A Carnot engine takes 5000 kcal of heat from a reservoir at 727°C and gives heat to a sink at 127°C. The work done by the engine is

Solution

Physics sir · 4 steps

Convert to kelvin, find the Carnot efficiency, then turn that share of the heat into joules.

1. Kelvin temperatures. The source is at T₁ = 727 + 273 = 1000 K and the sink is at T₂ = 127 + 273 = 400 K. The Carnot formula only works with absolute temperatures.

   η = 1 - T₂/T₁ = 1 - 400/1000 = 0.6

2. Work in kcal. Work is the efficiency times the heat taken in: W = 0.6 × 5000 kcal = 3000 kcal. The other 2000 kcal goes to the sink.
3. Into joules. With 1 cal = 4.2 J, W = 3000 × 10³ × 4.2 J = 1.26 × 10⁷ J.
4. So. The work done is 12.6 × 10⁶ J, which is option (c).

The idea to keep. For any Carnot engine, W = Q₁(1 - T₂/T₁) with temperatures in kelvin. Then check the units of heat: calories must be multiplied by 4.2 to get joules.

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