Question

what is degree of freedom and value for mono atomic ,diatomic and linear gas

Answer 1

The total number of independent modes(ways) in which a system can possess energy is called Degree of freedom.

Monoatomic GAS The Molecules pf monoatomic gas can move in any direction in space so it can have three independent motions and hence 3 degree of freedom (all translational).

Diatomic GAS A molecule of diatomic gas has five degrees of freedom (3 tanslational and 2 rotational).

Triatomic GAS (non-linear) A molecule of non linear gas can rotate about any of three co-ordinate axes.Hence it has six degrees of freedom (3 translational and 3 rotational).

Answer 2

Degree of freedom is the number of independent ways in which a molecule of gas can move is known as the degree of freedom. The value for mono atomic, diatomic and linear gas is 3, 5 and 5 respectively.

Explanation:

• A gas molecule can move in different directions.
• There can be a number of different ways in which a gas molecule can move, vibrate or rotate in space.
• The number of these independent ways in which the gas molecule can move is the degree of freedom.
• The degree of freedom for a system can be calculated by the formula:

        $f=3N-K$

       where, $N=$ the number of particles in the system

       and $K=$ independent relation between the particles

• For a monoatomic gas, the degrees of freedom is

        $\[f = 3 \times 1 - 0 = 3\]$

• For a diatomic gas, the degrees of freedom is

        $\[f = 3 \times 2 - 1 = 5\]$

• For a linear gas, the degree of freedom is 5, i.e., three translational and two rotational degrees of freedom.

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