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Helmholtz and Gibbs function

1 kg of air i...

Question

1 kg of air is compressed polytropically from 1 bar pressure and temperature of 300 K to a pressure of 6.8 bar and temperature of 370 K.

Assume

$R = 0.287 k J / k g K, c_{p} = 1.005 k J / k g K, c_{v} = 0.716 k J / k g K$ . If the sink temperature is 293 K the reversible work done by air is _____ $k J / k g$ .

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Solution

$- W_{m a x} = (u_{2} - u_{1}) - T_{0} (s_{2} - s_{1})$

$= c_{o} (T_{2} - T_{1}) - T_{n} (c_{p} ln \frac{T_{2}}{T_{1}} - R ln \frac{P_{2}}{P_{1}})$

$- W_{m a x} = 0.716 (370 - 300) - 293 (1.0051 ln \frac{370}{300} - 0.287 l n \frac{6.8}{1})$

$W_{m a x} = - 149.53 k J / k g$

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