Question

What is the degree of freedom for monoatomic gas?

Answer 1

Step 1: Degree of freedom:

• It refers to the number of independent ways in which a gas molecule can move, vibrate or rotate in space. It is represented by “$\mathrm{f}$”.

Step 2: Formula for the degree of freedom:

• Formula for finding the degree of freedom is : $\mathrm{f}=3\mathrm{N}-\mathrm{K}$
• Here, $\mathrm{f}$ is degree of freedom, N is the number of particles in the system and K is the independent relation among the particles.

Step 3: Monoatomic gas :

• A monoatomic gas is composed of a single atom.
• Example: Helium gas, Neon gas, etc.
• For monoatomic gas, the value of N is $1$ as it is composed of only one atom, and the independent relationship among the particles, K is $0$ (again because it is composed of only one atom).

Step 4: Calculation for the degree of freedom of monoatomic gas:

Using formula, $\mathrm{f}=3\mathrm{N}-\mathrm{K}$

$$\begin{gathered} \mathrm{f}=3\times 1-0 \\ \mathrm{f}=3-0 \\ \mathrm{f}=3 \end{gathered}$$

Hence, the degree of freedom for monoatomic gas is $3$.