Question

A Carnot engine operates between heat reservoirs differing in temperature by 80 °C. The efficiency of the Carnot engine is \(20\%\). The temperature of the cold reservoir is:

• A. 440 K
• B. 400 K
• C. 250 K
• D. 320 K

Hint:

For a Carnot engine, use \(\eta = 1 - \frac{T_c}{T_h}\) with temperatures in Kelvin. If given temperature difference, express \(T_h = T_c + \Delta T\) and solve for \(T_c\).

Answer 1

The Correct Option is D

Step 1: Carnot efficiency formula.
η = 1 - T_c/T_h.

Step 2: Temperature difference.
ΔT = T_h - T_c = 80°C = 80 K.

Step 3: Expressing T_h.
T_h = T_c + 80.

Step 4: Solving for T_c.
0.20 = 1 - T_c/(T_c + 80) → T_c/(T_c + 80) = 0.80 → T_c = 0.80 T_c + 64 → 0.20 T_c = 64 → T_c = 320 K.

Step 5: Conclusion.
The cold reservoir temperature is 320 K.