Question

A heat engine utilizes a heat source at ${850.0}^{\circ }$ Celsius and has an ideal (Carnot) efficiency of $35.00$ %.
Without changing anything else, what must be the temperature of the heat source to increase the Carnot efficiency of this engine to $45.00$%?

• A. ${1889}^{\circ }Celsius$
• B. ${1004}^{\circ }Celsius$
• C. ${382.5}^{\circ }Celsius$
• D. ${1054}^{\circ }Celsius$
• E. ${895.0}^{\circ }Celsius$

Answer 1

Answer: (D)

${1054}^{\circ }Celsius$

Efficiency of Carnot heat engine $\eta =1-\frac{T_L}{T_H}$

Case 1 : $\eta =0.35$ $T_H=850+273=1123$ $K$

$\therefore$ $0.35=1-\frac{T_L}{1123}$ $⟹T_L=730$ $K$

Case 2 : $\eta =0.45$ $T_L^{\prime }=730$ $K$

$\therefore$ $0.45=1-\frac{730}{T_H^{\prime }}$ $⟹$ $T_H^{\prime }=1327$ $K$

$\therefore$ $T_H^{\prime }=1327-273={1054}^{o}C$