I'm trying to tutor my cousin but don't am having trouble recalling physics...?

His homework problem reads:


5.50 L vessel contains nitrogen gas at 31.0°C and a pressure of 2.60 atm.


And he is asked to find total translational kinetic energy (of the gas molecules) and the average kinetic energy per molecule





Does anyone know how to do this? Thanks

I'm trying to tutor my cousin but don't am having trouble recalling physics...?
For an ideal gas, the equipartition of energy tells us that the average internal energy per particle, E, is given by the relation,





E = n/2 *k*T,





where k is the Boltzmann constant, T is the temperature in Kelvin, and n is the number of degrees of freedom. Nitrogen is a diatomic molecule, so it has 3 degrees of freedom in which it can translate, and 2 degrees of freedom in which it can rotate, and 2 degrees of freedom in which it can vibrate. The total internal energy per molecule is then





E = 7/2 k*T,





but the question is only interested in the kinetic (translational) energy. So,





KE_avg = 3/2 k*T





To find the total kinetic energy multiply the average energy per particle by the total number of particles. Use the ideal gas relation,





P*V = n*k*T





to find the total number of particles. Remember, pressure is usually in N/m^2, and volume is usually in m^3. And always use absolute temperature. And above all, pay attention to the units of 'k'.