300 cal. of heat is given to a heat engine and it rejects 225 cal. If source temperature is 227°C, then the temperature of sink will be ______________ °C.

Solution

Physics sir · 4 steps

For a Carnot engine, heat ratio equals temperature ratio, but only when temperatures are in kelvin.

1. Carnot relation. In a reversible (Carnot) engine, the heat taken from the source and the heat given to the sink are in the same ratio as the absolute temperatures.

   Q₂/Q₁ = T₂/T₁

2. Convert to kelvin. Source temperature T₁ = 227 + 273 = 500 K. The heat ratio is Q₂/Q₁ = 225/300 = 0.75.
3. Find the sink. T₂ = 0.75 × 500 = 375 K. Back in Celsius, 375 - 273 = 102 °C.
4. So. The sink is at 102 °C.

The common slip: 170.25. Using the ratio directly on the Celsius value gives 0.75 × 227 = 170.25, which is wrong because the relation holds only for absolute temperatures.

The idea to keep. In Q₂/Q₁ = T₂/T₁, always put temperatures in kelvin, then convert back to Celsius only if the question asks for it.

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