In which case will the efficiency of a Carnot cycle be higher: when the hot body temperature is incr — Thermodynamics and Thermochemistry Chemistry Question

💡 Solution & Explanation

$\eta = 1 - \frac{T_C}{T_H}$. Decreasing $T_C$ by $\Delta T$ evaluates to $1 - \frac{T_C - \Delta T}{T_H}$. Increasing $T_H$ by $\Delta T$ yields $1 - \frac{T_C}{T_H + \Delta T}$. Since $T_C < T_H$, mathematically $\frac{T_C - \Delta T}{T_H} < \frac{T_C}{T_H + \Delta T}$, meaning the efficiency increases more by decreasing the cold body temperature.