The thermodynamic energy of a collection of N harmonic oscillators (approximate representations of molecular vibrations) is given by

(a) Drawa rough sketch of the thermodynamic energy as a function of T.

(b) The heat capacity of this system is given by C = dU/dT.

Show that the heat capacity is given by

(c) Find the limit of the heat capacity as T → 0 and as T → ∞. Note that the limit as T → ∞ is the same as the limit ν → 0.

(d) Draw a rough graph of C as a function of T.

Transcribed Image Text:

Nhv U = ehv/kgT – 1