How Is the Internal Energy of Helium Calculated in an Ideal Gas Scenario?

[jdog6]

A tank of volume 0.413 m3 contains 2.79 mol
of helium gas at 5C. Assume that the helium
behaves like as an ideal gas.
The universal gas constant is
8.31451 J/Kmol, and Boltzmann's constant
is 1.38066 x10^-23 J/K.
Find the total thermal energy of the system.
Answer in units of J.
Would the right equation be Eint = 3/2NKbT =3/2nRT ?

 

[Chi Meson]

Both are the same. The first (with "Boltzman" constant) is for use when observing idividual atoms or molecules. N=number of molecules.

The second is for use when observing large quantities. n = number of moles. The only difference between R and k is Avogadro's number (k = R/N)

So, what are you given. number of molecules, or number of moles?

Oh yeah, what's the temperature? Are you ABSOLUTELY sure?

 

[quicknote]

Yes, the correct equation to use in this scenario would be Eint = 3/2NKbT =3/2nRT, where Eint is the internal energy, N is the number of moles of helium, Kb is Boltzmann's constant, T is the temperature in Kelvin, and R is the universal gas constant. Plugging in the given values, we get:

Eint = (3/2)(2.79 mol)(8.31451 J/Kmol)(278.15 K) = 10,372.77 J

Therefore, the total thermal energy of the system is 10,372.77 J.