The efficiency of a Carnot cycle is 1/6. On decreasing the temperature of the sink by , the efficien — Thermodynamics and Thermochemistry Chemistry Question

💡 Solution & Explanation

$\eta_1 = 1 - \frac{T_2}{T_1} = \frac{1}{6} \implies T_2 = \frac{5}{6} T_1$. $\eta_2 = 1 - \frac{T_2 - 65}{T_1} = \frac{1}{3} \implies \frac{T_2 - 65}{T_1} = \frac{2}{3}$. Substituting $T_2$ yields $\frac{5}{6} T_1 - 65 = \frac{4}{6} T_1 \implies \frac{1}{6} T_1 = 65 \implies T_1 = 390 \text{ K}$. In Celsius, $390 - 273 = 117^\circ\text{C}$.