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Thermal Physics

The Equation of State of an Ideal Gas

The three experiments referred to above can be easily carried out (in a school laboratory) for a range of temperatures and pressures not too far from "normal"; for example, between 0°C and 100°C and between about ½ to 2 atmospheres of pressure. Within these limits real gases give the results described above. However, if gases are compressed to extreme pressures at low temperature, their behaviour is very different.

An (imaginary) gas which obeys the gas laws perfectly for any temperature and pressure is called an ideal (or perfect) gas.

Consider a quantity of gas which experiences the following changes.

.........A

B

.......C

From A to B

Energy supplied to increase T and V at constant p. We can apply Charles’ law to this change.

Therefore

From B to C

Compress the gas slowly to change V and p at constant T. We can apply the Boyle/Marriotte law to this change.

Therefore

p1V' = p2V2

It is clear that V’ can be eliminated from these two equations giving
 

This is called the equation of state of an ideal gas and is usually written in the following form

pV = (a constant)×T

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