A rigid, insulated tank is initially evacuated. The tank is connected with a supply line through which air (assumed to be ideal with constant specific heats) passes at 1NPa, $350^{0}$ .
A valve connected with the supply line is opened and the tank is charged with air until the final pressure inside the tank reaches 1 MPa. The final temperature inside the tank

Is greater than

350^{0} C

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Is less than

350^{0} C

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Is equal to

350^{0} C

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May be greater than, less than, or equal to

350^{0} C

, depending in the volume if the tank.

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Solution

The correct option is A Is greater than $350^{0} C$

Applying unsteady flow energy equation,

$Q = m_{2} u_{2} - m_{1} u_{1} + m_{e} (h_{e} + \frac{V_{e}^{2}}{2} + g z_{e})$
$- m_{i} (h_{i} + \frac{V_{i}^{2}}{2} + g z_{i})$ +W...(i)

For given problem,
$m_{1} = 0$ . evacuated tank
$m_{e} = 0$ . no exit
$V_{i}$ is neglected
$Z_{i} = 0; Q = 0; W = 0$
Above Eq. (i) becomes
$0 = m_{2} u_{2} - m_{i} h_{i}$
or $m_{i} h_{i} = m_{2} u_{2}$
$h_{i} = u_{2}$ $∵ m_{i} = m_{2}$
$C_{p} T_{i} = C_{v} T_{2}$
$\frac{C_{p}}{C_{v}} T_{i} = T_{2}$ where $γ = \frac{C_{p}}{C_{v}}$
$γ T_{i} = T_{2}$
or $T_{2} = γ T_{i} = 1.4 \times 623 k$

$= 872.3 k = {599.2}^{0} C$
The final temperature, $T_{2} = {599.2}^{0} C$ inside the tank is greater than $350^{0} C$ .

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