Question

A 4 m3 storage tank containing 2 m3 of liquid is about to be pressurized with air from a large, high-pressure reservoir through a valve at the top of the tank to permit rapid ejection of the liquid (see figure). The air in the reservoir is maintained at 100 bar and 300 K. The gas space above the liquid contains initially air at 1 bar and 280 K. When the pressure in the tank reaches 5 bar, the liquid transfer valve is opened and the liquid is ejected at the rate of 0.2 m3 /min while the tank pressure is maintained at 5 bar. a) What is the air temperature when the pressure reaches 5 bar ?. b) What is the air temperature when the liquid has been drained completely?

Answer 1

Answer:

A 4-m3 storage tank containing 2 m3 of liquid is about to be pressurized with air from a large, high-pressure reservoir through a valve at the top of the tank to permit rapid ejection of the liquid. The air in the reservoir is maintained at 100 bar and 300 K.

The gas space above the liquid contains initially air at 1 bar and 280 K. When the pressure in the tank reaches 5 bar, the liquid transfer valve is opened and the liquid is ejected at the rate of 0.2 m3/min while the tank pressure is maintained at 5 bar.

What is the air temperature when the pressure reaches 5 bar and when the liquid has been drained completely?

Neglect heat interactions at the gas-liquid and gas-tank boundaries. It may be assumed that the gas above the liquid is well mixed and that air is an ideal gas with a constant Cv = 20.9 J/mol-K

Answer 2

Answer:

The air temperature when the pressure reaches 5 bar is 382K and when the liquid has been drained completely is 336K

Explanation:

Given volume of tank and liquid as $4 m^{3}$ and $2m^{3}$ respectively.

The pressure($P_{a}$) and temperature($T_{a}$ ) of air in the reservoir are 100 bar and 300 K respectively.

The pressure($P_{i}$) and temperature($T_{i}$ ) of gas above the liquid initially at 1 bar and 280 K respectively.

Final pressure in the tank,  $P_{f} =5 bar$

The liquid is ejected at the rate of 0.2 m3 /min.

a) Taking the ratio of the specific heats of air,

$\gamma=\frac{C_{p} }{C_{v} } =1.4$

Consider the simple gas system, i.e., a simple open system at constant total volume, the final temperature is given by

$T_{f} =\frac{\gamma\times T_{a} }{1+(P_{i} /P_{f})(\gamma(T_{a}/T_{i})-1 )}$

$=\frac{1.4\times 300 }{1+(1 /5)(1.4(300/280)-1 )}$

$=\frac{420 }{1.1}\approx382K$

Therefore, the air temperature when the pressure reaches 5 bar is 382K.

b) Now consider the case of pressure remains constant and volume changes, then the temperature when the liquid has been drained completely is given by

$T_{f} =\frac{ T_{a} }{1+(V_{i} /V_{f})((T_{a}/T_{f})-1 )}$

Since the liquid is completely drained, the final volume of air is volume of  tank $V_{f} =4 m^{3}$

And initially there was half liquid, so remaining half is air, therefore $V_{i} =2 m^{3}$

$T =\frac{ 300 }{1+(2/4)((300/382)-1 )}$

$=\frac{ 300 }{0.892}=336K$

Therefore, the air temperature when the liquid has been drained completely is 336K.