Answer
See the detailed answer below.
Work Step by Step
a) If we know that the closed work done in one cycle of a heat engine is 400 kJ where the gas compresses and stretches between the two volumes of 1 m$^3$ to 3 m$^3$, while the minimum pressure is 100 kPa, what is the maximum pressure if you know that the closed area of this cycle is a triangle.
b) Solving for $P_{max}$;
$$P_{max}=\dfrac{2(400\times 10^3)}{(3-1)}+(100\times 10^3)$$
$$P_{max}=\color{red}{\bf 500}\;\rm kPa $$
