Part a: A monoatomic ideal gas is confined to move in two dimensions. What is Cv for this gas?
Part b: Consider a system composed of N independent harmonic oscillators in two dimensions. What is Cv for the system?
Cv = ∂U/∂T
U = (number of degrees of freedom)(1/2 NAkBT = (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 Cv = 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 Cv = 2R? I'm not sure what to do with the N though, since it's an average, it shouldn't affect the Cv? Or am I misunderstanding?