Ratio of Specific Heats and Degree of Freedom:
To determine the degree of freedom for a gas with a given ratio of specific heats (γ), we need to consider the thermodynamic properties of the gas.

Ratio of Specific Heats:
The ratio of specific heats (γ) is defined as the ratio of the specific heat at constant pressure (Cp) to the specific heat at constant volume (Cv). Mathematically, it is represented as:
γ = Cp/Cv

Degree of Freedom:
In thermodynamics, the degree of freedom (f) is the number of independent parameters that specify the state of a system. For a gas, the degree of freedom is related to its ability to store and transfer energy in different ways.

Relation between Ratio of Specific Heats and Degree of Freedom:
For a monatomic gas, the degree of freedom (f) is given by:
f = 3
For a diatomic gas, the degree of freedom (f) is given by:
f = 5
The relation between the ratio of specific heats (γ) and the degree of freedom (f) for a gas is:
f = 2 + 2/(γ - 1)

Calculating Degree of Freedom:
To determine the degree of freedom for a gas with a given ratio of specific heats (γ), we can use the formula:
f = 2 + 2/(γ - 1)

Example:
If the ratio of specific heats (γ) for a gas is 1.4, then the degree of freedom (f) would be:
f = 2 + 2/(1.4 - 1)
f = 2 + 2/0.4
f = 7
Therefore, for a gas with a ratio of specific heats of 1.4, the degree of freedom would be 7.