A system executes a power cycle while receiving 1000 kJ by heat transfer at a temperature of 500 K and discharging 700 kJ by heat transfer at a temperature of 300 K. There are no other heat transfers. Determine the cycle efficiency. Use the Clausius Inequality to determine , in kJ/K. Determine if this cycle is internally reversible, irreversible, or impossible.

The cycle efficiency using clausius inequality is;

σ_cycle = 0.333 kJ/kg and is internally irreversible

η = 1 - Q_c/Q_h

Thus;

Q_c = (1 - η)Q_h

σ_cycle = -∫(dQ/dt)ₐ

Thus; σ_cycle = -[(Q_h/T_h) - (Q_c/T_c)]

We are given;

Q_h = 1000 kJ

T_h = 500 k

T_c = 300 k

Q_c = 700 kJ

σ_cycle = -[(1000/500) - (700/300)]

σ_cycle = -(2 - 2.333)

σ_cycle = 0.333 kJ/kg

Since σ_cycle > 0, then the cycle is internally irreversible

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, , , The cycle is irreversible.

Explanation:

The real cycle efficiency is:

The theoretical cycle efficiency is:

The reversible and real versions of the power cycle are described by the Clausius Inequalty:

Reversible Unit

Real Unit

The cycle is irreversible.

answer:

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