State the first law of thermodynamics in words or as an equation.
Using Fig. 4.1 and Fig. 4.2, find the general expression for the internal energy $U$ of the gas when its pressure is $p$ and its volume is $V$.
An ideal gas at thermodynamic temperature $T$ contains $N$ molecules. Using your answer in (b)(i) and the equation of state for an ideal gas, deduce an expression for $U$ in terms of $N$ and $T$. Identify any other symbols you use.
Find expressions, in terms of $X$ and $Y$, for the work $W$ done on the gas during change AB.
Find expressions, in terms of $X$ and $Y$, for the work $W$ done on the gas during change CD.
Using your answers in (c) and the first law of thermodynamics, determine an expression, in terms of $X$ and $Y$, for the net thermal energy $Q$ supplied to the gas in one complete cycle ABCDA. Explain your reasoning.