Question

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Problem 4. A Carnot cycle using 2 mol mono-atomic gas works between a hot reservoir Ti 400K and a cold reservoir T2 300K The 1-2 and 3-4 processes are isothermal The 2-3 and 4-1 processes are adiabatic. Given Vi 12 L, V2 -8 L a) (3 pts) Find Pi, P2, Ps, Ps, Vs, V4 b) (4 pts) What is the heat received by the gas during the 1-2 process? o (4 ptsy) What is the heat dissipated during a, T,>T, 2 T, Q, 3 the 3-4 process? d) (4 pts) What is the work done by the gas during the cycle? e) (3 pts) What is the efficiency of the cycle? f)* (10 pts) Prove that the efficiency η = (Ti-T2)/T1 (without real number calculation)

Answer 1

Q_1 = Intersection R T_1 [ln [12/ 8]] = 26.63 I = w_1 - 2 Q_2 = Intersection T_2 [ln (v_4/v_3)] = Intersection R T_2 [ln (P_3 P_4)] because v_3 = n R T_2/P_3 v_4 = n R T_2/P_4 w_3 - 4 = Q_2 = -20.0935 almostequalto -20.09 J heat dissipated d rightarrow work dine = w_1 - 2 + w_2.3 + w_3 - 4 + w_4 - 1 w_2 - 3 = work dine in adiabatic process = n R T_1 [(P_3/P_2)^r - 1/r - 1] = -n R [T_2 - T_1/r - 1] = + 16.42/r - 1 = + 24.63 J w_4 - 1 = -n R [T_1 - T_2]/r - 1 = -24.63 J = > w = [26.63 + 24.63 - 24.63 - 20.09] J w = 6.5480 J almostequalto 6.54 J \r\n From of monatomic gas or r = 5/3. T_1 = 400 k, T_2 = 300 k v_2 = 12
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