Question

A gas-cooled nuclear reactor operates between hot and cold reservoir temperatures of 700ºC and 27.0ºC.

(a) What is the maximum efficiency of a heat engine operating between these temperatures?
a) 47.6%
b) 55.3%
c) 62.8%
d) 71.4%

Answer 1

The maximum efficiency of a heat engine operating between hot and cold reservoir temperatures can be calculated using the Carnot efficiency formula. In this case, the maximum efficiency is approximately 69.2%.

Step-by-step explanation:

The maximum efficiency of a heat engine operating between the given hot and cold reservoir temperatures can be calculated using the Carnot efficiency formula: Efficiency = 1 - (Tc/Th). Where Tc is the cold reservoir temperature in Kelvin and Th is the hot reservoir temperature in Kelvin.

Converting the given temperatures to Kelvin, we have Tc = 27.0°C + 273.15 = 300.15K and Th = 700°C + 273.15 = 973.15K. Plugging these values into the formula, we get:

Efficiency = 1 - (300.15/973.15) = 69.2%

Therefore, the maximum efficiency of the heat engine operating between the given temperatures is approximately 69.2%.