Determining heat transferred from the volume

Question

Solve the following problem:

The initial state of 0.1 mol of an ideal monatomic gas is P_o = 32Pa and V_o = 8m³ . The final state is P₁ = 1 Pa and V₁ = 64 m³. Suppose that the gas undergoes a process along a straight line joining these two states with an equation P = aV + b, where a = -31/56 and b = 255/7. Plot this straight line to scale on a PV diagram. Calculate:

(a) Temperature T as a function of V along the straight line.

(b) The value of V at which T is a maximum.

(c) The values of To, T_max, and T₁

(d) The heat Q transferred from the volume V_o to any other volume V along the straight line.

(e) The values of P and V at which Q is a maximum.

(f) The heat transferred along the line from V_o to V when Q is a maximum.

(g) The heat transferred from V at maximum Q to VI.