Topic: Thermodynamics
300 kJ/sec of heat is applied at a constant fixed temperature of $290^{\circ}C$ to a heat engine. The heat rejection takes place at $8.5^{\circ}C.$ Then match the following:
Cycle
(A) 215kJ/sec are rejected
(B) 150kJ/sec are rejected
(C) 75kJ/sec are rejected
Results obtained
(1) reversible
(2) irreversible
(3) impossible
- A. A-1, B-2, C-3
- B. A-2, B-1, C-3
- C. A-3, B-2, C-1
- D. A-1, B-3, C-2
Answer: B. A-2, B-1, C-3
Explanation: Given, $Q_{1}=300~kJ/sec$, $T_{1}=290+273=563~K$, $T_{2}=8.5+273=281.5~K$. Using Clausius Inequality: $\oint\frac{dQ}{T}=0$ for reversible, $<0$ for irreversible, $>0$ for impossible. (A) When $Q_{2}=215$: $\frac{300}{563}-\frac{215}{281.5}=-0.23$ (irreversible). (B) When $Q_{2}=150$: $\frac{300}{563}-\frac{150}{281.5}=0$ (reversible). (C) When $Q_{2}=75$: $\frac{300}{563}-\frac{75}{281.5}=0.27>0$ (impossible).