Value of gamma in adiabatic process

In summary: He mentions that the mixture, called heliox, has a molar average of 3 R. He is unsure of the value of γ for this mixture and wonders if he should take the average of the individual gases' heat capacities. The answer is that yes, the molar average of the heat capacities should be taken, as the heat of mixing for ideal gases is zero. In summary, Chetan is seeking clarification on the specific heat capacity of a mixture of helium and oxygen, and it is determined that the molar average of the heat capacities of the individual gases should be used.
  • #1
Pouyan
103
8
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?
 
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  • #2
Can someone help me ?!
 
  • #3
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
 

FAQ: Value of gamma in adiabatic process

1. What is the value of gamma in an adiabatic process?

The value of gamma, also known as the adiabatic index or heat capacity ratio, in an adiabatic process is a ratio that represents the relationship between the specific heats at constant pressure and constant volume. It is typically denoted by the symbol γ and has a value of approximately 1.4 for diatomic gases.

2. How is gamma related to the adiabatic process?

Gamma is directly related to the adiabatic process because it is a measure of how the specific heat changes as the temperature changes in an adiabatic process. It is a key factor in determining the change in temperature and pressure during an adiabatic expansion or compression.

3. What is the significance of the value of gamma in an adiabatic process?

The value of gamma is significant in an adiabatic process because it affects the efficiency and behavior of the process. A higher value of gamma indicates a greater change in temperature and pressure for a given change in volume, resulting in a more efficient process. It also determines the speed of sound in a medium and has other implications in fluid dynamics and thermodynamics.

4. Can the value of gamma vary in an adiabatic process?

Yes, the value of gamma can vary in an adiabatic process depending on the gas or medium being used. For example, monoatomic gases have a lower value of gamma (1.4) compared to diatomic gases (1.6), which affects the behavior of the adiabatic process. In addition, the value of gamma may also change at high temperatures or pressures due to changes in molecular interactions.

5. How is the value of gamma calculated in an adiabatic process?

The value of gamma can be calculated by taking the ratio of the specific heats at constant pressure and constant volume for a given gas or medium. It can also be determined experimentally by measuring the change in temperature and pressure during an adiabatic process and using the ideal gas law. Additionally, there are empirical equations and tables that can be used to estimate the value of gamma for different gases at various conditions.

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