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## Homework Statement

Part a: A monoatomic ideal gas is confined to move in two dimensions. What is C

_{v}for this gas?

Part b: Consider a system composed of N independent harmonic oscillators in two dimensions. What is C

_{v}for the system?

## Homework Equations

C

_{v}= ∂U/∂T

U = (number of degrees of freedom)(1/2 N

_{A}k

_{B}T = (number of degrees of freedom)(1/2)RT

## The Attempt at a Solution

I'm not very confident about this:

Part a: Since the gas is monatomic, it only has translational degrees of freedom, and it is given that these are restricted to two.

(2)(1/2)RT = RT and C

_{v}= R

Part b: Since it's a harmonic oscillator, there's a degree of freedom for U and K for each dimension, so 4 degrees of freedom, and C

_{v}= 2R? I'm not sure what to do with the N though, since it's an average, it shouldn't affect the C

_{v}? Or am I misunderstanding?