A Carnot's cycle operating between $T_H=600 \mathrm{~K}$ and $T_c=300 \mathrm{~K}$ produces 1.5 kJ of…

A Carnot's cycle operating between $T_H=600 \mathrm{~K}$ and $T_c=300 \mathrm{~K}$ produces 1.5 kJ of mechanical work per cycle. The heat transferred to the engine by the reservoir is
  1. 2.5 kJ
  2. 3.0 kJ
  3. 3.5 kJ
  4. 4.0 kJ

Solution

Efficiency of Carnot's engine $\begin{aligned} \begin{aligned} \eta=1 & -\frac{T_C}{T_H} \\ & =1-\frac{300}{600} \\ \eta & =\frac{1}{2}...(i) \end{aligned} \end{aligned}$
Efficiency $(\eta)=\frac{\text { Work done per cycle }(W)}{\text { Heat transformed per cycle }(Q)}$ $\begin{aligned} & \frac{1}{2}=\frac{1.5}{Q} \\ & \mathrm{Q}=1.5 \times 2=3 \mathrm{~kJ} \end{aligned}$ ...[From (i)]

Asked in: MHT CET 2024 (10 May Shift 2)

Practice more Thermodynamics questions on Aicharya