# Homework Help: In terms of Einstein's theory of heat capacity

1. Oct 26, 2004

### stunner5000pt

A) What temperature will the energy per mole of a solid achieve one third its classical value of 3RT. Express in terms of einstein temperature
Einstein Temperature $$T_{e} = \frac {h \nu}{k}$$

where h is plancks constant
k = boltzmann's constant

Not really sure on how to do this?

Do i use this formula

$$C_{v} = \frac{3 N_{a} h^2 \nu^2}{k T^2} \frac{e^\frac{h\nu}{kT}}{(e^\frac{h\nu}{kT} - 1)^2}$$

i know that the term hv / kT must be the exponent of e but i cant get it to work. but that is beside the point
but how do i manipulate it to get what i need?

Now onto the Blackbody radiation topic
IIfyou have the wavelength and the temperature then which function would you use for finding the Total Radiancy?

R = Sigma T^4 or the big formula 2pi h c^2 / lambda ^5 ( 1 / e^ hc / lambda k T)

Which is the the Total radiancy function?

Last edited: Oct 27, 2004
2. Oct 27, 2004

### Tide

How about integrating C_v from 0 to T and setting it equal to 3RT? Then solve the resulting equation for T.

To help with the integration use the transformation T = 1/u!

3. Oct 27, 2004

### James R

The total radiated intensity (power per unit area) of a black body is given by the Stefan-Boltzmann law:

$$R = \sigma T^4$$.