Suppose that, in Iceland, scientists discover geothermal vents that produce pressurized steam at $300^{\circ} \mathrm{C}$. Engineers construct a heat engine that uses this steam as a hot reservoir and a nearby glacier as a cold reservoir. What is the maximum possible efficiency of this engine?
A) $300 \%$
B) $100 \%$
C) $52 \%$
D) $45 \%$
E) $22 \%$
F) Other

Question

Quizplus · Accepted Answer

The maximum possible efficiency of a heat engine is given by the Carnot efficiency, which is $1 - \frac{T_c}{T_h}$, where $T_c$ and $T_h$ are the cold and hot reservoir temperatures in Kelvin, respectively. Converting $300^{\circ}C$ to Kelvin gives $573K$. Assuming the glacier is at $0^{\circ}C$ or $273K$, the maximum efficiency is $1 - \frac{273}{573} \approx 0.52$ or $52\%$.

Suppose That, in Iceland, Scientists Discover Geothermal Vents That Produce 300∘C300^{\circ} \mathrm{C}300∘C

Suppose That, in Iceland, Scientists Discover Geothermal Vents That Produce $300^{\circ} \mathrm{C}$