Question

A Carnot engine does $750.0$ Joules of work for each cycle while using $1655Joules$ of heat from a source at ${815}^{\circ }$ Celsius.
At what temperature is the waste heat exhausted?

• A. ${446}^{\circ }Celsius$
• B. ${322}^{\circ }Celsius$
• C. ${369}^{\circ }Celsius$
• D. ${493}^{\circ }Celsius$
• E. ${302}^{\circ }Celsius$

Answer 1

Answer: (B)

${322}^{\circ }Celsius$

Given : $W=750$ J $Q_H=1655$ J

Efficiency of engine $\eta =\frac{W}{Q_H}=\frac{750}{1655}=0.453$

Temperature of the source $T_H={815}^{o}C=815+273=1088$ K

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

$\therefore$ $0.453=1-\frac{T_L}{1088}$ $⟹T_L=595$ K

$⟹T_L=595-273={322}^{o}C$