Problem #0009 Quantum Physics Problem #0011 Chapters Chapters

711.

Problem 49.21 (RHK)

In terms of Einsteinís theory of heat capacity, we have to find (a) the molar heat capacity at constant volume of a solid at its Einstein temperature, and express our answer as a percentage of its classical value of 3R. (b) We have to find the molar internal energy at the Einstein temperature, and express our answer as a percentage of its classical value of .

Solution:             Click For PDF Version

The molar internal energy of a solid, according to Einsteinís theory of heat capacity, can be expressed as

in which , where is the Einstein temperature.

 

 

 

Specific heat at constant volume


Therefore, the molar heat capacity at constant volume of a solid at its Einstein temperature will be

It is 33.8% of its classical value 3R.

(b)

The molar internal energy at the Einstein temperature will be

which is 58.2% of its classical value .