# Volume and Temperature

1. May 11, 2010

### Gersty

Charles Law says that a gas will expand (increase its volume) as it is heated. Is it also true therefore that the temperature of a gas will rise if it's volume increases somehow?

2. May 11, 2010

### espen180

It depends on the system.

Charles' law is a spesific case of the ideal gas law,

$$pV=nRT$$

In this equation, internal energy is held constant, meaning it applies for isothermal processes. In Charles' law the pressure and amount of gas is kept constant.

The following discussion is valid when the gas expands against a uniform external pressure.

If you have an isobaric process (constant pressure) where the volume increases, it means that the gas is doing work on the surroundings. In an ideal gas, there is no potential energy between particles, so

$$U= \sum E_k + 0=\frac{3}{2}nRT$$

for a monoatomic gas. From there we get that

$$\Delta U=\frac{3}{2}nR\Delta T=q-w$$

If there is no heat from the surroundings, the temperature will sink.

In the special case when the external pressure is zero, the gas expands without doing work and the temperature is constant.