Question

A heat engine operates between a cold reservoir at temperature $T_2=400\text{K}$ and a hot reservoir at temperature $T_1.$ It takes $300\text{J}$ of heat from the hot reservoir and delivers $240\text{J}$ of heat to the cold reservoir in a cycle. The minimum temperature of the hot reservoir has to be $\text{K}$

• A. 500
• B. 500.0
• C. 500.00

Answer 1

Answer: (A), (B), (C)

Efficiency of heat engine is given by
$\eta =1-\frac{T_2}{T_1}=1-\frac{Q_2}{Q_1}$
$\frac{Q_1}{T_1}=\frac{Q_2}{T_2}$

Here
$Q_1=300\text{J}$
$Q_2=240\text{J}$
$T_2=400\text{K}$

on substitution we get
$\frac{300}{T_1}=\frac{240}{400}$
$T_1=500\text{K}$