How do you work out the total translational kinetic energy of N2 gas?

What is the total translational kinetic energy in a test chamber filled with nitrogen (N_2) at 2.23×10^5 Pa and 20.7°C?

The dimensions of the chamber are 1.00 m × 6.00 m × 6.50 m.

The atomic weight of nitrogen is 28.0 g/mol, Avogadro's number is 6.022 × 10^23 molecules/mol and the Boltzmann constant is 1.38 × 10^-23 J/K.

1 Answer
Mar 11, 2018

75 J

Explanation:

Volume of the chamber(V)=39 m^3
Pressure=(2.23*10^5)/(1.01*10^5)=2.207 atm

Temp=293.7 K

BY Equation of state;

n=p*v/(RT)=3.5696 moles

total molecules=3.5696*6.022*10^23=21.496*10^23

now energy for Each diatomic molecule

=(DOF)*1/2*k*t

For a diatomic gas degree of freedom =5

Therefore energy= (no of molecule) *(energy of each molecule)

Energy=5*21.496*10^23*0.5* 1.38 *10^-23
=74.168 J