Question

Two carnot engines $A$ and $B$ are operated in series. The first one, $A$ received heat at $T_1(=600\text{K})$ and rejects to a reservoir at temperature $T_2$. The second engine $B$ receives heat rejected by the first engibe and in turn, rejects to a heat reservoir at $T_3=\left(400\text{K}\right)$. Calculate the temperature $T_2$ if the work outputs of the two engines are equal

• A. $\text{600 K}$
• B. $\text{400 K}$
• C. $\text{500 K}$
• D. $\text{300 K}$

Answer 1

The correct option is C $\text{500 K}$



${\eta }_A=\frac{T_1-T_2}{T_1}=\frac{{\text{W}}_{\text{A}}}{Q_1}$

and

${\eta }_B=\frac{T_2-T_3}{T_2}=\frac{{\text{W}}_{\text{B}}}{Q_2}$
According to question,

$W_A=W_B$
$\therefore \frac{Q_1}{Q_2}=\frac{T_1}{T_2}\times \frac{T_2-T_3}{T_1-T_2}=\frac{T_1}{T_2}$
$\therefore T_2=\frac{T_1+T_3}{2}=\frac{600+400}{2}=500\text{K}$