Question

For which combination of temperatures the efficiency of Carnot's engine is highest?

• A. $80\text{K},60\text{K}$
• B. $100\text{K},80\text{K}$
• C. $60\text{K},40\text{K}$
• D. $40\text{K},20\text{K}$

Answer 1

The correct option is D $40\text{K},20\text{K}$

Efficiency of Carnot's engine is given as,
$\eta =\frac{T_1-T_2}{T_1}$
(a). $80\text{K},60\text{K}$
${\eta }_a=\frac{80-60}{80}=\frac{1}{4}$
(b). $100\text{K},80\text{K}$
${\eta }_b=\frac{100-80}{100}=\frac{1}{5}$
$60\text{K},40\text{K}$
(c). ${\eta }_c=\frac{60-40}{60}=\frac{1}{3}$
$40\text{K},20\text{K}$
(d). ${\eta }_d=\frac{40-20}{40}=\frac{1}{2}$
$\therefore n_b<n_a<n_c<n_d$
Hence, option (d) is correct.