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## Homework Statement

Ideal gas. In an ideal-gas model. N molecules move almost indepdently with very weak interactions between, in a three-dimensional box of volume V. Find the heat capacity of the system.

SHO. Consider N independent SHOs in a system. each osciallating about a fixed point. The spring constant is assumed to be k and the mass of oscillator m. FInd the heat capacity.

## Homework Equations

I understand heat capacity can be described as change of energy (E) over time (T) so:

Cv (heat capacity) = (dE/dT * dS/dE)*T

= dS/dT*T

## The Attempt at a Solution

I have S, but I am having trouble with taking the derivative of dS/dT. do i bring the T over so i can take dS/dT?

The S that I have is:

S = N*Kb*ln((V/h^3)*(((4*pi*m*E)/(3N)))*^(3/2)+3/2N

having trouble going from here since if it is S/T, my heat capacity would just be -S/T^2??

Thanks in advance for the help