If heat enters a gas container, the gas can respond in one of three ways.

#### Temperature rise

The gas may increase in temperature, with a consequential increase in the pressure acting on the walls of the container. This is an increase in *internal energy*. Internal energy is defined as the sum of the kinetic and potential energies of the molecules in the container:

\(U=\sum{E_\textrm{K}}+\sum{E_\textrm{P}}\)

Modelling the gas as *ideal*, with no intermolecular forces and hence no potential energy: \(U=\sum{E_\textrm{K}}\)

We can recall from gases that the mean kinetic energy of the gas molecules is proportional to temperature: \(\bar{E_\textrm{K}}={3\over2} kT\)

The change in internal energy is equal to the total change in kinetic energy of the molecules.

\(\Delta U=N\Delta \bar{E_\textrm{K}}={3\over 2}Nk\Delta T={3\over 2}nR\Delta T\)

#### Expansion

An expansion of the gas container into the surroundings may occur, to maintain a constant pressure. This is *work done*. Work done is the product of the force exerted by a body and the distance travelled parallel to the force:

\(W=Fs\cos \theta\)

The force emerges from the combined pressure of the collisions by gas molecules across the surface area of the walls of the container: \(F=pA\)

Taking the surface area of the container as constant (e.g. piston), the displacement of the container walls will be perpendicular to the plane of the walls. This results in a change in volume: \(\Delta V=As\)

With the expansion at constant pressure:

\(W=p\Delta V\)

- \(W\) is work done by the gas on the surroundings (J)
- \(p\) is the pressure of the gas (Pa)
- \(\Delta V\) is the change in volume of the container (m
^{3})