# Internal energy of a gas

## Main Question or Discussion Point

Hello all,

So the total internal energy of a gas as far as I've been told is 3/2(NKT) but it can also be written as 3/2(PV). Why then is the internal energy only a function of temperature and not volume and pressure as well? Thanks in advance for the help.

## Answers and Replies

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You should check the First Law of Thermodynamics.

$$\Delta U = Q\, + \, W$$

Change in pressure or volume, say if the gas is compressed, and hence work is done on the gas, will cause the internal energy to increase.

Chestermiller
Mentor
Hello all,

So the total internal energy of a gas as far as I've been told is 3/2(NKT) but it can also be written as 3/2(PV). Why then is the internal energy only a function of temperature and not volume and pressure as well? Thanks in advance for the help.
The internal energy is a function of temperature only for an ideal gas. Beyond the ideal gas region, the internal energy is also a function of pressure. The internal energy is determined by the mean kinetic energy of the molecules (including vibrations and rotations) plus the interactions between the molecules (which is related to the pressure). In the ideal gas region, the contribution of the molecular interactions is negligible.