# Homework Help: Value of gamma in adiabatic process

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1. Sep 30, 2015

### Pouyan

In conjunction with diving, a mixture of helium and oxygen called heliox. It will form the background to the following model invoice. Suppose that 1 mole of He and 1 mole of O2 is compressed as fast at half the volume that no heat exchange with the environment have time to take place. Temperature at the start is 298 K. What will be the final temperature?!

I know this is an adiabatic process in this case
T1 * (V1 ^(γ-1)) = T2 * (((V1/2) ^(γ-1)))
And T2 = T1 * (2 ^ (γ-1))

The attempt at a solution
I know that Helium is a mono atomic gas and value for Cp= 5/2 R and Cv= 3/2 R. That means γ = 5/3
Oxygen is a gas with two atoms and Cp= 7/2 R and Cv = 5/2 R. The value of γ = 7/5

I don't understand the value of γ when we have a mixture. I see a solution that says we have equal quantities of He and O2 when the Cp for heliox 3 R and gamma is 3/2.
Why ?! Should I take the average of the Cp of Helium and Oxygen?

2. Sep 30, 2015

### Pouyan

Can someone help me ?!

3. Sep 30, 2015

### Staff: Mentor

The heat capacity of an ideal gas mixture is equal to the molar average of the heat capacities of the individual gases. This is because the heat of mixing of ideal gases is zero.

Chet