Introduction:
The ratio of specific heats (Cp/Cv) of a gas is a measure of the gas's ability to store and transfer heat. It is defined as the ratio of the heat capacity at constant pressure (Cp) to the heat capacity at constant volume (Cv). In this question, we are given two monoatomic gases, A and B, with equal volumes at the same temperature and pressure. We need to find the ratio of specific heats of the mixture when these gases are mixed.

Explanation:
When two gases are mixed, the total volume of the mixture is the sum of the individual volumes of the gases. Since the volumes of gases A and B are equal, the total volume of the mixture will be twice the volume of each gas.

Step 1: Finding the ratio of specific heats for individual gases:
The ratio of specific heats for a monoatomic gas is given by the formula:
γ = Cp/Cv = 1 + 2/f

Here, f is the degree of freedom of the gas, which is equal to 3 for a monoatomic gas.

For gas A:
γA = 1 + 2/3 = 5/3

For gas B:
γB = 1 + 2/3 = 5/3

Step 2: Finding the ratio of specific heats for the mixture:
When the gases are mixed, the total volume is twice the volume of each gas. Since the temperature and pressure are the same, the total energy of the mixture will be the sum of the energies of the individual gases.

The total energy of the mixture is given by:
E = nA * CvA * TA + nB * CvB * TB

Since the volumes of gases A and B are equal, the number of moles of each gas can be represented as:
nA = nB = n

Thus, the total energy of the mixture becomes:
E = n * (CvA * TA + CvB * TB)

To find the ratio of specific heats for the mixture, we need to find the heat capacities at constant volume and constant pressure for the mixture.

Step 3: Understanding the relationship between Cp and Cv:
For an ideal gas, the relationship between Cp and Cv is given by the equation:
Cp - Cv = R

Where R is the specific gas constant.

Step 4: Finding the ratio of specific heats for the mixture:
Since the gases A and B are monoatomic, their specific gas constants are the same.

The heat capacities at constant volume for the mixture (CvM) can be given as:
CvM = (nA * CvA + nB * CvB) / (nA + nB)
CvM = (n * CvA + n * CvB) / (2n)
CvM = (CvA + CvB) / 2

The heat capacities at constant pressure for the mixture (CpM) can be given as:
CpM = CvM + R
CpM = (CvA + CvB) / 2 + R

The ratio of specific heats for the mixture can be given as:
γM = CpM / CvM
γM = [(CvA + CvB) / 2 + R] / [(C