The ocean thermal energy conversion project uses the surface water near tropical islands with a temperature of $20 ^ { \circ } \mathrm { C }$ as the hot temperature reservoir, and the water at some depth, with a temperature of $5.0 ^ { \circ } \mathrm { C }$, as the cold temperature reservoir for a heat engine. What is the maximum possible efficiency of an engine running between those two temperatures?
A) $7.9 \%$
B) $4.7 \%$
C) $30 \%$
D) $5.1 \%$
E) $15 \%$

Question

Quizplus · Accepted Answer

The maximum possible efficiency of a heat engine operating between two temperatures is given by the Carnot efficiency formula: $\eta = 1 - \frac{T_{c}}{T_{h}}$, where $\eta$ is the efficiency, $T_{c}$ is the cold reservoir temperature in Kelvin, and $T_{h}$ is the hot reservoir temperature in Kelvin. To use this formula, first convert the given temperatures from Celsius to Kelvin: $20 ^{\circ}C = 293K$ and $5.0 ^{\circ}C = 278K$. Then, $\eta = 1 - \frac{278}{293} = 1 - 0.949$, which gives $\eta \approx 0.051$ or $5.1\%$.

The Ocean Thermal Energy Conversion Project Uses the Surface Water 20∘C20 ^ { \circ } \mathrm { C }20∘C

The Ocean Thermal Energy Conversion Project Uses the Surface Water $20 ^ { \circ } \mathrm { C }$