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### Topic: Puzzle in thermodynamics by Dr Lehninger.  (Read 1418 times)

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#### GeLe5000

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##### Puzzle in thermodynamics by Dr Lehninger.
« on: December 25, 2014, 10:18:52 AM »
Hello.

In a Chemistry  book I read that

dSuniv = dSext + dSsyst (relation 1)
(the change in entropy of a system during a chemical reaction + the change in entropy of the environment = the change in entropy of the universe)

And also

dSext = - dH / T (relation 2)
(when a chemical reaction produces heat, it causes an increase in the entropy of the environment)

dSuniv = - dG / T (relation 3)
(it's more difficult to understand why a change in the entropy of the universe is linked to dG which is called change in "free energy" or the "energy available for work")

And we have the well-known relation

dG = dH – TdS
(relation 4) (S is Ssyst)

The relations seem correct since if we change in relation 4, dH for – TdSext, we get

dG = - TdSext – TdSsyst = - T (dSext + dSsyst) = -TdSuniv  , thus relation 3.

However, in the book "Bioenergetics" by Dr A. L. Lehninger (W. A. Benjamin, 1971), we read p.27

dG = dE – TdS

There are 2 differences with relation 4 :

1)   S is Suniv instead of Ssyst
2)   dE replaces dH

So I write dG = dE – TdSuniv (relation 5)

dE is said to be the change in "total energy" of the system.

What is the "total energy of the system"

Moreover, if we combine the books, we can write

dG = dH – TdSsys = dE - TdSuniv

dE = dH + TdSuniv – T dSsyst

dE = dH + T(dSuniv – dSsyst)

dE = dH + TdSext

since dSext = - dH / T (relation 2)

dE = dH + T(- dH / T)

dE = dH – dH = 0

It's a puzzle to me. If you have some energy to spare in order to decrease my "informational entropy"… Thank you.

#### GeLe5000

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##### Re: Puzzle in thermodynamics by Dr Lehninger.
« Reply #1 on: January 14, 2015, 02:43:48 PM »
Never mind, I've the solution by myself.

It was a bit difficult to admit, but Dr Lehninger was wrong in his book.

It's ΔSSyst instead of ΔSUniv.

ΔE is ΔH (change in Enthalpy) and Enthalpy is sometimes called "total energy of the System".

Thus, when we write ΔGSyst = ΔHSyst - TΔSSyst and divide with T, we get ΔGSyst/T = ΔHSyst/T - ΔSSyst

ΔGSyst/T = -ΔSext - ΔSSyst = - (ΔSext + ΔSSyst) = - ΔSuniv

Thus, ΔSuniv = -  ΔGSyst/T which is given in the first book (relation 3)

ΔSext in a book in French was ΔSSurr (Surr for Surrounding)