An engine takes in 150 J of energy from a 400 K thermal source. If the engine discharges energy into a thermal reservoir at 150 K, then what is the maximum amount of work one can get out of the engine?
A) 93.8 J
B) 84.2 J
C) 28.5 J
D) 168 J

Question

Quizplus · Accepted Answer

The maximum amount of work that can be extracted from an engine operating between two thermal reservoirs is given by the efficiency of an ideal Carnot engine, which is $1 - \frac{T_{\text{cold}}}{T_{\text{hot}}}$, where $T_{\text{cold}}$ and $T_{\text{hot}}$ are the temperatures of the cold and hot reservoirs, respectively. In this case, $T_{\text{hot}} = 400 \, K$ and $T_{\text{cold}} = 150 \, K$. The efficiency is $1 - \frac{150}{400} = 0.625$. The maximum work output is then the product of this efficiency and the energy input, which is $150 \, J \times 0.625 = 93.75 \, J$, which rounds to $93.8 \, J$.

An Engine Takes in 150 J of Energy from a 400