Question

The ocean thermal energy conversion project uses the surface water near tropical islands with a temperature of 20.0°C as the hot temperature reservoir, and the water at some depth, with a temperature of 5.0°C, as the cold temperature reservoir for a heat engine. What is the maximum efficiency of an engine running between those two temperatures?

A) 7.9%
B) 15%
C) 5.1%
D) 4.7%
E) 30%

Answer 1

The maximum efficiency of an engine running between a hot reservoir at 20.0°C and a cold reservoir at 5.0°C is 5.12%, which means the closest provided answer is (C) 5.1%.

Step-by-step explanation:

The maximum efficiency of a heat engine operating between two temperatures can be estimated using the Carnot efficiency, which is based on the temperature difference between the hot and cold reservoirs in Kelvin. The formula for Carnot efficiency (e) is given by e = 1 - (Tc/Th), where Tc is the absolute temperature of the cold reservoir and Th is the absolute temperature of the hot reservoir. To calculate these, we must first convert the Celsius temperatures to Kelvin by adding 273.15 to each.

The hot reservoir temperature is 20.0°C, which becomes 293.15 K (20 + 273.15), and the cold reservoir temperature is 5.0°C, which becomes 278.15 K (5 + 273.15). So, the maximum efficiency (e) can be calculated as follows:

e = 1 - (278.15 K / 293.15 K) = 1 - 0.9488 = 0.0512 or 5.12%

Thus, the answer closest to our calculation is (C) 5.1%.