Question

A Carnot engine operates between a source and sink. The efficiency of the engine is 40\% and the sink temperature is \( 27^\circ \text{C} \). If the efficiency is to be increased to 50\%, then by how much should the source temperature be increased?

• A. 80 K
• B. 120 K
• C. 100 K
• D. 160 K

Hint:

Use \( \eta = 1 - \frac{T_C}{T_H} \) to relate temperatures and efficiency in Carnot engines.

Answer 1

The Correct Option is C

Efficiency of Carnot engine: \[ \eta = 1 - \frac{T_C}{T_H} \] Given initial efficiency \( \eta = 0.4 \), \( T_C = 300 \, \text{K} \)
\[ 0.4 = 1 - \frac{300}{T_H} \Rightarrow T_H = 500 \, \text{K} \] New efficiency \( \eta = 0.5 \): \[ 0.5 = 1 - \frac{300}{T_H'} \Rightarrow T_H' = 600 \, \text{K} \] Increase = \( 600 - 500 = 100 \, \text{K} \)