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Helmholtz and Gibbs Function

Air enters a ...

Question

Air enters a compressor in a steady flow manner at 140 kPa and $17^{\circ} C$ and leaves it at 350 KPa and $127^{\circ} C$ During the flow change in enthalpy and kinetic energy are 110.55 kJ/kg and 3.6 kJ/kg respectively. The minimum reversible work input required is kJ/K.

A

97.29 (k J / k g K)

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B

87.29 (k J / k g K)

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C

75 (k J / k g K)

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D

80 (k J / k g K)

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Solution

The correct option is A $97.29 (k J / k g K)$

$(S_{2} - S_{1}) = C_{p} ln \frac{T_{2}}{T_{1}} - R ln \frac{P_{2}}{P_{1}}$

$= 1.005 ln \frac{400}{290} - 0.28 ln \frac{350}{140}$

$= 0.0602 k J / K g - K$

Minimum reversible work input required

$W_{r e v} = Δ h + Δ K E - T_{o} . Δ S$

$= 110.55 + 3.6 - 280 \times 0.0602$

$= 97.29 (k J / k g K)$

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