Question

A Carnot engine performs 100 J of work while discharging 200 J of heat each cycle. After the temperature of the hot reservoir only is adjusted, it is found that the engine now does 130 J of work while discarding the same quantity of heat.

(a) What are the initial and final efficiencies of the engine?
(b) What is the fractional change in the temperature of the hot reservoir?

a) Initial efficiency = 0.50, Final efficiency = 0.65, Fractional change = 0.3
b) Initial efficiency = 0.60, Final efficiency = 0.55, Fractional change = 0.1
c) Initial efficiency = 0.75, Final efficiency = 0.80, Fractional change = 0.2
d) Initial efficiency = 0.45, Final efficiency = 0.50, Fractional change = 0.4

Answer 1

The initial efficiency of the Carnot engine is 0.50 and the final efficiency is 0.65. The fractional change in the temperature of the hot reservoir is 0.3.

Step-by-step explanation:

(a) The initial efficiency of the Carnot engine can be calculated by dividing the work done by the heat input:

Initial Efficiency = Work Done / Heat Input

Initial Efficiency = 100 J / 200 J = 0.5

The final efficiency of the Carnot engine can be calculated using the same formula, but with the work done equal to 130 J:

Final Efficiency = 130 J / 200 J = 0.65

(b) The fractional change in the temperature of the hot reservoir can be calculated using the formula:

Fractional Change = (Final Efficiency - Initial Efficiency) / Initial Efficiency

Fractional Change = (0.65 - 0.5) / 0.5 = 0.3