# Thermodynamics- Charging an air tank

1. Nov 3, 2013

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

A scuba diver's 2ft3 air tank is to be filled with air from a compressed air line at 120 psia and 100F. Initially, the air in this tank is at 20 psia and 70F. Presuming that the tank is well insulated, determine the temperature and mass in the tank when it is filled to 120 psia.

2. Relevant equations

$$m_ih_i = m_2u_2 - m_1u_1$$

From my property tables booklet.

$$h_1 = 133.86 Btu/lbm$$
$$u_1 = 90.33 Btu/lbm$$

3. The attempt at a solution

Not entirely sure where to take this. If I do just a mass balance I'll get $m_i = m_2-m_1$, but I'm not sure how this will help me.

If I could do an energy balance like this $h_i=u_2-u_1$, then it would be fairly simple to solve for the internal energy at the second state, and find the temperature. However, I don't think that's a legal move.

I've played with specific volumes, tried to find flow rates, and played with the Ideal Gas Law.

Any help is appreciated,

Thanks,
Mac

2. Nov 4, 2013

Thank you Mod's for moving this to the appropriate forum. I wasn't sure exactly what category Thermodynamics fell into.

3. Nov 5, 2013

### Staff: Mentor

How much mass m1 is in the tank to start with? Let mi represent the mass of air injected into the tank. How many moles are in the tank at the beginning and, in terms of mi, how many moles are in the tank at the end? Call T the final temperature. Use the ideal gas law to calculate the value of T in terms of mi. Now you only have 1 unknown. u2 is a function of T, which in turn is a function of mi. So use your equation $m_ih_i = m_2u_2 - m_1u_1$ and your table to solve for mi.

Incidentally, considering the magnitude of the pressure, maybe you're not comfortable using the ideal gas law. If your table has specific volume as a function of temperature and pressure, you can use that instead.

Chet

Last edited: Nov 5, 2013