Question

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 $-273^{\circ} C$ temperature of cold reservoir
Reason R: The efficiency of Carnot's engine depends not only on temperature of cold reservoir but it depends on the temperature of hot reservoir too and is given as $n =\left(1-\frac{T_2}{T_1}\right)$
In the light of the above statements, choose the correct answer from the options given below

• A. $A$ is true but $R$ is false
• B. Both $A$ and $R$ are true and $R$ is the correct explanation of $A$
• C. Both $A$ and $R$ are true but $R$ is NOT the correct explanation of $A$
• D. A is false but $R$ is true

Answer 1

Answer: (B)

Both $A$ and $R$ are true and $R$ is the correct explanation of $A$

Answer 2

Assertion A is true, stating that the efficiency of a reversible heat engine will be highest at -273°C (0 Kelvin), which is the temperature of the cold reservoir.
Reason R is also true, explaining the efficiency of Carnot's engine using the formula: η = 1 - $\frac {T_2}{T_1}$, where Tc is the temperature of the cold reservoir and Th is the temperature of the hot reservoir.
However, Reason R doesn't directly explain why the efficiency is highest at -273°C, which is stated in Assertion A. The formula in Reason R does show how the efficiency is affected by the temperatures of both the hot and cold reservoirs, but it doesn't directly correlate with the statement in Assertion A about the temperature of -273°C being the point of highest efficiency.
So, the correct option is (B): Both A and R are true and R is the correct explanation of A