JEE PYQ: Thermal Properties Of Matter Question 16
Question 16 - 2019 (10 Jan 2019 Shift 1)
Three Carnot engines operate in series between a heat source at a temperature $T_1$ and a heat sink at temperature $T_4$. There are two other reservoirs at temperature $T_2$ and $T_3$, as shown, with $T_1 > T_2 > T_3 > T_4$. The three engines are equally efficient if:
(1) $T_2 = (T_1 T_4)^{1/2}$; $T_3 = (T_1^2 T_4)^{1/3}$
(2) $T_2 = (T_1^2 T_4)^{1/3}$; $T_3 = (T_1 T_4^2)^{1/3}$
(3) $T_2 = (T_1 T_4^2)^{1/3}$; $T_3 = (T_1^2 T_4)^{1/3}$
(4) $T_2 = (T_1^3 T_4)^{1/4}$; $T_3 = (T_1 T_4^3)^{1/4}$
Show Answer
Answer: (2)
Solution
Equal efficiency means $\frac{T_2}{T_1} = \frac{T_3}{T_2} = \frac{T_4}{T_3}$. Solving: $T_2 = (T_1^2 T_4)^{1/3}$, $T_3 = (T_1 T_4^2)^{1/3}$
BETA
