A vessel contains 1 mole of O2 and 1 mole of He. The value of for the mixture is

To find the value of γ for the mixture of O2 and He, we need to calculate the effective degrees of freedom (f_eff) for the mixture.

The formula to calculate f_eff is given by:

f_eff = Σ(xi * fi)

Where xi is the mole fraction of each component and fi is the degrees of freedom for each component.

In this case, we have 1 mole of O2 and 1 mole of He, so the mole fractions are equal for both components, i.e., xi = 0.5 for O2 and He.

Now, we need to determine the degrees of freedom for each component. For a diatomic gas like O2, the degrees of freedom (fi) is equal to 5. This is because a diatomic gas has 3 translational degrees of freedom, 2 rotational degrees of freedom, and no vibrational degrees of freedom at room temperature.

For a monatomic gas like He, the degrees of freedom (fi) is equal to 3. This is because a monatomic gas only has 3 translational degrees of freedom.

Now, we can calculate the effective degrees of freedom (f_eff) for the mixture:

f_eff = (0.5 * 5) + (0.5 * 3) = 2.5 + 1.5 = 4

Finally, the value of γ for the mixture is given by the formula:

γ = (f_eff + 2) / f_eff

Substituting the value of f_eff into the formula:

γ = (4 + 2) / 4 = 6 / 4 = 1.5

Therefore, the value of γ for the mixture of O2 and He is 1.5.