home  | más sobre termo | otros temas de Física | lecciones del maestro Ciruela | tonterías |  @ 
   NO ME SALEN
   (APUNTES TEÓRICOS DE BIOFÍSICA DEL CBC)
   EVOLUCIONES REVERSIBLES DE GASES IDEALES - ENTROPIA

 

nomesalen

 

Entropy variations in reversible evolutions of ideal gases

The Second Law of Thermodynamics assures us that any transformation that occurs in the universe occurs in such a way that makes the total entropy increase. The above is often summarized by writing:

ΔSU > 0

The immediate consequence of this is that NOTHING can go in reverse. All the processes of the universe are irreversible if you consider the process as a whole..

However, it is very useful for practical purposes to keep in mind the precise limit of this statement: an scenario where the entropy of the universe does not vary. This isn't useful because we expect that there could a process of this kind that could occur, but because that limit situation shows us interesting properties of the universe itself. A (hypothetical) process that could occur under that extreme condition would be reversible.

Finally, always keep in mind that it is impossible for a process to occur, and that because of it the entropy of the universe decreases ... is not going to happen.

To sum up:

ΔSu > 0        irreversible transformation (real)

ΔSu = 0         reversible transformation (ideal)

ΔSu < 0         impossible transformation (science fiction)

Among the interesting properties that can be studied of this limit situation, there are the evolutions of the ideal gases. To calculate the entropy changes in some typical evolutions you can use the formulas in the following table. Keep in mind that they represent the entropy change of the gas, ΔSG, not the one of the universe. In any process, the entropy variation of the universe will be equal to the sum of the variations of your gas - or your system - plus the entropy variation of the environment, ΔSM.

ΔSU = ΔSG + ΔSM
 
 
  isobaric isochoric isothermal adiabatic cycle any
ΔS
cp n ln   TF  
T0

cp n ln   VF  
V0
cv n ln   TF  
T0

cv n ln   PF  
P0
n R ln   VF  
V0

n R ln   P0  
PF
0 0 Join the initial and final states by any known path
Where cV and cP, are the specific molar heat at constant volume
and the specific molar heat at constant pressure, respectively;
for ideal monatomic gases cV = 1,5 R and cP = 2,5 R, and for diatomics cV = 2,5 R and cP = 3,5 R,
and where R is the ideal gas constant:
R = 8,314 J/mol K = 0,08207 l atm/mol K = 1,987207 cal/K mol

Without many details, the basic guidelines for finding the expressions in the table are as follows:

  • The definition of entropy variation: is the sum of all "pieces" of heat exchanged, divided - each one - by the absolute temperature at which that exchange occured ... during a reversible evolution.



So, the entropy variation between two states must be calculated considering a reversible transformation, no matter how it actually evolved from the initial to the final state.

  • The heats are "set" with the same criteria as in calorimetry;

  • For ideal gases it is true that:

Que te aproveche.

 

 

  

NOTE: Don’t use this page as a summary. Don’t be a bad boy...
 
     
Some rights reserved. Reproduction permitted if quoting the source. Last updated on Feb-17.Translated by Esteban Djeordjian. Buenos Aires, Argentina.