# A heat engine is supplied with 800 kJ/s of heat at 600 K, and heat rejection takes place at 300 K. Which of the following results report a reversible

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A heat engine is supplied with 800 kJ/s of heat at 600 K, and heat rejection takes place at 300 K. Which of the following results report a reversible cycle?
1. 200 kJ/s are rejected
2. 400 kJ/s are rejected
3. 100 kJ/s are rejected
4. 500 kJ/s are rejected

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Correct Answer - Option 2 : 400 kJ/s are rejected

Concept:

As per Clausius Inequality

If $\oint \frac{{\partial Q}}{T} = 0$ the cycle is reversible.

If $\oint \frac{{\partial Q}}{T} < 0$ the cycle is irreversible.

If $\oint \frac{{\partial Q}}{T} > 0$ the cycle is impossible.

Calculation:

Given:

Q1 = 800 kJ/sec, T1 = 600 K, T2 = 300 K.

As per Clausius Inequality

For reversible cycle:

$\oint \frac{{\partial Q}}{T} = 0$

$\frac{Q_1}{T_1}+\frac{Q_2}{T_2}=0$

$\frac{800}{600}+\frac{Q_2}{300}=0$

∴ Q2 = -400 kJ/sec rejected (∵ negative implies rejected).