NORTH CAROLINA STATE UNIVERSITY

Department of Chemistry                            Name________________________________

 

CH 431                                                                                                                       Quiz 4

Physical Chemistry II                                                                                 October 21, 2001

                                                                                                                 Due: Oct. 30, 2001

 

1.      Boltzmann's definition of entropy is S = k ln W where W is the number of possible combinations in the system, W = N!/n1!n2!n3!…nn!. 

  1. Considering an explicit system of N = 6 particles distributed over 3 energy levels shown determine the populations of the three levels that gives the maximum W and therefore the maximum entropy.  Give the value for W. (5 Points)

 

  1. How does this distribution compare to a thermal distribution?  In other words, at what temperature will the entropy be maximum for the system? (5 Points)

 

 

 

 

 

 

 

 

 

2.     

We state the Gibb's paradox; the entropy depends on volume as S = nS0 + nR lnV.  If the volume is halved by a partition, the combined entropy of the two halves of the system is

This clearly does not make sense since S' ¹ S.  To understand this paradox, derive an expression for the entropy of a gas of distinguishable ideal gas particles (translation only) and compare this to entropy calculated in Eqn. 20.45 in McQuarrie and Simon.  (Note the factor gel is the electronic degeneracy, which we assume to be equal to one).  Hint: what is assumed about the volume in the Gibb’s paradox that is analogous to the difference in your derivation for particles?

(5 Points)

 

 

 

 

 

3.      The boiling point of water at a pressure of 25 atm is 223 oC.  Compare the theoretical efficiencies of a steam engine operating between 200 oC and the boiling point of water at 1 atm and 25 atm.  (5 Points)

 

 

 

 

 

 

 

4.      The molar heat capacity of H2O(l) has an approximately constant value of Cp = 75.3 J/mole-K.  Calculate the entropy change of 2 moles of liquid water heated from 10 oC to 90 oC. (5 Points)

 

 

 

 

 

 

 

 

 

 

 

 

5.     

The molar heat capacity of C2H4 (g) can be expressed by

      Calculate DS if one mole of ethene is heated from 300 K to 600 K at constant volume.

       (10 Points)

 

 

 

 

 

 

 

 

6.      Calculate the equilibrium temperature of 90 ml. of coffee initially at 330 K poured into a stainless steel camp cup (assume molar mass of iron) with a mass of 10 g initially at 270 K.  Assume that the coffee and cup are adiabatically insulated from the rest of the universe. [Cp = 75.3 J/mol-K for the coffee and Cp = 25.1 for iron]  

(5 Points)