The efficiency of a Carnot engine found to increase from $25 \%$ to $40 \%$ on increasing the temperature (…

The efficiency of a Carnot engine found to increase from $25 \%$ to $40 \%$ on increasing the temperature ( $\mathrm{T}_1$ ) of source alone through 100 K . The temperature $\left(\mathrm{T}_2\right)$ of the sink is given by
  1. 300 K
  2. 250 K
  3. 325 K
  4. 125 K

Solution

$\begin{aligned} & \text {} \eta_1=25 \%=0.25 \\ & \therefore \eta_1=1-\frac{T_2}{T_1} \Rightarrow 0.25=1-\frac{T_2}{T_1} \Rightarrow \frac{T_2}{T_1}=0.75 \\ & \therefore T_1=\frac{4 T_2}{3}\end{aligned}$
$\begin{aligned} & \text { Now, } \eta_2=40 \%=0.4 \\ & \eta_2=1-\frac{T_2}{T_1+100} \Rightarrow \frac{T_2}{\frac{4 T_2}{3}+100}=0.6 \\ & \Rightarrow \frac{4 T_2}{3}+100=\frac{5}{3} T_2 \Rightarrow \frac{T_2}{3}=100 \\ & \therefore \quad T_2=300 \mathrm{~K}\end{aligned}$

Asked in: AP EAMCET 2024 (21 May Shift 2)

Practice more Thermodynamics questions on Aicharya