Posted by **martin** on Sunday, March 11, 2012 at 1:20pm.

Consider a system of N identical particles. Each particle has two energy levels: a ground

state with energy 0, and an upper level with energy . The upper level is four-fold degenerate

(i.e., there are four excited states with the same energy ).

(a) Write down the partition function for a single particle.

(b) Find an expression for the internal energy of the system of N particles.

(c) Calculate the heat capacity at constant volume of this system, and sketch a graph to

show its temperature dependence.

(d) Find an expression for the Helmholtz free energy of the system.

(e) Find an expression for the entropy of the system, as a function of temperature. Verify

that the entropy goes to zero in the limit T ! 0. What is the entropy in the limit

T ! 1? How many microstates are accessible in the high-temperature limit?

## Answer This Question

## Related Questions

- Physics (please help!) - 1000 dust particles are trapped on a surface. There are...
- Physics - Dust particles are trapped on a surface. There are two energy levels ...
- Science ENGR - Consider a laser which emits photons with a wavelength of 1.55 ...
- Chemistry - Last ones: 32. There could be eight electrons in the first energy ...
- physics - The drawing shows three energy levels of a laser that are involved in ...
- mastering quantum mechanics - Problem 4: Variational principle and bounds (3 ...
- chemistry - which of the following statements correctly describes energy levels...
- chemistry - Which of the following statements correctly describes energy levels...
- chemistry - Which of following statements correctly describes energy levels? A. ...
- Chemistry - 24. A quantum is a finite amount of energy gained or lost by an atom...

More Related Questions