# Thermodynamics question

**URL:** <https://boards.straightdope.com/t/thermodynamics-question/236386>\
**Category:** Factual Questions\
**Created:** [March 25, 2004, 6:07pm UTC](https://boards.straightdope.com/t/thermodynamics-question/236386 "2004-03-25T18:07:59Z")\
**Posts on this page:** 7\
**Page:** 1

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**Author:** ![gtbiehle](https://avatars.discourse-cdn.com/v4/letter/g/5f8ce5/32.png) [@gtbiehle](https://boards.straightdope.com/u/gtbiehle)\
**Post date:** [March 25, 2004, 6:07pm UTC](https://boards.straightdope.com/t/thermodynamics-question/236386/1 "2004-03-25T18:07:59Z")

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Help! This is a question in elementary thermodynamics.  
I was deriving the expression for Gibb’s free energy today:  
delta G = delta H - T delta S  
that is  
delta G = delta E + P delta V - T delta S  
But is it not true that the first law of thermodynamics is  
delta E = T delta S - P delta V ?  
That would make delta G = 0.  
What am I missing here?

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**Author:** ![Jurph](https://avatars.discourse-cdn.com/v4/letter/j/50afbb/32.png) [@Jurph](https://boards.straightdope.com/u/Jurph)\
**Post date:** [March 25, 2004, 8:31pm UTC](https://boards.straightdope.com/t/thermodynamics-question/236386/2 "2004-03-25T20:31:22Z")

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I suspect this is a homework question… nonetheless, I wrestled with an inadequate textbook in Thermo as well. I always found [http://scienceworld.wolfram.com/physics/](http://scienceworld.wolfram.com/physics/) to be a great help in looking up the “basic” or “standard” derivations of thermodynamic equations. If it’s not homework, I can come back and help you finish this puppy off (I ended up with a B+ in Thermo).

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**Author:** ![Hyperelastic](https://avatars.discourse-cdn.com/v4/letter/h/a3d4f5/32.png) [@Hyperelastic](https://boards.straightdope.com/u/Hyperelastic)\
**Post date:** [March 25, 2004, 8:39pm UTC](https://boards.straightdope.com/t/thermodynamics-question/236386/3 "2004-03-25T20:39:43Z")

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You are doing fine. The first law is dE=dQ-dW. dW=PdV, and for reversible processes, dQ=TdS, so you can write dE=TdS-PdV for reversible processes. You concluded dG=0, which is true for reversible processes. For irreversible processes, you have to allow dQ\<TdS.

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**Author:** ![Hyperelastic](https://avatars.discourse-cdn.com/v4/letter/h/a3d4f5/32.png) [@Hyperelastic](https://boards.straightdope.com/u/Hyperelastic)\
**Post date:** [March 25, 2004, 8:45pm UTC](https://boards.straightdope.com/t/thermodynamics-question/236386/4 "2004-03-25T20:45:01Z")

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Out of respect for your professor, I probably shouldn’t have given you an answer that explicit. Please read the above post as “Hint: It involves reversibility”.

Or maybe you are just deriving the Gibbs Free Energy on your own time, for fun 🙂

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**Author:** ![gtbiehle](https://avatars.discourse-cdn.com/v4/letter/g/5f8ce5/32.png) [@gtbiehle](https://boards.straightdope.com/u/gtbiehle)\
**Post date:** [March 25, 2004, 10:04pm UTC](https://boards.straightdope.com/t/thermodynamics-question/236386/5 "2004-03-25T22:04:17Z")

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Actually I am a high school teacher, and I had this problem bring my class to a screeching halt this morning. I did not know there was a caveat to the equation  
dE = T dS - P dV  
Anyway, thanks.

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**Author:** ![Hyperelastic](https://avatars.discourse-cdn.com/v4/letter/h/a3d4f5/32.png) [@Hyperelastic](https://boards.straightdope.com/u/Hyperelastic)\
**Post date:** [March 25, 2004, 10:21pm UTC](https://boards.straightdope.com/t/thermodynamics-question/236386/6 "2004-03-25T22:21:46Z")

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Let me just say that the fact you are teaching about Gibbs Free Energy in high school is awesome. I don’t think we ever got beyond the proverbial “pith balls and inclined planes.”

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**Author:** ![Dr\_Paprika](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr_paprika/32/3042_2.png) [@Dr\_Paprika](https://boards.straightdope.com/u/Dr_Paprika)\
**Post date:** [March 25, 2004, 11:36pm UTC](https://boards.straightdope.com/t/thermodynamics-question/236386/7 "2004-03-25T23:36:02Z")

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I’m pretty sure we learned something about Gibbs’ free energy in high school, but in chemistry class, not physics. That helped me to get an A in university thermo 1 and 2.

Hyperelastic already explained the answer. Kudos for teaching this early.