Question

What is the value of gamma for polyatomic gas?

Answer 1

Hint: We have to remember that degrees of freedom in mechanics describes the number of independent motions that are allowed to a body, or, in case of a mechanism made of several bodies, the number of possible independent relative motions between the pieces of the mechanism.

Complete answer:
The ratio of the specific heats $\gamma ={\displaystyle \frac{C_P}{C_V}}$ is a factor in adiabatic engine processes and in determining the speed of sound in a gas. This ratio $\gamma =1.66$ for an ideal monatomic gas and $\gamma =1.4$ for air, which is predominantly a diatomic gas.
The most common polyatomic gasses are those of several elements. In the form X2 we have hydrogen, nitrogen, oxygen, fluorine, chlorine, and bromine. At temperatures well above standard, phosphorus, sulfur, and iodine form diatomic gasses, as do also vaporized lithium, sodium, and the rest of Group I elements. In hetero element gasses there are polar types such as ammonia, water vapor, hydrogen fluoride, hydrogen chloride, carbon monoxide, nitrogen oxide ( $NO$—also a stable free radical molecule, odd number electrons), sulfur dioxide, nitrogen dioxide, hydrogen cyanide, phosgene, formaldehyde, chloramine (the deadly gas that forms if you mix bleach with household ammonia), etc. These molecules are polar because they’re bent at angles because of filled molecular orbitals or have different elements at each end of the molecule.
A polyatomic gas has 3 translations. Hence, the degree of freedom for polyatomic gas is $⩾6$.
$\gamma$ for polyatomic gases is $\gamma >1$

Note:
We need to know that the molecular degrees of freedom refer to the number of ways a molecule in the gas phase may move, rotate, or vibrate in space. Degree of freedom is defined as the number of coordinates required to specify the position of all the atoms in a molecule.