Question

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.​

Answer 1

Answer:

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Answer 2

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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