Numerical - efficiency of reversible heat engines of different capacities at same temperature difference

If a reversible heat engine A is operating between the temperature levels T1 and T2 and another reversible heat engine B of different capacity is also operating between the same temperature difference T1 and T2, then the efficiency of reversible heat engine B is

Options:

a. greater than efficiency of the reversible heat engine A
b. less than the efficiency of the reversible heat engine A
c. equal to the efficiency of the reversible heat engine A
d. can not say

Correct Answer: c. equal to the efficiency of the reversible heat engine A

Explanation

According to Carnot's theorem, the efficiency of a reversible heat engine operating between a constant temperature heat source and constant temperature sink is always highest among the other heat engines which operate between the same constant temperature heat source and constant temperature sink. Therefore when the two heat engines which are reversible are operating between the same constant temperature heat source and constant temperature sink then both the reversible heat engines have equal efficiency which is highest. This is a corollary of Carnot's theorem. The efficiency of all reversible heat engines operating between the same temperature level is the same.