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Energy

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Question

The pressure, temperature and velocity of air flowing in pipe are 5 bar, 500 K and 50m/s, respectively. The specific heats of air at a constant pressure and at constant volume are 1.005 kJ/kgK and 0.718 kJ/kgK, respectively. Neglect potential energy. If the pressure and temperature of the surroundings are 1 bar and 300 K, respectively, the available energy in kJ/kg of he air stream is

A

170

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B

191

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C

187

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D

213

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Solution

The correct option is C 187
(b)
$P_{0} = 100 k P a, T_{0} = 300 K$
Available energy
$= (h_{1} - h_{0}) - T_{0} (s_{1} - s_{0}) + (\frac{v_{1}^{2}}{2} - \frac{v_{2}^{2}}{2})$
where, $s_{1} - s_{0} = c_{p} I n \frac{T_{1}}{T_{0}} - R I n \frac{p_{1}}{p_{0}}$ $(V_{2} = 0)$
$= 1.005 I n (\frac{500}{300}) - 0.287 I n (\frac{5}{1})$
$= 0.05147 k J / k g K$
$∴$ Available energy
$= 1.005 (500 - 300) - 300 (0.5147) + \frac{(50)^{2}}{2} \times 10^{- 3}$
$= 186.8 k J / k g \approx 187 k J / k g$

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