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State and Path Variables, Functions

A steam turbi...

Question

A steam turbine receives steam steady at 10 bar with a enthalpy of 3000 kJ/kg and discharges at 1 bar with an enthalpy of 2700 kJ/kg. The work output is 250 kJ/kg. The changes in kinetic and potential energies are negligible. The heat transfer from the turbine casing to the surroundings is equal to

A

0 kJ

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B

50 kJ

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C

150 kJ

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D

250 kJ

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Solution

The correct option is B 50 kJ
(b)
$p_{1} = 10 b a r;$ $h_{1} = 3000 k J / k g;$ $p_{2} = 1 b a r$
$h_{2} = 2700 k J / k g;$ $w = 250 k J / k g$
$q = ?$
The steady flow energy equation for unit mass flow rate,
$h_{1} + \frac{V_{1}^{2}}{2} + g z_{1} + q = h_{2} + \frac{V_{1}^{2}}{2} + g z_{2} + w$
Change in KE and PE are negligible
$h_{1} + q = h_{2} + w$
$3000 + q = 2700 + 250$
or $q = - 50 k J / k g$
The heat transfer from the turbine casing to the surroundings is equal to 50 kJ\kg.

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