Thermodynamics

16.1 Internal energy

The internal energy of a system is the sum of the random distribution of kinetic and potential energies of its molecules. It is determined by the state of the system: its temperature, volume and phase.

• The kinetic part depends on temperature.
• The potential part depends on the separation of the molecules, so it changes when a substance melts or boils.

A rise in temperature means a rise in the mean kinetic energy of the molecules, which means a rise in internal energy.

During melting or boiling, the temperature is constant, so the kinetic energy is unchanged, but the potential energy rises, so the internal energy still rises.

16.2 The first law of thermodynamics

Work done by a gas

When a gas expands at constant pressure $p$, pushing a piston of area $A$ through a distance $d$, the work it does is $Fd = pAd$:

$W = p\Delta V$

• When a gas expands, it does work on the surroundings. Work done on the gas is negative.
• When a gas is compressed, work is done on it. Work done on the gas is positive.

On a pressure–volume graph, the work done is the area under the line, which still applies when the pressure varies.

The first law

$\Delta U = q + W$

Common processes

A bicycle pump warms up because you do work on the gas quickly, leaving little time for heat to escape, so $q \approx 0$ and $\Delta U \approx W$.