7.10. The initial state of 0.1 mol of an ideal monatomic gas is Po = 32 Pa and V₁ = 8 m³. The final state is P₁ = 1 Pa and V₁ = 64 m³. Suppose that the gas undergoes a pro- cess along a straight line joining these two states with an equation P = a + 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, Tmax, and T₁. CHAPTER 7: The Carnot Cycle 185 (d) The heat Q transferred from the volume Vo 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 Vo to V when Q is a maximum. (g) The heat transferred from V at maximum Q to V1.