Question

The Kelvin temperature of the hot reservoir of a Carnot engine is twice that of the cold reservoir, and work done by the engine per cycle is 18 J. (a) Calculate the efficiency of the engine.

Answer 1

η = 0.5 = 50%

Step-by-step explanation:

The efficiency of a Carnot engine is given by the following formula:

η = (T₁ - T₂)/T₁

η = 1 - T₂/T₁

where,

η = Efficiency of the engine

T₁ = Absolute Temperature of Hot Reservoir

T₂ = Absolute Temperature of Cold Reservoir

but, according to given question the absolute temperature of hot reservoir is twice that of the cold reservoir. Therefore,

T₁ = 2 T₂

Substituting this in equation, we get:

η = 1 - T₂/2T₂

η = 1 - 1/2

η = 0.5 = 50%