Relations – Ideal gas
B.Prabhu, T.Suresh, P.Selvan
Assistant Professor – Mechanical Engineering
Kamaraj College of Engineering & Technology,
Virudhunagar

2. Ideal and Real Gases
References:
• 1. Thermodynamics – An Engineering
Approach – Yunus A. Cengel &
Michael A. Boles
• 2. Fundamentals of Engineering
Thermodynamics - Michael J. Moran &
Howard N. Shapiro

3. IdealGases - An Intro

4. A gas does not have a fixed volume or pressure
In a container, the gas expands to fill the container
Most gases at room temperature and pressure behave
approximately as an ideal gas (one in which there
is simple relationship between P, V, and T)
Characteristics of ideal gas:
Collection of atoms or molecules that move randomly
Exert no long-range force on one another
Occupy a negligible fraction of the volume of their container
Understanding ideal gases is useful because all real
gases approach an ideal gas at low enough densities
(when molecules are far enough apart that they do not
interact with each other)

5. It’s convenient to express the amount of gas in a given
volume in terms of the number of moles, n:
One mole is the amount of the substance that contains
as many atoms as there are atoms in 12 g of the
carbon–12 isotope
1 mol of a substance contains the same number of atoms as
in 1 mol of any other substance
The number of atoms in one mole is called Avogadro’s
Number = NA = 6.02 ×1023
atoms/mol
We can use this number to calculate the mass of an
individual atom:
massmolar
mass
=n
AN
m
massmolar
atom =

6. Ideal Gas Law
Boyle’s Law
At a constant temperature, pressure is inversely
proportional to the volume
Charles’ Law
At a constant pressure, the temperature is
directly proportional to the volume
Gay-Lussac’s Law
At a constant volume, the pressure is directly
proportional to the temperature
These 3 laws are summarized by the Ideal Gas Law:
R = universal gas constant = 8.31 J/mol⋅K
nRTPV = (P = absolute pressure, T = temp. in Kelvin)

7. Forms of Ideal Gas Equation

9. Real Gases
• Gases which do not obey Equation of state or
Ideal Gas equation is generally treated as real
gases.
• They deviate from ideal gas behavior since
their heat capacities vary with state.
• They deviate much in the saturation region
and in the vicinity of critical point.
• This deviation from ideal gas behavior at given
temperature and pressure can be accounted
by introducing a correction factor.

10. Equations for ideal and real gases

16. Reduced Properties & Principle of
corresponding states

17. Compressibility Factor, z

19. Generalized compressibility chart

23. Observations from Charts
• At very low pressures (PR < < 1), gases
behave as an ideal gas regardless of
temperature.
• At high temperatures ( TR > 2), ideal gas
behavior can be assumed with good
accuracy regardless of pressure.
• The deviation from ideal gas behavior is
greatest in the vicinity of critical point.