In the first stage of a two-stage carnot engine, energy is absorbed as heat q1 at temperature t1 = 500 k, work w1 is done, and energy is expelled as heat q2 at a lower temperature t2 = 430 k. the second stage absorbs that energy as heat q2, does work w2, and expels energy as heat q3 at a still lower temperature t3 = 240 k. what is the efficiency of the engine?

Efficiency = 52%

Explanation:

Given:

First stage

heat absorbed, Q₁ at temperature T₁ = 500 K

Heat released, Q₂ at temperature T₂ = 430 K

and the work done is W₁

Second stage

Heat released, Q₂ at temperature T₂ = 430 K

Heat released, Q₃ at temperature T₃ = 240 K

and the work done is W₂

Total work done, W = W₁ + W₂

Now,

The efficiency is given as:

or

Work done = change in heat

thus,

W₁ = Q₁ - Q₂

W₂ = Q₂ - Q₃

Thus,

or

or

also,

or

thus,

thus,

or

or

Efficiency = 52%

hotter stars = bluer stars