# Thermal Properties - Energy and velocity of molecules

Thermal Properties -- Energy and velocity of molecules

Hello all,

## Homework Statement

(a) Calculate the total rotational kinetic energy of the molecules in 1.00 mol of a diatomic gas at 300K.

(b) Calculate the moment of inertia of an oxygen molecule. Treat the molecule as two massive points (representing the oxygen atoms) separated by a distance of 1.21 x 10^-10 m. The molar mass of oxygen atoms is 16g/mol.

(c) Find the rms angular velocity of rotation of an oxygen molecule. How does your answer compare to the angular velocity of a typical piece of rapidly rotating machinery (10,000 rev/min)?

## Homework Equations

KE = 1/2Iω^=3/2kt
v(rms)=√(3kt/m)
Moment of inertia for this particle case...?

## The Attempt at a Solution

I'm honestly not at all sure how to go about this. My initial thought is to use KE=1/2Iω^2 for the first portion, but I do not see how to consider temperature given that equation alone. For part B, I'm not sure which moment of inertia equation is correct for the two points rotating about an axis...I'm thinking 1/12mL^2, but I'm really not sure.

Any help or direction at all would be greatly appreciated. Thank you!