For an ideal heat engine, the temperature of the source is 127°C. In order to have 60% efficiency the temperature of the sink should be ___________°C. (Round off to the Nearest Integer)

Solution

Physics sir · 3 steps

Carnot efficiency only works in kelvin, so convert 127°C first and convert back at the very end.

1. Use kelvin. An ideal engine is a Carnot engine. Its efficiency depends on absolute temperatures, so the source is at T₁ = 127 + 273 = 400 K.

   η = 1 - T₂/T₁

2. Put in numbers. With η = 0.6, you get T₂/T₁ = 1 - 0.6 = 0.4. So T₂ = 0.4 × 400 = 160 K.
3. So. In Celsius, T₂ = 160 - 273 = -113°C. The sink temperature is −113.

The common slip: 160. Leaving the sink temperature in kelvin gives 160, not −113. Subtract 273 because the answer is asked in °C.

The idea to keep. In η = 1 - T₂/T₁, both temperatures must be in kelvin. Convert to kelvin before you calculate, and convert back only if the question asks in °C.

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