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 Assignments and Solutions
IS HELL EXOTHERMIC OR ENDOTHERMIC?

A thermodynamics professor had written a take home exam for his graduate students. It had one question:

"Is hell exothermic or endothermic? Support your answer with a proof."

Most of the students wrote proofs of their beliefs using Boyle's Law or some variant. One student, however, wrote the following:
First, we postulate that if souls exist, then they must have some mass. If they do, then a mole of souls can also have a mass. So, at what rate are souls moving into hell and at what rate are souls leaving? I think that we can safely assume that once a soul gets to hell, it will not leave. Therefore, no souls are leaving.

As for souls entering hell, lets look at the different religions that exist in the world today. Some of these religions state that if you are not a member of their religion, you will go to hell. Since, there are more than one of these religions and people do not belong to more than one religion, we can project that all people and all souls go to hell.
With birth and death rates as they are, we can expect the number of souls in hell to increase exponentially.

Now, we look at the rate of change in volume in hell. Boyle's Law states that in order for the temperature and pressure in hell to stay the same, the ratio of the mass of souls and volume needs to stay constant.

#1 So, if hell is expanding at a slower rate than the rate at which souls enter hell, then the temperature and pressure in hell will increase until all hell breaks loose.

#2 Of course, if hell is expanding at a rate faster than the increase of souls in hell, then the temperature and pressure will drop until hell freezes over.

So which is it?

If we accept the postulate given to me by Theresa Banyan during Freshman year, "that it will be a cold night in hell before I sleep with you" and take into account the fact that I still have not succeeded in having sexual relations with her, then #2 cannot be true, and hell is exothermic.

The student got the only A.

(A true story from Indiana University, Bloomington, IN.)

2nd assignment: Callen 1.3-8.  (deadline: Sept. 24)
 

3rd assignment: Callen p.21, Example 1  (deadline: Sept. 30)

       Calculate W(ACB), Q(ACB), W(AB linear), and Q(AB linear).
 

4th assignment: Callen 1.10-1. & 1.10-2.  (deadline: Sept. 30)

       Only the first 5 (a through e) have to be considered,  f through j are optional.
 
 
5th assignment: Callen 2.6-3, 2.6-4  (deadline: Oct. 8)

 
6th assignment: Chemical equilibrium in adiabatic systems  (deadline: Oct. 8)

       Equilibrium conditions derived in Chapter 2-8. of the Callen book should be derived but in an adiabatic system instead of isolated.
 

7th assignment: Callen 2.3-5 a, b, c.  (deadline: Oct. 16)

       
8th assignment: Efficiency of a Rankine engine  (deadline: Oct. 16)

       Calculate the thermal efficiency of a Rankine engine cycle using the potentials  U, H, and F, and the variables P, V, T and S. Hint: replace step 4 (compression of the liquid to the boiler) with two other  steps: 4a, adiabatic compression, and 4b, isobaric heating. 
 

9th assignment:   (deadline: Oct. 22)

       Show that (dH/dP)T = V - T(dV/dT)P , (where d is for partial derivation!!)

       Derive an expression for (dH/dP)T for an ideal gas, AND for a van der Waals gas. Calculate its value for the van der Waals argon gas at 298 K temperature and 10 atm pressure assuming b/Vm << 1. By how much does the enthalpy of argon gas change when the pressure is increased isothermally to 11 atm?
 
10th assignment:   (deadline: Oct. 22)

       The Joule coefficient "mu" is defined as
                                                                         "mu" = (dT/dV)U .
              (again, d is for partial derivation!!)

       Show that
                                "mu"CV = P - ("alpha"T) / "kappa"T .
 
11th assignment:   (deadline: Nov. 4)

       Calculate the vapour pressure of ice at -15 C. Data available: Delta_H(evaporation) = 44.820 kJ/mole, Delta_H(fusion) = 6.003 kJ/mole, and the vapour pressure of water at 0 oC is 611 Pa.
 
12th assignment:  Atkins: Excersise 8.13 (a) and (b)  (deadline: Nov. 11)
 
13th assignment: Atkins: Excercises 7.11, 8.9 (a) and (b); Problem 8.4  (deadline: Nov. 18)
 
14th assignment:  Atkins: Excersise 9.10 (a) and (b)  (deadline: Nov. 25)
        Optional: Exercises 9.15 (a) and (b),  9.16 (a) and (b)
 
 

Departmental website : http://www-PhCh.chem.elte.hu

Last modified: 20/11/98