Answer to Question #136260 in Molecular Physics | Thermodynamics for RIYAS ASLAM M

Question

Two reversible engine operate between thermal reservoirs at 1200 K, T2K and 300 K such that 1st engine receives heat from 1200 K reservoir and rejects heat to thermal reservoir at T2K, while the 2nd engine receives heat from thermal reservoir at T2K and rejects heat to the thermal reservoir at 300 K. Calculate T2 in K If the efficiency of both the engines is equal.

Answer 1

The efficiency of engine with temperatures of T_i and T_j is (if T_i > T_j) equal to

$\eta = \dfrac{T_i-T_j}{T_i}.$

In our case $\dfrac{1200-T_2}{1200} = \dfrac{T_2-300}{T_2}$ . $T_2^2 = 300\cdot1200, \; T_2 = 600\,K$ .

The efficiency is 50%.