Question

A Carnot engine $C_1$ operates between temperature $T_1$ and $T_2\left(T_1>T_2\right).$ A second Carnot engine $C_2$ uses all the heat rejected by the engine $C_1$ and operates between temperature $T_2$ and $T_3$ (where $T_2>T_3$ ). The efficiency of this combined $(C_1$ and $C_2$ together $)$ engine is

• A. $1-\frac{T_3}{T_1}$
• B. $1-\frac{T_3}{T_2}$
• C. $1-\frac{\left(T_2+T_3\right)}{T_1}$
• D. $1-\left(1-\frac{T_2}{T_2}\right)\left(1-\frac{T_3}{T_2}\right)$

Answer 1

Answer: (C)

Efficiency of Carnot's engine $C_1$ is given as
${\eta }_l=1-\frac{T_2}{T_l}\dots$ (i)
where, $T_2=$ temperature of $\sin k$
and $T_1=$ temperature of source.
Similarly, efficiency of second Carnot's engine,
${\eta }_2=1-\frac{T_3}{T_2}\dots$ (ii)
The efficiencyof combined engine $(C_1$ and $C_2)$ is given as
$\eta ={\eta }_l+{\eta }_2=1-\frac{T_2}{T_1}+1-\frac{T_3}{T_2}$
$=2-\left(\frac{T_2}{T_1}+\frac{T_3}{T_2}\right)$