A piston/cylinder contains 2 lbm of water at 70 F with a volume of 0.1 ft^3, shown in Fig. P3.225. Initially the piston rests on some stops with the top surface open to the atmosphere, Po, so a pressure of 40 lbf/in.^2 is required to lift it. To what temperature should the water be heated to lift

Question

A piston/cylinder contains 2 lbm of water at 70 F with a volume of 0.1 [latex]ft ^{3}[/latex], shown in Fig. P3.225. Initially the piston rests on some stops with the top surface open to the atmosphere, Po, so a pressure of 40 lbf/[latex]in .^{2}[/latex] is required to lift it. To what temperature should the water be heated to lift the piston? If it is heated to saturated vapor find the final temperature, volume, and the heat transfer.

Accepted Answer

C.V. Water. This is a control mass.

[latex]m _{2}= m _{1}= m ; \quad m \left( u _{2}- u _{1} ight)={ }_{1} Q _{2}-{ }_{1} W _{2}[/latex]

State 1: 20 C, [latex]v _{1}= V / m =0.1 / 2=0.05 ft ^{3} / lbm[/latex]

[latex]x =(0.05-0.01605) / 867.579=0.0003913[/latex]

[latex]u _{1}=38.09+0.0003913 imes 995.64=38.13 Btu / lbm[/latex]

To find state 2 check on state 1a:

P = 40 psia, [latex]v = v _{1}=0.05 ft ^{3} / lbm[/latex]

Table F.7.1: [latex]v _{ f }< v < v _{ g }=10.501, x _{1 a }>0[/latex]

State 2 is saturated vapor at 40 psia as state 1a is two-phase. [latex]T _{2}=267.3 F[/latex]

[latex]v _{2}= vg =10.501 ft ^{3} / lbm , V _{2}= m v _{2}=21.0 ft ^{3}, u _{2}= ug =1092.27 Btu / lbm[/latex]

Pressure is constant as volume increase beyond initial volume.

[latex]{ }_{1} W _{2}=\int P d V = P _{ lift }\left( V _{2}- V _{1} ight)=40(21.0-0.1) imes 144 / 778=154.75 Btu[/latex]

[latex]{ }_{1} Q _{2}= m \left( u _{2}- u _{1} ight)+{ }_{1} W _{2}=2(1092.27-38.13)+154.75=2263 Btu[/latex]

Question 3.301E: A piston/cylinder contains 2 lbm of water at 70 F with a vol...

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