If the cold temperature reservoir of a Carnot engine is held at a constant 331 K, what temperature should the hot reservoir be kept at so that the engine efficiency is 0.55?

735.56 K

Explanation:

Carnot Engine: A Carnot engine is a an engine that operates on Carnot cycle.

A Carnot cycle: is defined as an ideal reversible closed thermodynamic operation, in which there are four successive and reversible cycles. These operations include isothermal expansion, adiabatic expansion, isothermal compression, and adiabatic compression.

The efficiency of a Carnot engine is given below,

η = (Th-Tc) / Th ... Equation 1

η = 1 - (Tc/Th) ... Equation 2

Where Th = temperature of the hot reservoir, Tc = temperature of the cold reservoir, η = efficiency of the Carnot engine.

Given: Th = 331 K, η = 0.55

Substitute into equation 2

0.55 = 1 - (331/Th)

0.55-1 = - 331/Th

-0.45 = - 331/Th

331/Th = 0.45

Th = 331/0.45

Th = 735.56 K.

Thus the temperature of the hot reservoir is 735.56 K.