## Average Kinetic Energy vs U?

$\Delta U=q+w$

Manya Bali 4E
Posts: 66
Joined: Fri Sep 28, 2018 12:23 am

### Average Kinetic Energy vs U?

How are average kinetic energy and U (internal energy) related? I know we have the equation U = nRT(3/2) for an ideal gas, and then in 8.103 (6th edition), the question asks for average kinetic energy. The solution manual gives the equation, average kinetic energy = RT(3/2) so I'm a little confused about their relationship.

Michael Torres 4I
Posts: 92
Joined: Thu May 10, 2018 3:00 am
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### Re: Average Kinetic Energy vs U?

Internal energy is composed of kinetic and potential energy. Specifically, the translational and rotational energy components of internal energy are fully composed of kinetic energy, while the vibrational component is composed of both kinetic and potential energy.

U(m) = 3/2nRT because the internal energy in this case is being measured in terms of moles. Because Kr(g) is a single atom, it only possesses translational energy in three dimensions (x, y, z). This energy is represented as 1/2kT per dimension. Therefore, as a particle, its translational kinetic energy in 3/2kT (k is the boltzmann constant). Now, when k is multiplied by Avogadro's number, you get R, the gas constant value. Because only one mole is considered, n=1.