August 03, 2020, 11:24:15 AM
Forum Rules: Read This Before Posting

### Topic: Puzzle in thermodynamics by Dr Lehninger.  (Read 1417 times)

0 Members and 1 Guest are viewing this topic.

#### GeLe5000

• Regular Member
• Posts: 64
• Mole Snacks: +0/-1
##### 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

• Regular Member
• Posts: 64
• Mole Snacks: +0/-1
##### 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.