Question

What is the degree of freedom of mono-atomic gas?

Answer 1

Hint: In order to solve the above that is to find the degree of freedom of mono-atomic gases we will first discuss what is degree of freedom then what is mono-atomic gases and then find how degree of freedom is calculated for different gases in the system.

Complete step-by-step solution:
To find the degree of freedom of mono-atomic gases let us first discuss what degree of freedom is and how it is calculated thereafter we will discuss what is mono-atomic gases
Degree of freedom of any gas is defined as the total number of independent modes (ways) in which a system can possess energy.
So, to calculate the degree of a system we use the following formula
\[f=3N-k\]
Where, f is the degree of freedom
N is the number of particles in the system
And, K is the independent relationship among the system
Now, let us discuss what mono-atomic gas is.
A monatomic gas is defined as the one where the atoms of the gas that do not chemically combine to form molecules of more than one atom. Normally, the only atoms which act this way are the inert gases which are present at the rightmost column of the periodic table. These are Helium, argon, neon etc. Their outer electron shells are naturally entirely filled, so they have no openings to form covalent bonds, and the atoms are electrically neutral so they will not form ionic bonds.
So, here in mono-atomic gases the number of particles in the system is 1 and the independent relationship among the particles is 0.
So, according the formula of degree of freedom
\[f=3N-k\]
for monatomic molecules \[N=1\]and\[k=0\].
\[\begin{align}
  & =3\times 1-0 \\
 & =3 \\
\end{align}\]
So, here according to the above solution we can say that the degree of freedom of the monatomic gases is 3.

Note: In the above question we got to know that the degree of freedom of monatomic gases is 3. The same way we found the degree of freedom of monoatomic gases we can also find the degree of freedom of diatomic is 5 and for high temperature its degree of freedom is 7 and degree of freedom for triatomic gases is 6.