Question

Consider a cylindrical gas cylinder that is initially filled with N2 gas at a pressure of 5atm. The tank height is 1.0m, and its internal diamter is 18cm. At t=0, a valve is opened and the gas is pumped out at a constant mass flow rate of 4.5g/min. Select and state an appropriate control value, and then derive an expression for the pressure in the tank as a function of time remains at constant temperature (25C). How long will it take for the pressure in the tank to reduce to 1.5 atm?

Answer 1

Height of tank = 1.0 m = 100 cm

Internal diameter of tank = 18 cm

Volume of tank = r²h

= (9)²100

= 25446.9 cm³

= 25.45 L

Mass flow rate of gas = 4.5g/min

Molar mass of N2 = 28 g/mol

Molar flow rate of N2 = 4.5/28 = 0.16 moles/min

- (dn/dt) = 0.16 moles/min

Using PV = nRT

Differentiating both sides w.r. to t:

(dP/dt) * V = - (dn/dt)*RT

(dP/dt) * 25.45 = - 0.16*0.0821*298

(dP/dt) = - 0.154

dP = - 0.154* dt

Integrating both sides:

dP = - 0.154* dt

P = - 0.154*t + c

At t = 0 pressure in tank = 5 atm

Putting these initial cndition in equation:

5 = - 0.154*0 + c

c = 5

So,

P = - 0.154*t + 5

When P = 1.5 atm:

1.5 = - 0.154*t + 5

3.5 = 0.154*t

t = 22.72 min