Calculate the total thermal energy in a liter of helium at room temperature and atmospheric pressure. Then repeat the calculation for a liter of air.
Solution to 23P
In this question, we are asked to find the thermal energy of a litre of Helium(He) and air at room temperature and atmospheric pressure.
To find the thermal energy we will use the Equipartition theorem which states that,
At temperature T, the average energy of any quadratic degree of freedom is given by
For a system with N particles and with degree of freedom f, with no other forms of energy (Non-quadratic) dependent on temperature then the thermal energy is given by,
N=Number of molecules
f=Degrees of freedom
We need to find the thermal energy of the litre of Helium at room temperature:
Number of molecules of Helium:N
We know from ideal gas equation that,
Thus the equipartition theorem equation becomes,
Degrees of freedom for monatomic gas=3
Volume of gas=1 litre=
Thus thermal energy of the litre of Helium is 1.5x102J