1.4 Problems for Chapter 1

(b) Using the specific values , and , calculate the entropy increase per second.

Discuss the role of the ideal gas assumption: is it necessary / unnecessary / convenient ?

Draw up Maxwell's square and use it to complete the following equations:

(a) ; (b) ;

(c) (in terms of derivatives of and );

(d) .

(a) Draw a histogram of the empirical probability (i.e. event frequency) of . Compare the shape of your to the bottom right histogram in Applet

(b) Normalize the histogram such that a sum over all bins equals one. What is the value of ?

(a) Calculate the mean number of molecules (not discerning between and ) that are to be found at a pressure of in a cube with a side length of the wave length of light ( ). What is the standard deviation of the particle number, both absolutely and relative to the mean particle number? (Air is to be treated as an ideal gas at normal temperature .)

(b) Compute the value of the probability density of the event , i. e. the probability of finding an integer number next to the mean number of particles in the sample volume? (Hint: Don't attempt to evaluate factorials of large numbers, such as appear in the binomial distribution ; rather, use that distribution which resembles when becomes large.)

What is the probability of finding only percent of the mean particle number in the sample volume?

a) What is the probability of finding in a snapshot of the system the partitioning ? Explain the formula.

b) Demonstrate

c) (1 bonus point) Prove

- What does the entropy balance tell us about the reversibility/irreversibility of a process? Demonstrate, using a specific example.

- Describe the process of thermal interaction between two bodies. When will the energy flow stop?

- Which thermodynamic potential is suited for the description of isothermal-isochoric systems?

- Describe 2-3 model systems of statistical mechanics.

- What quantities are needed to completely describe the momentary state of a classical ideal gas of particles?

- What quantities are needed for a complete specification of the state of a quantum ideal gas?

- Explain the concepts ``distribution function'' and ``distribution density''; give two examples.

- What are the moments of a distribution? Give a physically relevant example.

2005-01-25