A tank contains 10 ft^3 air at 15 psia, 540 R. A pipe flowing air at 150 psia, 540 R is connected to the tank and it is filled slowly to 150 psia. Find the heat transfer to reach a final temperature of 540 R.

Question

A tank contains 10 [latex]ft ^{3}[/latex] air at 15 psia, 540 R. A pipe flowing air at 150 psia, 540 R is connected to the tank and it is filled slowly to 150 psia. Find the heat transfer to reach a final temperature of 540 R.

Accepted Answer

C.V. The tank volume and the compressor.
This is a transient problem (filling of tank).

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}={ }_{1} Q _{2}-{ }_{1} W _{2}+ m _{ in } h _{ in }[/latex]

Process: Constant volume [latex]{ }_{1} W _{2}=0[/latex],

States: [latex]u _{1}= u _{2}= u _{ in }= u _{540} ; \quad h _{ in }= u _{ in }+ RT _{ in }[/latex]

[latex]\begin{array}{l}m _{1}= P _{1} V _{1} / RT _{1}=15 imes 144 imes 10 /(53.34 imes 540)=0.75 lbm \m _{2}= P _{2} V _{2} / RT _{2}=150 imes 144 imes 10 /(53.34 imes 540)=7.499 lbm\end{array}[/latex]

Heat transfer from the energy equation

[latex]\begin{aligned}{ }_{1} Q _{2} &= m _{2} u _{2}- m _{1} u _{1}- m _{ in } h _{ in }=\left( m _{1}+ m _{ in } ight) u _{1}- m _{1} u _{1}- m _{ in } u _{ in }- m _{ in } RT _{ in } \&= m _{1} u _{1}- m _{1} u _{1}+ m _{ in } u _{1}- m _{ in } u _{ in }- m _{ in } RT _{ in }=- m _{ in } R T _{ in } \&=-(7.499-0.75) lbm imes 53.34 ft - lbf / lbm - R imes 540 R \&=-194395 ft - lbf =- 2 5 0 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 4.206E: A tank contains 10 ft^3 air at 15 psia, 540 R. A pipe flowin...

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