A Carnot's engine working between 400 K and 800 K has a work output of 1200 J per cycle. The amount of heat energy supplied to the engine from the source in each cycle is :

Solution

Physics sir · 3 steps

Find the Carnot efficiency from the two temperatures, then the heat input is just work divided by efficiency.

1. Carnot efficiency. A Carnot engine's efficiency depends only on the source temperature T₁ and the sink temperature T₂, both in kelvin. Here T₁ = 800 K and T₂ = 400 K.

   η = 1 - T₂/T₁ = 1 - 400/800 = 0.5

2. Link to heat. Efficiency is the fraction of the heat supplied that becomes work: η = W/Q₁. So Q₁ = W/η = (1200 J)/0.5 = 2400 J.
3. So. The source supplies 2400 J each cycle. Of this, 1200 J becomes work and the other 1200 J goes to the sink. The answer is (a).

The idea to keep. For any Carnot question, first get η = 1 - T₂/T₁ in kelvin. Then W = η Q₁ and Q₂ = Q₁ - W give you every other quantity.

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