A mass-loaded piston/cylinder containing air is at 45 lbf/in.^2, 60 F with a volume of 9 ft^3, while at the stops V = 36 ft^3. An air line, 75 lbf/in.^2, 1100 R, is connected by a valve, as shown in Fig. P4.154. The valve is then opened until a final inside pressure of 60 lbf/in.^2 is reached, at

Question

A mass-loaded piston/cylinder containing air is at 45 [latex]lbf / in .^{2}[/latex], 60 F with a volume of 9 [latex]ft ^{3}[/latex], while at the stops V = 36 [latex]ft ^{3}[/latex]. An air line, 75 [latex]lbf / in .^{2}[/latex], 1100 R, is connected by a valve, as shown in Fig. P4.154. The valve is then opened until a final inside pressure of 60 [latex]lbf / in .^{2}[/latex] is reached, at which point T = 630 R. Find the air mass that enters, the work, and heat transfer.

Accepted Answer

C.V. Cylinder volume.

Continuity Eq.4.20: [latex]m _{2}- m _{1}= m _{ in }[/latex]

Energy Eq.4.21: [latex]m _{2} u _{2}- m _{1} u _{1}= m _{ in } h _{ ext {line }}+{ }_{1} Q _{2}-{ }_{1} W _{2}[/latex]

Process: [latex]P _{1}[/latex] is constant to stops, then constant V to state 2 at [latex]P _{2}[/latex]

State 1: [latex]P _{1}, T _{1}[/latex] [latex]m _{1}=\frac{ P _{1} V }{ RT _{1}}=\frac{45 imes 9 imes 144}{53.34 imes 519.7}=2.104 lbm[/latex]

State 2: Open to: [latex]P _{2}=60 lbf / in ^{2}, T _{2}=630 R[/latex]

Table F.5:

[latex]\begin{array}{l}h _{ i }=266.13 btu / lbm \u _{1}=88.68 Btu / lbm \u _{2}=107.62 Btu / lbm\end{array}[/latex]

[latex]{ }_{1} W _{2}=\int PdV = P _{1}\left( V _{ ext {stop }}- V _{1} ight)=45 imes(36-9) \frac{144}{778}= 2 2 4 . 9 Btu[/latex]

[latex]m _{2}= P _{2} V _{2} / RT _{2}=60 imes 36 imes 144 /(53.34 imes 630)=9.256 lbm[/latex]

[latex]m _{ i }= m _{2}- m _{1}=9.256-2.104=7.152 lbm[/latex]

[latex]\begin{aligned}{ }_{1} Q _{2} &= m _{2} u _{2}- m _{1} u _{1}- m _{ i } h _{ i }+{ }_{1} W _{2} \&=9.256 imes 107.62-2.104 imes 88.68-7.152 imes 266.13+224.9 \&=- 8 6 8 . 9 Btu\end{aligned}[/latex]

........................................

Eq.4.20: [latex]\left(m_{2}-m_{1} ight)_{ C.V. }=\sum m_{i}-\sum m_{e}[/latex]

Eq.4.21:

[latex]\begin{aligned}E_{2}-E_{1}=Q_{ C.V. }-W_{ C.V. } &+\sum m_{i}\left(h_{i}+\frac{1}{2} V _{i}^{2}+g Z_{i} ight) \&-\sum m_{e}\left(h_{e}+\frac{1}{2} V _{e}^{2}+g Z_{e} ight)\end{aligned}[/latex]

Question 4.211E: A mass-loaded piston/cylinder containing air is at 45 lbf/in...

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