J. E. Meany Central Washington University Ellensburg, Washington 98926
Process Reversibility, Work, and Entropy
T o many beginning physical chemistry students, the relationship between process reversibility, work, and entropy is less than obvious. This is particularly evident in the case of nonchemistry majors for whom a brief course in physical chemistry is appropriate. I have found the teaching aid described below most helpful for use in a one-quarter course presently offered at Central Washington University. Consider a cylinder with a weightless, frictionless piston resting at equilibrium on 3 lof 0.5 mole of an ideal gas at 293°K (state 1in the figule). The four weights on the piston are such that the pressure exerted on the gas is p = 4 atm; i.e., 1atm of pressure is contributed by each weight. Assume that the system is allowed to do work by any of three different isothermal paths described below. Process A: Spontaneous (state 1 to state 4 in one step). Three weights are at once removed. The piston immediately assumes the position as in state 4. Process B: "Pseudo-reversible" (steowise oroeression from state . . . .. 1 to stare4,; achieved by removing one weight at a time. Pmcrsr C': The reversible isothermal expansion from state 1 u, itate For each process, the work done by the system is calculated (see the table). For Process A, wld4 = pAV; Process B, w,-,-,-~ = ZpAV; and Process C, w,. = 2.3nRTlog(Vzl Vl). It then is noted that since entropy is a thermodynamic function of state, the change in the entropy of the system is independent of the path by which the process takes place. Thus for processes A, B, and C, ASswt = q...,,~ = w,,r. T h e changes in the entropy of the surroundings are next considered. For simplicity, it is assumed that the system is in contact with a reservoir so large that when each respective process is carried out, no significant decrease in the temperature of the surroundings occurs. Thus, regardless of how the process is carried out, the heat given u p by the surroundings = q,,,,~ = is done so reversibly. For each process, AS,,. -WIT. A summary of parameters for the model is listed in the table.
238 1 Jwmal of Chemlcal Education
The calculated values vividly demonstrate to the student 1) a fundamental statement of the second law of thermodynamics uis. for spontaneous changes ASnet > 0,whereas for reversible processes, ASmt > = 0. 2) that as a process approaches reversihilitv, more work is done hv ..
the syst&.
3) that the ability to do an amount of work equivalent to T A S is
lost when the process is carried out at various degrees of spontaneity.
Acknowledgment
Special thanks to Drs. Emken and Habib for helpful discussions on this and related topics. Summary of Parameters for the Model
Process
Work
(call
"spontaneous" 220 "pseudo-reversible" 320 C) "reversible" 410 A) 0)
stare,
stare 2
P.48,rn V = 3 lhierr
P = 3 arm V = 4 lilem
q
t
A%.
AS,
ASM
-0.75 -1.10 -1.40
0.65 0.30 0.00
Ical) (calldeg) (calldeg) (calldeg) 220 320 410
1.4
1.4 1.4
state 3 P-2atm V = 6 hierr
Cylinder and piston for &mstrating thermodynamic concepts.
state 4 P = ,arm V = lllifers
