A piston pump containing 2 liters of nitrogen gas at 3000 psia (absolute) pressure empties its entire contents into a 10 liter pressure container. Before the transfer of gas the 10 liter container already contained nitrogen gas at 100 psia (absolute) pressure. Assuming nitrogen behaves as an ideal gas, and assuming the temperature is the same throughout what is the final pressure in the container?
PV=nRT
V, R and T constant for 10 liter container
P2 /N2 = P1 /N1
now work on how many molecules
10 liters 100 psi:
n = pV/RT = 100*10/RT = 1000/RT = N1
2 liters at 3000 psi
n = 3000*2/RT = 6000/RT
so total n at the end in the 10 liters is = 7000/RT = N2
Now do P2/N2 =P1/N1 for the 100 liters
P2/7000 = 100/1000
P2 = 700 psi
To find the final pressure in the container, we can use the ideal gas law, which states:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles of gas
R = ideal gas constant
T = temperature
Given that the temperature is the same throughout and the nitrogen gas behaves as an ideal gas, we can use the equation:
P1V1 = P2V2
where:
P1 = initial pressure of the piston pump
V1 = initial volume of the piston pump
P2 = final pressure in the container
V2 = final volume in the container
Initial conditions:
P1 = 3000 psia (absolute)
V1 = 2 liters
Final conditions:
P2 = ? (to be determined)
V2 = 10 liters
We also need to convert the pressures from absolute to gauge pressure by subtracting the atmospheric pressure (which we assume is 0 psia).
Using the equation:
(P1 - 0) * V1 = (P2 - 0) * V2
(3000 psia - 0) * 2 liters = (P2 - 0) * 10 liters
6000 = 10P2
Dividing both sides of the equation by 10:
6000 / 10 = P2
P2 = 600 psia
Therefore, the final pressure in the container is 600 psia (gauge pressure).