Q138 / 160 · AP EAMCET 2024 (20 May Shift 2) · Physics

The efficiency of a Carnot's engine is $25 \%$, when the temperature of sink is 300 K . The increase in the temperature of source required for the efficiency to become $50 \%$ is

  • A
    225 K
  • B
    400 K
  • Correct answer
    C
    200 K
  • D
    100 K

Solution

for carnot engine, $\begin{aligned} & \eta_1=1-\frac{T_2}{T_1} \Rightarrow \frac{1}{4}=1-\frac{300}{T_1} \therefore T_1=400 \mathrm{~K} \\ & \text { Again, } \eta_2=1-\frac{T_2}{T_1+x} \Rightarrow \frac{1}{2}=1-\frac{300}{400+x} \\ & \therefore \quad x=200 \mathrm{k} \end{aligned}$

Hence, the correct answer is option: 'C'.

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