Cvmix=(1×3R/2+1×5R/2)÷(1+1)=2Rformula cvmix=n1*cv1+n2cv2/n1+n2Cv=fR/2,fmono=3,fdiat=5

Explanation:

Specific heat at constant volume (Cv):
The specific heat at constant volume (Cv) is the amount of heat required to raise the temperature of a substance by 1 degree Celsius while keeping the volume constant. It is a measure of the internal energy of the substance.

Monoatomic Gas:
A monoatomic gas consists of individual atoms that do not form any bonds with other atoms. Examples of monoatomic gases include noble gases like helium (He) and argon (Ar). Monoatomic gases have only translational degrees of freedom, which means they can only move in three dimensions.

Diatomic Gas:
A diatomic gas consists of molecules made up of two atoms bonded together. Examples of diatomic gases include oxygen (O2) and nitrogen (N2). Diatomic gases have both translational and rotational degrees of freedom, as the molecules can move and rotate in three dimensions.

Mixing Monoatomic and Diatomic Gases:
When a monoatomic gas is mixed with a diatomic gas, the total number of moles of gas particles increases, but the individual characteristics of the gases remain the same. The specific heat of the mixture at constant volume can be calculated using the law of mixtures.

Law of Mixtures:
According to the law of mixtures, the specific heat of a mixture can be calculated by taking the weighted average of the specific heats of the individual components, based on their mole fractions.

Calculating the Specific Heat:
In this case, we are mixing 1 mole of a monoatomic gas with 1 mole of a diatomic gas. Since the mole fractions of both gases are equal, the weighted average will be equal to the arithmetic mean of the specific heats.

Cv_mixture = (Cv_monoatomic + Cv_diatomic) / 2

Specific Heats of Monoatomic and Diatomic Gases:
The specific heat at constant volume for a monoatomic gas is given by the equation Cv = (3/2)R, where R is the molar gas constant.

The specific heat at constant volume for a diatomic gas is given by the equation Cv = (5/2)R.

Calculating the Specific Heat of the Mixture:
Using the law of mixtures, we can substitute the specific heats of the monoatomic and diatomic gases into the equation for the specific heat of the mixture.

Cv_mixture = ((3/2)R + (5/2)R) / 2
= (8/2)R / 2
= 4R / 2
= 2R

Therefore, the specific heat of the mixture at constant volume will be 2R (option c).