Ratio of Specific Heats for Diatomic and Monoatomic Gases

When two moles of a diatomic gas and one mole of a monoatomic gas are mixed, we need to find the ratio of their specific heats. Let's denote the diatomic gas as "A2" and the monoatomic gas as "B".

Specific Heat Ratio for Diatomic Gas (A2)
The specific heat ratio, γ, is defined as the ratio of the molar specific heat at constant pressure (Cp) to the molar specific heat at constant volume (Cv).

For a diatomic gas, the ratio of specific heats, γ, is given by the formula:
γ = Cp / Cv

For diatomic gases, at room temperature and normal pressure, the specific heat ratio is approximately 7/5 or 1.4.

Specific Heat Ratio for Monoatomic Gas (B)
For a monoatomic gas, the ratio of specific heats, γ, is given by the formula:
γ = Cp / Cv

For monoatomic gases, at room temperature and normal pressure, the specific heat ratio is approximately 5/3 or 1.67.

Ratio of Specific Heats for the Mixture
To find the ratio of specific heats for the mixture of two moles of diatomic gas (A2) and one mole of monoatomic gas (B), we need to consider the contribution of each gas to the overall ratio.

Let's assume the specific heat ratio of the mixture is γ_mix.

The contribution of the diatomic gas (A2) to the overall ratio can be calculated as follows:
Contribution of A2 = (moles of A2 * γ_A2) / (total moles)

Similarly, the contribution of the monoatomic gas (B) to the overall ratio can be calculated as follows:
Contribution of B = (moles of B * γ_B) / (total moles)

Since we have 2 moles of A2 and 1 mole of B, the total moles is 3.

Therefore, the contribution of A2 to the overall ratio is:
Contribution of A2 = (2 * 1.4) / 3 = 2.8 / 3

And the contribution of B to the overall ratio is:
Contribution of B = (1 * 1.67) / 3 = 1.67 / 3

Now, we can calculate the overall ratio of specific heats for the mixture:
γ_mix = (Contribution of A2 + Contribution of B) = (2.8 / 3) + (1.67 / 3) = 4.47 / 3

Simplifying the expression, we get:
γ_mix = 4.47 / 3 = 1.49

Therefore, the ratio of specific heats for the mixture of two moles of diatomic gas and one mole of monoatomic gas is approximately 1.49, which can be expressed as 19/13.

Hence, the correct answer is option 'C': 19/13.