Heat and Thermodynamics

9.6 Efficiency of A Carnot's Engine Is Independent of Nature of the Working Substance

Let us have two Carnot’s engines X and Y (Fig. 9.5) working with two substance x and y between two limits of temperature θ₁ and θ₂ (θ₁ > θ₂) independently.

 

 

Fig. 9.5 Carnot's engine

 

Let the engine X draw Q₁ quantity of heat at θ₁ and reject Q_x2 quantity of heat at θ₂ after doing W_x amount of work when running independently. Let the engine Y draw Q₁ quantity of heat at θ₁ and reject Q_y2 quantity of heat at θ₂ after doing W_y amount of work when running independently

Then by the first law,

 

Q₁ = Q_x2 + W_x

 

and

 

Q₁ = Q_y2 + W_y

 

so that

 

Q_y2 + W_y = Q