JEE PYQ: Thermodynamics Question 26
Question 26 - 2020 (06 Sep Shift 2)
An engine operates by taking a monatomic ideal gas through the cycle shown in the figure. The percentage efficiency of the engine is close to __________.
[P-V diagram showing rectangular cycle: A$(P_0, V_0)$ $\to$ B$(3P_0, V_0)$ $\to$ C$(3P_0, 2V_0)$ $\to$ D$(P_0, 2V_0)$ $\to$ A]
Show Answer
Answer: 19
Solution
From the figure,
Work, $W = 2P_0 V_0$
Heat given, $Q_{\text{in}} = W_{AB} + W_{BC} = n \cdot C_v \Delta T_{AB} + nC_p \Delta T_{BC}$
$= n\frac{3R}{2}(T_B - T_A) + \frac{n5R}{2}(T_C - T_B)$
$\left(\because C_v = \frac{3R}{2} \text{ and } C_p = \frac{5R}{2}\right)$
$= \frac{3}{2}(P_0 V_B - P_A V_A) + \frac{5}{2}(P_C V_C - P_B V_B)$
$= \frac{3}{2}{3P_0 V_0 - P_0 V_0} + \frac{5}{2}{6P_0 V_0 - 3P_0 V_0}$
$= 3P_0 V_0 + \frac{15}{2}P_0 V_0 = \frac{21}{2}P_0 V_0$
Efficiency, $\eta = \frac{W}{Q_{\text{in}}} = \frac{2P_0 V_0}{\frac{21}{2}P_0 V_0} = \frac{4}{21}$
$\eta% = \frac{400}{21} \approx 19%$
BETA
