= Solution
For the numbered engine, denote the low and high <pressures> by $p_1=p_4=p_l$ and $p_2=p_3=p_h$. Let $R_g$ denote the <molar gas constant>. The <ideal gas law> makes the constant-pressure branches straight rays in a <temperature>-<volume> diagram:
$$
T=\frac{p_h}{nR_g}V\quad(2\to3),\qquad
T=\frac{p_l}{nR_g}V\quad(4\to1).
$$
The high-pressure ray is steeper. For a constant <heat capacity ratio> $\gamma$, each <reversible ideal-gas adiabat> obeys
$$
TV^{\gamma-1}=\text{constant}.
$$
Consequently $1\to2$ curves upward and left during compression; $2\to3$ goes upward and right along the steeper ray; $3\to4$ curves downward and right during expansion; and $4\to1$ goes downward and left along the shallower ray.
\Image[/past-exam-of-the-physics-b-course-of-the-university-of-cambridge/2022/paper-2-c8-brayton-tv.png]
{title=Temperature-volume solution sketch for the two-pressure gas-engine cycle}
The plot is an original calculation for $\gamma=7/5$, $p_h/p_l=10$ and $V_3/V_2=2$; its state directions follow the original paper. The dashed extensions identify the two constant-pressure rays, not additional stages of the cycle.
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