Temperature CONFUSION in derivation for Helmholtz Free Energy

In summary, the author is trying to figure out how to derive Helmholtz free energy and is confused by the terms "temperature of the system" and "temperature of the surrounds." He quotes a book to try to figure out what T is, but is still unsure.
  • #1
daniel_r35
1
0
Dear all,

I have been spending 12 hours on this and cannot seem to come up with a solution.

We derive Helmholtz Free Energy (A) from the second law of thermodynamics.

dS(Total) = dS(system) + dS(surrounds)

we try to express dS(surrounds) with properties of the system.

Assuming constant volume (so q=W) and constant temperature (WHICH AS FAR AS I UNDERSTAND it means that the system and surrounds each remain at their original temperatures but CAN HAVE DEIFFERENT temperatures - which they must if not dS(Total) is zero and you can't derive A),

so we get dS(surrounds) = -dU(system)/T...Now NOBODY, not my books, not the internet, NOBODY!says what 'T' is! THEY SAY IT'S the ABSOLUTE TEMPERATURE! But is it that of the SYSTEM or SURROUNDS?!

If it WAS THE SYSTEM, then it WILL NOT MAKE SENSE, because:

dS(system) is ALREADY +dU(system)/Tsystem.

if you say dS(surrounds) is -dU(system)/Tsystem then dS(total) = ZERO and you can't prove A because A = -TdS!

IF it WAS THE SURROUNDS, IT STILL DOESN'T MAKE SENSE:

because we will get A = -TdS(Total) = dU(system) - T(surrounds).dS(system)

What on Earth will Tsurrounds.dSsystem get you?!

EVERY BOOK will say in Helmholtz free energy, we have expressed it in terms of the internal energy of the system and the TEMPERATURE OF THE SYSTEM! (As though they MEANT for the Temperature to be of the system and not the surrounds)!

but based on my knowledge of entropy shouldn't it be temperature of surrounds, because the entropy of the surrounds should be the heat exchanged AT THAT TEMPERATURE belonging to the surrounds?! we know the heat exchanged is -dUsystem. No doubt about that. But what about T?! Either case doesn't work!

PLEASE! HELP ME!
 
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  • #2
Let me quote from D.V. Schroeder, Thermal Physics (Addison Wesley Longman, 2000):
[The Helholtz free energy] is the total energy needed to create the system, minus the heat you can get for free from an environment at temperature ##T##.
 

1. What is temperature confusion in derivation for Helmholtz Free Energy?

Temperature confusion in the derivation for Helmholtz Free Energy refers to a common mistake in which the temperature is incorrectly assumed to be constant during the derivation process. This can lead to incorrect results and must be carefully accounted for in the derivation.

2. Why is temperature confusion a problem in deriving Helmholtz Free Energy?

Temperature confusion is a problem because it violates one of the fundamental assumptions in the derivation of Helmholtz Free Energy, which is that the temperature must remain constant. This can lead to incorrect calculations and undermine the accuracy of the results.

3. How can one avoid temperature confusion in the derivation for Helmholtz Free Energy?

To avoid temperature confusion, one must carefully track the temperature throughout the derivation process and ensure that it is correctly accounted for in each step. It is also important to understand the underlying assumptions and limitations of the derivation method being used.

4. What are some consequences of temperature confusion in the derivation for Helmholtz Free Energy?

Temperature confusion can lead to incorrect results, which can have significant consequences in scientific research. It can also lead to a lack of understanding and misinterpretation of the underlying principles and theories related to Helmholtz Free Energy.

5. Are there any common misconceptions about temperature confusion in the derivation for Helmholtz Free Energy?

One common misconception is that temperature confusion is a minor error that does not significantly affect the final results. However, even small errors in the derivation process can compound and lead to significant discrepancies in the final results. It is important to carefully consider and account for temperature in the derivation of Helmholtz Free Energy.

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