Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A : Efficiency of a reversible heat engine will be highest at -273° C temperature of cold reservoir.
Reason R : The efficiency of Carnot's engine depends not only on the temperature of the cold reservoir but it depends on the temperature of the hot reservoir too and is given as η=(1-T₂/T₁)
In the light of the above statements, choose the correct answer from the options given below

Solution

Physics sir · 4 steps

Put the cold reservoir at absolute zero in the Carnot formula and see where efficiency goes.

1. Check Reason R. For a reversible (Carnot) engine working between a hot reservoir at T₁ and a cold reservoir at T₂, the efficiency is the formula below. It contains both temperatures, so R is a correct statement.

   η = 1 - T₂/T₁

2. Check Assertion A. For a fixed T₁, a smaller T₂ makes T₂/T₁ smaller and η larger. The lowest possible T₂ is -273°C, which is about 0 K. That gives η = 1 - 0 = 1, the highest value the formula allows. So A is true.
3. Link them. We only knew that efficiency peaks at -273°C because of the formula in R. So R is the correct explanation of A.
4. So. Both statements are true and R explains A. The answer is (a).

The idea to keep. Carnot efficiency rises as the cold reservoir gets colder or the hot one gets hotter. Always use kelvin in η = 1 - T₂/T₁. Absolute zero is the limit that would give η = 1.

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