Gas Expansion Question: Calculating Temperature Change for CO2 Release

[Keyzeroff]

1. There is gas tank, contains 5 liters of CO2 under pressure 14.7 MPa, temperatute is 300K. I try to calculate, what temperature gas will have after release (to atmospheric 0.1 MPa and 2000 liters volume). But I cannot :(
2. volume * pressure / temperature = const

The Attempt at a Solution

To simplify, let's say it releases without any other expenses and all at once (ideal container without ability to transfer or store energy, no resistence from atmospheric air, etc).

5 liters *14.7 MPa /300Kelvin = 2000 liters *0.1 MPa /t2
73.5/300 = 200 /t2
0.245=200/t2
t2=816. Whoa! It become hot instead!

Can anybody point me where I am wrong?
Thank You.

 

[kuruman]

Hi Keyzeroff and welcome to PF.

You have to assume an adiabatic expansion, i.e. that no heat leaves or enters the gas, and use the appropriate equation for such an expansion instead of the ideal gas law.

*** On edit ***
Have you stated the problem correctly? It seems that you value for the volume is too large for an adiabatic expansion.

 

[Keyzeroff]

kuruman, what equation for this case?

 

[kuruman]

pV^γ = constant where γ = C_p/C_V.

 

[Keyzeroff]

kuruman,
Maybe. In simple words - there is gas container with co2, and i want to calculate roughly temperature of releasing gas stream. I thought I can assume ideal gas equation ( no energy lost during release).

 

[kuruman]

OK, but how do you know that the final volume is 2000 liters? Is that given to you or did you guess a value? I agree with your assessment that the temperature has to drop. For that to happen the final product pV must be less than the initial product pV. In your case it is not. What I suggest that you do is
(a) Assume an adiabatic expansion as your model for the process.
(b) Calculate the final volume assuming that the final pressure is atmospheric.
(c) Use the ideal gas law to find the final temperature.

 

[RTW69]

If this is similar to a slow leak from an insulated tank we can assume an adiabatic reversible expansion as described by kuruman above where Y=k and q=0. You can look up k (or Y) for thermodynamic properties of CO2 but it should about 1.32 for larger molecules, 1.4 for diatomic gases.

T2/T1=(P2/P1)^(k-1)/k