Question

A number of Carnot engines are operated at identical cold reservoir temperatures (T_L). However, their hot reservoir temperatures are kept different. A graph of the efficiency of the engines versus hot reservoir temperature (T_H) is plotted. The correct graphical representation is

• A.
• B.
• C.
• D.

Answer 1

The Correct Option is B

The efficiency of a Carnot engine is given by:

$\eta = 1 - \frac{T_L}{T_H}$

where:

• $T_L$ is the absolute temperature of the cold reservoir, and
• $T_H$ is the absolute temperature of the hot reservoir.

When $T_H = T_L$, the efficiency is $\eta = 1 - \frac{T_L}{T_L} = 0$. This means the graph should start at the point $(T_L, 0)$.

As $T_H$ increases, the efficiency increases. 

However, the efficiency can never exceed 1. As $T_H$ approaches infinity, the efficiency approaches 1. 

Therefore, the graph should asymptotically approach $\eta = 1$.

Rearranging the efficiency equation, we get:

$\eta = 1-\frac{T_L}{T_H} $ $1 - \eta = \frac{T_L}{T_H} $ $T_H = \frac{T_L}{1-\eta}$

The correct answer is (B)