# Internal energy of a gas

In summary, the total internal energy of a gas is 3/2(NKT) or 3/2(PV), but for an ideal gas, it is only a function of temperature due to negligible molecular interactions. Outside the ideal gas region, the internal energy is also affected by pressure.

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.

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.

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.

## 1. What is the definition of internal energy of a gas?

The internal energy of a gas is the total energy possessed by the molecules of a gas due to their random motion and interactions with each other.

## 2. How is the internal energy of a gas related to temperature?

The internal energy of a gas is directly proportional to its temperature. As the temperature of a gas increases, the molecules move faster and have more energy, resulting in an increase in the internal energy of the gas.

## 3. What factors affect the internal energy of a gas?

The internal energy of a gas is affected by its temperature, pressure, and number of moles. It is also influenced by the type of gas and its molecular structure.

## 4. Can the internal energy of a gas be negative?

Yes, the internal energy of a gas can be negative. This indicates that the gas has lost energy, either through work done by the gas or through heat transfer to its surroundings.

## 5. How is the internal energy of a gas measured?

The internal energy of a gas can be measured using a calorimeter or by measuring the change in temperature of the gas during a chemical reaction. It can also be calculated using the ideal gas law and the measured pressure, volume, and temperature of the gas.