The data listed below are claimed for power cycles operating

The data listed below are claimed for power cycles operating between hot and cold reservoirs at 1000 K and 400 K, respectively. For each case determine whether such a cycle is in keeping with the first and second laws of thermodynamics. Q_H = 300 kJ, W_cycle = 160 kJ, Q_c = 140 kJ. Q_H = 300 kJ, W_cycle = 180 kJ, Q_c = 120 kJ. Q_H = 300 kJ, W_cycle = 170 kJ, Q_c = 140 kJ. Q_H = 300 kJ, W_cycle = 200 kJ, Q_c = 100 kJ.

Solution

In order to satisfy the first law of thermodynamics, each cycle should follow this rule

      Q_H = Q_C + W_cycle

Only cycle (c) violates this rule, hence it does not obey first law.

In order to satisfy the second law of thermodynamics, each cycle should follow this rule

W_cycle/Q_H 1 - T_C/T_H

Only cycle (d) violates this rule, hence it does not obey second law.