State what the term internal energy of a system means.
Explain why the internal energy of an ideal gas is directly proportional to the thermodynamic temperature of the gas.
An ideal gas sample has thermodynamic temperature $T$ and internal energy $U$. It is compressed so that its temperature rises to $3T$. Work $W$ is done on the gas during this compression. The gas is then cooled at constant volume so that its temperature falls to $2T$. Fill in Table 4.1, using some or all of $W$, $T$ and $U$, to show the work done on the gas, the thermal energy transferred to the gas and the rise in internal energy of the gas for each process.