Question

To find out degree of freedom, the correct expression is:
A.\[f = \dfrac{2}{{\gamma - 1}}\]
B.\[f = \dfrac{{\gamma + 1}}{2}\]
C.\[f = \dfrac{2}{{\gamma + 1}}\]
D.\[f = \dfrac{1}{{\gamma + 1}}\]

Answer 1

Hint: Degrees of freedom is the mathematical expression which is used to calculate how many different values can be obtained using that expression. Degrees of freedom depend on the number of parameters to be measured and the value of observations made, the alignment of the molecules.

Complete step by step solution:
In the case of gas, degree of freedom is defined as the number of different values with which the molecules of a gas can move independently in different possible ways. Degrees of freedom are related to the ratio of specific heat. The relation between them is given by the formula,
\[\gamma = 1 + \dfrac{2}{f}\]
\[f = \dfrac{2}{{\gamma - 1}}\]
Where ‘f’ is the degree of freedom and \[\gamma \] is the ratio of specific heats.
Therefore, in order to find out the degrees of freedom for a g as, the correct expression is \[f = \dfrac{2}{{\gamma - 1}}\].

Hence, Option A is the correct answer.

Note: The degree of freedom is of three types namely translational, rotational and vibrational degrees of freedom. In translational degrees of freedom, the molecules of a gas can move independently and freely in the x, y and z plane of the Cartesian coordinate system. In the case of rotational degree of freedom, the molecules of a gas can rotate freely in a number of different ways. In a vibrational degree of freedom, the inter particle distance between the molecules changes because the particles start vibrating. But the vibrational degree of freedom is only possible if the temperature is very high since they need very high energy to vibrate. The degrees of freedom can be there for monoatomic, diatomic as well as polyatomic gases.