A Carnot engine operates between a warmer reservoir at a temperature T 1 and a c

Question

A Carnot engine operates between a warmer reservoir at a temperature T1 and a cooler reservoir at a temperature T2. It is found that increasing the temperature of the warmer reservoir by a factor of 3.00 while keeping the same temperature for the cooler reservoir increases the efficiency of the Carnot engine by a factor of 9.00. Find the efficiency of the engine and the ratio of the temperatures of the two reservoirs in their original form.

=

The ratio of the temperatures of the two reservoirs in their original form is T2/T1=

Explanation / Answer

u = 1 - T2/T1

==> T2/T1 = 1 - u

9 u = 1 - T2/(3 T1)

==> 9 u = 1 - (1/3) (1 - u)

==> 9 u = 1 - 1/3 + 1/3 u

==> (9 - 1/3) u = 1 - 1/3

==> (27 - 1) u = 3 - 1

==> (26) u = 2

==> u = 1/13

==> u = 0.0769

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T2/T1 = 1 - u = 0.923

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