Question

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.

Answer 1

Answer:

$\eta_{th} = 30\,\%$, $\eta_{th,max} = 40\,\%$, $\Delta S = \frac{1}{3}\,\frac{kJ}{K}$, The cycle is irreversible.

Explanation:

The real cycle efficiency is:

$\eta_{th} = \frac{1000\,kJ-700\,kJ}{1000\,kJ} \times 100\,\%$

$\eta_{th} = 30\,\%$

The theoretical cycle efficiency is:

$\eta_{th,max} = \frac{500\,K-300\,K}{500\,K} \times 100\,\%$

$\eta_{th,max} = 40\,\%$

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

Reversible Unit

$\frac{1000\,kJ - 600kJ}{300\,K}= 0$

Real Unit

$\Delta S = \frac{1000\,kJ-600\,kJ}{300\,K} -\frac{1000\,kJ-700\,kJ}{300\,K}$

$\Delta S = \frac{1}{3}\,\frac{kJ}{K}$

The cycle is irreversible.