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A cylinder fitted with a movable piston contains water at 3 MPa with 50% quality, at which point the volume is 20 L. The water now expands to 1.2 MPa as a result of receiving 600 kJ of heat from a large source at 300◦C. It is claimed that the water does 124 kJ of work during this process. Is this possible?

User Sgonzalez
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2 Answers

4 votes

Answer:

Yes it is possible

Step-by-step explanation:

Attached is the solution

A cylinder fitted with a movable piston contains water at 3 MPa with 50% quality, at-example-1
A cylinder fitted with a movable piston contains water at 3 MPa with 50% quality, at-example-2
User Hoo
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Answer:

The process is possible:

Step-by-step explanation:

We are going to find out if the entropy generated is greater than 0, if it is greater than 0, then the process is feasible. If it is not, the process is not feasible.


P_(1) = 3 MPa


x_(1) = 50 % = 0.5


V_(1) = 20 L = 0.02 m^(3)


P_(2) = 1.2 MPa


T_(H) = 300^(0) C = 573 K

Received heat energy,
Q_(12) = 600 kJ

Work done,
W_(12) = 124 kJ

At state 1, using the steam table:


T_(1) = T_(s) = 233.9^(0) C\\v_(f1) = 0.001216 m^(3) /kg\\v_(fg1) = 0.06546m^(3) /kg\\u_(f1) = 1004.76 kJ/kg\\u_(fg1) = 1599.34 kJ/kg\\s_(f1) = 2.6456 kJ/kg-K\\s_(fg1) = 3.5412kJ/kg-K


v_(1) = v_(f1) + x_(1) * v_(fg1)


v_(1) = 0.001216 + 0.5*(0.06546)\\v_(1) = 0.03395 m^(3) /kg


M = (V_(1) )/(v_(1) ) \\M = 0.02/0.03395\\M = 0.5892 kg


u_(1) = u_(f1) + x_(1) * u_(fg1)\\u_(1) = 1004.76 + 0.5*1599.34\\u_(1) = 1804.43 kJ/kg


s_(1) = s_(f1) + x_(1) * s_(fg1)\\s_(1) = 2.6456 + 0.5*3.5412\\s_(1) = 4.4162 kJ/kg


Q_(12) = m(u_(2) - u_(1) ) + W_(12) \\600 = 0.5892(u_(2) -1804.43) + 124\\

Solving for u₂


u_(2) = 2612.3 kJ/kg

Since P₂ = 1.2 MPa, u₂ = 2612.2 kJ/kg,

then from steam table, T₂ = 200°C, S₂ = 6.5898 kJ/kg-K

The entropy generated will be:


\triangle S = m(S_(2) -S_(1) ) - (Q_(12) )/(T_(H) )\\ \triangle S= 0.5892(6.5898 - 4.4162) - (600 )/(573 )\\ \triangle S =0.233 kJ/K

Since ΔS > 0, this process is possible

User Henry S
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