Anharmonic Oscillator Heat Capacity

[nyvane]

Homework Statement

Consider the anharmonic potential U(x)=cx²-gx³-fx⁴ and show that the approximate heat capacity of the classical unharmonic oscillator in one dimension is

C=k_b[1+(3f/2c²+15g²/8c³)kbT]

Homework Equations

U(x)=cx²-gx³-fx⁴
and heat capacity is C=dU/dT

The Attempt at a Solution

I have used Boltzmann distrşbution of x as 3g/4c²*kbT and took derivative of U according to T but I could not find the given heat capacity.

 

[G01]

Homework Statement

Consider the anharmonic potential U(x)=cx²-gx³-fx⁴ and show that the approximate heat capacity of the classical unharmonic oscillator in one dimension is

C=k_b[1+(3f/2c²+15g²/8c³)kbT]

Homework Equations

U(x)=cx²-gx³-fx⁴
and heat capacity is C=dU/dT

The Attempt at a Solution

I have used Boltzmann distrşbution of x as 3g/4c²*kbT and took derivative of U according to T but I could not find the given heat capacity.

OK. But, I can't help you find your mistake if you don't show your calculations.

 

[VanOosten]

where did the 3g/4c2*kbT come from?