Q. 1.18 - An Introduction to Thermal Physics

Question

Calculate the rms speed of a nitrogen molecule at room temperature.

Step-by-Step Solution

Answer

Root mean square speed is 515.9m/s.

Step1: Given information

Gas is Nitrogen.

Temp = room temp = 25^oC= 298 K

Step2: Explanation

The root mean square velocity is calculated as 

$v=\sqrt{\frac{3kT}{m}}............................\left(1\right)$

where 

T  = temperature 

k = Boltzmann constant

m = mass

Mass of Nitrogen is calculated as 

$$\begin{gathered} m=28\mathrm{u} \\ =28\times 1.6\times {10}^{-27} \mathrm{kg} \\ =4.65\times {10}^{-26} \mathrm{kg} \end{gathered}$$

Boltzmann constant is $=1.38\times {10}^{-23}{ \mathrm{m}}^2{\mathrm{kgs}}^{-2}{ \mathrm{K}}^{-1}$

Substitute the values in equation (1), we get 

$$\begin{gathered} v=\sqrt{\frac{3\times (1.38\times {10}^{-23} m^{2}kg{s}^{-2} K^{-1})\times (298 K)}{4.65\times {10}^{-26} kg}} \\ v=515.9{ \mathrm{ms}}^{-1} \end{gathered}$$

Root mean square speed is 515.9m/s.