Answer
The Carnot efficiency of an engine operating between two heat reservoirs at temperatures $T_1$ and $T_2$, where $T_1 > T_2$, is given by
$η =1− \frac{T_1}{T_2} $
In this case, the warm surface water is at a temperature of $T_1 = 25\ \mathrm{°C} = 298\ \mathrm{K}$ and the cool deep water is at a temperature of $T_2 = 5\ \mathrm{°C} = 278\ \mathrm{K}$. Therefore, the Carnot efficiency of an OTEC plant operating between these two temperatures is:
$ η = 1− \frac{298 K }{278 K}$
≈0.067=6.7%
Although this efficiency may seem low, as noted in the problem statement, OTEC's "fuel" is free, making it an attractive option for sustainable energy production.
Work Step by Step
The Carnot efficiency of an engine operating between two heat reservoirs at temperatures $T_1$ and $T_2$, where $T_1 > T_2$, is given by
$η =1− \frac{T_1}{T_2} $
In this case, the warm surface water is at a temperature of $T_1 = 25\ \mathrm{°C} = 298\ \mathrm{K}$ and the cool deep water is at a temperature of $T_2 = 5\ \mathrm{°C} = 278\ \mathrm{K}$. Therefore, the Carnot efficiency of an OTEC plant operating between these two temperatures is:
$ η = 1− \frac{298 K }{278 K}$
≈0.067=6.7%
Although this efficiency may seem low, as noted in the problem statement, OTEC's "fuel" is free, making it an attractive option for sustainable energy production.
