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Physics 410 Homework 11

# Physics 410 Homework 11 - 1(6 pts Free energy of a two...

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1. (6 pts) Free energy of a two state system. (a) Find an expression for the free energy as a function of τ =k B T of a system with two states, one at energy 0 and one at energy ε . (b) From the free energy, find expressions for the energy and entropy of the system. 2. (5 Pts) Quantum concentration. Consider one particle confined to a cube of side L; the concentration in effect is 3 L / 1 n = . Find the kinetic energy of the particle when in the ground orbital. There will be a value of the concentration for which this zero-point quantum kinetic energy is equal to the temperature τ =k B T. (At this concentration the occupancy of the lowest orbital is of the order of unity; the lowest orbital always has a higher occupancy than any other orbital.) Show that the concentration n o equal to the quantum concentration 2 / 3 2 Q 2 M n π τ = h , within a factor of the order of unity. 3. (6 pts) One-dymensional gas. Consider an ideal gas of N particles each of mass M, confined to a one-dimensional line of length L. Find the partition function, Helmholtz

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Physics 410 Homework 11 - 1(6 pts Free energy of a two...

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