# Total translational kinetic energy

[SOLVED] Total translational kinetic energy

1.A 0.03m3 vessel contains helium (monatomic) gas at 0.0C and 1.00 atm. The total translational kinetic energy of the gas molecules is (in KJ).

2. 3/2KbT

3. pV=nRT

where p is the pressure, V is the volume, n is the number of molecules present, R is the gas constant (8.31J/(mol*K)), and T is the temperature in Kelvins (273K = 0ºC)
The other equation is that the average translational kinetic energy K of a single molecule is

K = (3RT)/(2N)

where R and T are from the first equation and N is Avogadro's number (6.022E23).
Just sub in numbers:
K = (3 * 8.31 * 273) / ( 2 * 6.022E23) = 5.651E-21 Joules. This is the kinetic energy of one atom of helium at 0º C. Change the first equation around to get n = (pV) / (RT) and then multiply 5.65E-21 by n

The answer in the book shows its suppose to be 4.5kJ, but I'm yet to get that, I'm getting a way off number. Thanks for any help given :+)

hage567
Homework Helper
2. 3/2KbT

This doesn't look right. It should be $$K = \frac{3Nk_BT}{2}$$ where N is the number of molecules in the vessel.

K = (3RT)/(2N)

Again, you are missing the N in the numerator. This equation is just the one above with a substitution for k_B.

If you have the N in the numerator, you will have a ratio of $$\frac{N}{N_A}$$ which is the number of moles of gas, n.

So just start over with the right equation and you should come out to the right answer.

Awesome, Thanks for showing me where I made my mistake :+)