In terms of Einstein’s 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 .

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The molar internal energy of a solid, according to Einstein’s 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 .