Date: 10/16/2003                                                                            Name: …………………..

                                                       

Midsemester Exam

Thermal Physics

Presence: 10p

Questions (3p each, 45p total):

 

  1. What do we mean by the multiplicity of a configuration?

 

  1. How the entropy of a configuration is related to the multiplicity?

 

  1. Name three extensive and three intensive thermodynamic parameters.

 

  1. What was our fundamental assumption regarding the probability of microstates for closed and isolated thermodynamic systems?

 

  1. What does the ergodic hypothesis state?

 

  1. What is the relation between the fundamental temperature and the absolute temperature (in the Kelvin scale)? Specify the physical quantities in the formula, and their SI units.

 

  1. Which law of thermodynamic is related to the energy conservation principle? Enounce this law.

 

  1. How do we mathematically characterize the fluctuations of a physical quantity?

 

  1. How could one calculate the partition function Z, using a sum over all energy values instead of a sum over all states?

 

  1.  In the low and high temperature limit how does the specific heat of a solid body depend on temperature? What is the mathematical condition for the “low temperature limit”?

 

  1.  What are the phonons? What is common and different between phonons and photons?

 

  1.  What is Df in the Nyquist theorem?

 

  1.  How many polarizations does an elastic wave have? How many polarizations does an electromagnetic wave have?

 

  1. Write up the thermodynamic identity (differential form of the internal energy) when we consider a process in which the entropy, volume and particle number can all change. Specify the physical quantities in this equation.

 

  1. Let us consider an open thermodynamic system S, with a chemical potential m in contact with a heat-bath at temperature t. How would one calculate the probability that S has N particles at a given time-moment? Specify the physical quantities in your equation.

 

 

Problems (45p total):

 

1.  We consider a binary magnetic system (S) composed of six (6) non-interacting magnetic-moments (spins), inside an external magnetic field B. The magnetic moments of the individual spins are +/- m. (see the figure). The system is in contact with a heat-bath at temperature t.

6 binary magnetic moments in an external magnetic field B, and in contact with a heat-bath at temperature t.

 

a.)    Calculate the probability that at a given time-moment the S system will be in the state specified in the figure?  (5p)

b.)    Calculate the probability that at a given time-moment the S system will have a total magnetization: +2m ?  (5p)

c.)    Calculate the average magnetization of the S system for a t=mB temperature. (5p)

d.)    Calculate the average magnetization for a tฎฅ temperature. (5p)

 

 

2.   We consider a thermodynamic system composed of N particles in which the multiplicity of a configuration with a given U internal energy is given as: g(U)=C U7N/2. Show that the caloric equation of state for this system is U=7Nt/2. Specify a thermodynamic system, for which the above caloric equation of state is valid!  (10+5=15p)

 

 

3. Consider a system that may be unoccupied with energy zero or occupied by one particle in three possible states with energy 0, e and 2e (three level system). The system is in diffusive equilibrium with a heat-bath at temperature t. Assuming that the chemical potential of the particles is m, calculate the thermal average occupancy of the state with energy 2e.  (10 p)

 

 

                                                                            Total maximum: 100p  (25% in final)

                                                                                                            

                                                                             Total obtained: ……..

 

                                                                             Percent in the final grade:  …………..