Question

Two rigid tanks, each contain 10 kg N2 gas at 1000 K, 500 kPa. They are now thermally connected to a reversible heat pump, which heats one and cools the other with no heat transfer to the surroundings. When one tank is heated to 1500 K the process stops. Find the final (P, T ) in both tanks and the work input to the heat pump, assuming constant heat capacities.

Answer 1

Control volume of hot tank B,

Process = constant volume & mass so no work Energy equation and specific heat

U2 - U1 ≅ mCv(T2 - T1) = 1Q2 = 10 × 0.7448 × 500 = 3724 kJ

P2 = P1T2/T1 = 1.5(P1) = 750 kPa

State: 1 = initial,

2 = final hot

3 = final cold

To fix temperature in cold tank, C.V.: total

For this CV only WHP cross the control surface no heat transfer. The entropy equation for a reversible process becomes