Three Carnot heat engines are arranged in series. The first engine takes 4000 KJ of heat from a source at 2000K and delivers 1800KJ of work : the second and the third engine delivers 1200KJ and 500KJ of work respectively. The exhaust temperature of the second and third carnot cycle will be.
Answers
Answer:
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Answer:
The exhaust temperature of the second and third Carnot cycle is 2666.67KJ and 1111.11KJ respectively.
Explanation:
Given:
The heat taken by the first engine (Q₁) = 4000KJ
Work done by the first engine (W₁) = 1800KJ
Work done by the second engine (W₂) = 1200KJ
Work done by the third engine (W₃) = 500KJ
To find:
Amount of heat taken by the second and third engines (Q₂ and Q₃)
Formula:
η = W/Q
Step 1:
Since the three Carnot engines are in series, their efficiency will be equal. Therefore,
η₁ = η₂ = η₃
For the second heat engine,
η₁ = η₂
Using the given formula, we get
W₁/Q₁ = W₂/Q₂
1800/4000 = 1200/Q₂
Q₂ = (1200×4000)/1800
Q₂ = 2666.67KJ
Step 2:
For the third heat engine,
η₁ = η₃
Using the given formula, we get
W₁/Q₁ = W₃/Q₃
1800/4000 = 500/Q₃
Q₃ = (500×4000)/1800
Q₃ = 1111.11KJ
Therefore, the exhaust temperature of the second and third Carnot cycle will be 2666.67KJ and 1111.11KJ respectively.
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