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Question 4.207E: A 1-ft^3 tank, shown in Fig. P4.136, that is initially evacu...

A 1- ft ^{3} tank, shown in Fig. P4.136, that is initially evacuated is connected by a valve to an air supply line flowing air at 70 F, 120 lbf / in .^{2}. The valve is opened, and air flows into the tank until the pressure reaches 90 lbf / in .^{2}. Determine the final temperature and mass inside the tank, assuming the process is adiabatic. Develop an expression for the relation between the line temperature and the final temperature using constant specific heats.

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C.V. Tank:
Continuity Eq.4.20:    m _{2}= m _{ i }

Energy Eq.4.21:    m _{2} u _{2}= m _{ i } h _{ i }

Table F.5:    u _{2}= h _{ i }=126.78   Btu / lbm

\Rightarrow T _{2}= 7 4 0   R

 

m _{2}=\frac{ P _{2} V }{ RT _{2}}=\frac{90 \times 144 \times 1}{53.34 \times 740}= 0 . 3 2 8 3   lbm

Assuming constant specific heat,

h _{ i }= u _{ i }+ RT _{ i }= u _{2}, \quad RT _{ i }= u _{2}- u _{ i }= C _{ Vo }\left( T _{2}- T _{ i }\right)

 

C _{ Vo } T _{2}=\left( C _{ Vo }+ R \right) T _{ i }= C _{ Po } T _{ i },

 

T _{2}=\left(\frac{ C _{ Po }}{ C _{ vo }}\right) T _{ i }= k T _{ i }

 

For  T _{ i }=529.7   R \text { \& constant } C _{ Po },

 

T _{2}=1.40 \times 529.7= 7 4 1 . 6   R

………………………………………

Eq.4.20: \left(m_{2}-m_{1}\right)_{ C.V. }=\sum m_{i}-\sum m_{e}

Eq.4.21:

\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}\right) \\&-\sum m_{e}\left(h_{e}+\frac{1}{2} V _{e}^{2}+g Z_{e}\right)\end{aligned}
1
F.5.1
F.5.2

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