00:01
Hi there, so for this problem we are asked to calculate the thermal capacity of a mass oscillations of atoms of two -dimensional simple square grid by the einstein model.
00:13
We need to find the simplified expression of thermal capacity that applied to the limits low and high temperatures.
00:19
Now first of all we know that for a two -dimensional simple square grid we can assume that each atom has two degrees of freedom corresponding to the vibrations in the x and in the y direction.
00:31
Now the average energy in the einstein model so that average energy is just simply equal to h plam's constant this times the frequency and then this divided by the exponential of the parameter between h and the frequency this divided by boltzmann constant times the temperature and then this minus one.
00:59
Now for this we are asked to calculate the thermal capacity of mass oscillations of atoms.
01:08
Okay, so we know that to calculate the thermal capacity we need to differentiate the average energy with respect to the temperature.
01:22
Now so then we just take this expression and differentiate it with respect to the temperature.
01:30
Now as you can see in here first of all we will have to determine that depends on the temperature in the denominator.
01:36
So its derivative is we need to put in here minus one and then we are going to have all of this to the square and now we just multiply this by the internal derivative.
01:52
So that will be the derivative of this then we will have an exponential of this this times the internal derivative.
02:00
So that will be the internal derivative of this...