1. The problem statement, all variables and given/known data 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? 2. Relevant equations Cv = ∂U/∂T U = (number of degrees of freedom)(1/2 NAkBT = (number of degrees of freedom)(1/2)RT 3. 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?