Thermodynamics- Charging an air tank

[MacLaddy]

Homework Statement

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.

Homework Equations

$$m_ih_i = m_2u_2 - m_1u_1$$

From my property tables booklet.

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

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

 

[MacLaddy]

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

 

[Chestermiller]

Homework Statement

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.

Homework Equations

$$m_ih_i = m_2u_2 - m_1u_1$$

From my property tables booklet.

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

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

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

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