# (Thermo) Tank of N is heated, valve opened, find time duration

1. Apr 1, 2009

### Satchmo

1. The problem statement, all variables and given/known data
A nitrogen gas-liquid mixture is in a 20 cubic foot tank at a condition of 161 R with an initial quality of 0.1. Heating occurs at a rate of 10,000 Btu/h until the pressure reaches 100 psia. At this condition the BHE safety valve opens and maintains a constant pressure as saturated vapor is released from the top of the tank. At the final condition the last of the liquid has evaporated and th tank is just full of saturated vapor.

a) how long does it take until the valve opens?

b) how long does it take until the final state (sat. vapor) is reached? (This is the only part I cannot get)

c) how much mass leaves the tank while the valve is open?

2. Relevant equations
energy balance: Change in energy = mass*(change in specific internal energies) = Q - W

3. The attempt at a solution
No change in volume so W = 0
At the initial state, from a nitrogen v-u chart we have:
T = 161 Rankine
x = 0.1 (quality)
v = 0.14 cubic ft / lbm
P = 50 psia
u = 30 Btu/lbm
V = 20 ft^3
mass = V/v = 142.9 lbm

At state two, just before the valve is opened:
T = 177 Rankine
v = initial v = 0.14 cubic ft/lbm
P = 100 psia
u = 44 Btu/lbm
x = 0.2
mass = initial mass = 142.9 lbm

Change in internal energy is found by m(u2-u1) = 142.9(44-30) = 2000 Btu
It is heated at 10000 Btu/hour, so it takes 2000/10000 = 1/5 hours or 12 minutes to reach this point (part a is solved)

At state 3, after the valve has finished draining
P = 100 psia
T = 177 rankine
x = 1.0 (sat. vapor)
v = 1.4 cubic ft/ lbm
u = 92 Btu/lbm

Mass lost = V1/v1 - Vf/vf = 142.9 - 20/1.4 = 128.6 lbm lost (part C)

As for part B, I am pretty lost. It seems to me that more information about the valve would need to be given in order to find out how long it takes to go from state 2 to 3. Any ideas?

2. Apr 1, 2009

### Satchmo

I've figured it out. I was assuming that the heating stopped as the valve opened, but the heating continues.