A reversible engine has an efficiency of 1/4. If the temperature of the sink is reduced by 58°C, its efficiency becomes double. Calculate the temperature of the sink :

Solution

Physics sir · 4 steps

Write the efficiency twice, before and after, then subtract the two equations so only the 58 drop is left.

1. Before the change. For a reversible engine, η = 1 - T₂/T₁, with both temperatures in kelvin. With η = 1/4, this gives T₂/T₁ = 3/4.
2. After the change. The sink drops by 58 degrees and the efficiency doubles to 1/2. A drop of 58 °C is the same as a drop of 58 K, so (T₂ - 58)/T₁ = 1/2.

   T₂/T₁ - (T₂ - 58)/T₁ = 3/4 - 1/2 ⇒ 58/T₁ = 1/4

3. Find the source. This gives T₁ = 4 × 58 = 232 K.
4. So. The sink is at T₂ = 3/4 × 232 = 174 K. The answer is (a).

The idea to keep. In Carnot problems, always use kelvin for temperatures. A temperature change has the same size in °C and in K, so never add 273 to a difference.

Answer from the NTA final answer key. Solution by PrepWiser.