Question

The average thermal energy for a mono-atomic gas is (k_b is Boltzmann constant and T is absolute temperature)-

Answer 1

Thermal energy :

• Thermal energy refers to the energy present within a system that is responsible for its temperature
• Thermal energy is given by the relation

${\mathrm{\Delta E}}_{\mathrm{T}}={\mathrm{\mu }}_{\mathrm{k}}\mathrm{F}\mathrm{d}$ ,

where,

$$\begin{gathered} {\mathrm{\mu }}_{\mathrm{k}}-\mathrm{Coefficient}\mathrm{of}\mathrm{friction} \\ \mathrm{F}=\mathrm{force} \\ \mathrm{d}-\mathrm{distance} \end{gathered}$$

step 1: Formula for calculating the average thermal energy :

For the mono atomic gas the total degree of freedom = $3$( translational degree of freedom) i.e rotational, vibrational and translational

The average thermal energy for a mono-atomic gas (U) as:

=$(\mathrm{total}\mathrm{degree}\mathrm{of}\mathrm{freedom})\mathrm{x}½{\mathrm{K}}_{\mathrm{b}}\mathrm{T}$

Step 2: calculating the average thermal energy :

By putting the value of the degree of freedom we get,

$\mathrm{U}=(3/2){\mathrm{K}}_{\mathrm{b}}\mathrm{T}$

Hence The average thermal energy for a mono-atomic gas is $(3/2){\mathrm{K}}_{\mathrm{b}}\mathrm{T}$.