Question

Show all your work precisely. Label all the steps of your solution. Follow the problem solving procedure as mentioned in class. 1. Can saturated water vapor at 200 kPa be condensed to a saturated liquid in an isobaric, closed system process while only exchanging heat with an isothermal energy reservoir at 90 °C? (Hint: Determine the entropy generation.)

Answer 1

The saturation properties of water from steam tables are:

Pressure (kPa)	Temp (C)	hf (kJ/kg)	hg (kJ/kg)	sf (kJ/kgK)	sg (kJ/kgK)
200	120.2	504.7	2706.51	1.53	7.127

Now, Specific Entropy generation = $S_{gen}=(s_2-s_1)+\frac{dQ}{T_{source}}$

where

• s2 = specific entropy of final state = sf at 200 kPa = 1.53 kJ/kgK
• s1= specific entropy at initial state = sg at 200 kPa = 7.127 kJ/kgK
• dQ = Specific heat interaction during condensation = $dW_{1-2}+\Delta u=\Delta h=h_g-h_f$ = 2706.51 - 504.7 = 2201.81 kJ/kg
• T(source) = Temperature of source = 90 C = 363 K

$S_{gen}=(s_2-s_1)+\frac{dQ}{T_{source}}$

$S_{gen}=(1.53-7.127)+\frac{2201.81}{363}=>\mathbf{S_{gen}=0.4682\:kJ/kgK}$

As we can see. the Entropy Generation per unit mass is a positive quantity. Thus, this process is possible.

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