Water in a piston/cylinder, similar to Fig. P3.225, is at 212 F, x = 0.5 with mass 1 lbm and the piston rests on the stops. The equilibrium pressure that will float the piston is 40 psia. The water is heated to 500 F by an electrical heater. At what temperature would all the liquid be gone? Find

Question

Water in a piston/cylinder, similar to Fig. P3.225, is at 212 F, x = 0.5 with mass 1 lbm and the piston rests on the stops. The equilibrium pressure that will float the piston is 40 psia. The water is heated to 500 F by an electrical heater. At what temperature would all the liquid be gone? Find the final (P,v), the work and heat transfer in the process.

Accepted Answer

C.V. The 1 lbm water.

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

Process: V = constant if [latex]P < P _{ ext {lift }}[/latex] otherwise [latex]P = P _{ lift }[/latex] see P-v diagram.

State 1: (T,x) Table F.7.1

[latex]\begin{array}{l}v _{1}=0.01672+0.5 imes 26.7864=13.4099 ft ^{3} / lbm \u _{1}=180.09+0.5 imes 897.51=628.845 Btu / lbm\end{array}[/latex]

State 1a: (40 psia, [latex]v = v _{1}> v _{ g 40 psia }=10.501 ft ^{3} / lbm[/latex]) so superheated vapor

Piston starts to move at state 1a, [latex]{ }_{1} W _{1 a }=0[/latex],

State 1b: reached before state 1a so [latex]v = v _{1}= v _{ g }[/latex] see this in F.7.1

[latex]T _{1 b }=250+10(13.40992-13.8247) /(11.7674-13.8247)= 2 5 2 F[/latex]

State 2: [latex]\left( T _{2}> T _{1 a } ight)[/latex] Table F.7.2 => [latex]v _{2}=14.164, u _{2}=1180.06 Btu / lbm[/latex]

Work is seen in the P-V diagram (when volume changes [latex]P = P _{ ext {lift }}[/latex] )

[latex]\begin{aligned}{ }_{1} W _{2} &={ }_{1 a } W _{2}= P _{2} m \left( v _{2}- v _{1} ight) \&=40 psi imes 1 lbm (14.164-13.4099) ft ^{3} / lbm imes 144 in ^{2} / ft ^{2} \&=4343.5 lbf - ft = 5 . 5 8 Btu\end{aligned}[/latex]

Heat transfer is from the energy equation

[latex]{ }_{1} Q _{2}=1 lbm (1180.06-628.845) Btu / lbm +5.58 Btu = 5 5 6 . 8 Btu[/latex]

Question 3.305E: Water in a piston/cylinder, similar to Fig. P3.225, is at 21...

Related Answered Questions