State two basic assumptions of the kinetic theory of gases.
An ideal gas contains amount of substance $n$. Initially the gas is at state $X$, with pressure $2p$ and volume $V$. It is cooled at constant volume to state $Y$, where the pressure becomes $p$. It is then heated at constant pressure to state $Z$, where the volume becomes $2V$. Finally, the gas returns to state $X$ at constant temperature.
Find an expression for the gas temperature $T$ in state $X$, in terms of $n$, $p$ and $V$. State any additional symbols you use.
On Fig. 4.1, sketch how pressure varies with volume as the gas undergoes the three changes. The state $X$ is already labelled. Add labels for states $Y$ and $Z$.
Between $Y$ and $Z$, the gas's internal energy increases by $U$. Between $Z$ and $X$, the work done on the gas is $W$. Complete Table 4.1 to show, for each of the three state changes, the increase in internal energy of the gas, the thermal energy transferred to the gas, and the work done on the gas, in terms of $p$, $V$, $U$ and $W$.