# Dire need of help on this gas flowing into a vessel problem

1. Nov 21, 2011

### gharrington44

1. The problem statement, all variables and given/known data

An evacuated rigid vessel is filled adiabatically through a valve from a large constant pressure source of a certain gas, until the pressures inside and outside are equal. If the P-U-V relation for the gas is given by the equation:
U = 831 + 2PV where U is joules, P is pascals, and V is m^3
Find the ratio of the initial and final volumes of the gas which enters.
(Hint: This is an application of the non-steady flow energy equation)

2. Relevant equations
So we need to use the Non-steady flow energy equation. Does that mean I use the equation
dE/dt = Q - W + (dm/dt)*(h2-h1) + .5*(dm/dt)*(V1^2 - V2^2)
In this case, kinetic and potential energy contributions would be negligible and I'm guessing the equation reduces to:
ΔU = Q - W + (dm/dt)*(h2 - h1)

3. The attempt at a solution
Also since the process is adiabatic, then Q = 0 and W = 0 for the process so the above equation simplifies to:
dU/dt = (dm/dt)*(h2-h1)
I also think that the internal energy of the system is 831 since the initial pressure and volume are both 0. In other words, U(0,0) = 831, but I don't know how to figure out the rest of the problem. Please let me know if I'm doing this right or not.