DATE: Friday, 7 February 2020 4:09 PM
QUESTION:
Derivation of Internal Pressure on the homework
Hi Prof. Switkes,
I was working on the homework yesterday to get a head start since it was a long one and I managed to get all the way up through question 31, the question where we derive the internal pressure. I was following the framework given in the book, which involves a few different steps than the technique you showed in class today. The method of dividing through by the ∂ of V is much quicker than the steps I found, however I already have it nicely written out on the homework page I was going to turn in.
The method I used had the same basis of equating terms in the exact differential form and the entropy form of U, but used an equating of double ∂ derivatives that wasn't shown in the method you used. This method of deriving the internal pressure resulted in the same relationship, so am I fine to turn this derivation in for the homework, or would you rather I change my derivation to the method you showed in class?
Thank you,
[student's name]
RESPONSE:
Hello [student's name],
so am I fine to turn this derivation in for the homework, or would you rather I change my derivation to the method you showed in class?
Derivations can often take several routes so long as the steps you use are legitimate and lead to the same expression then fine to use your derivation . Our HW reader is sufficiently sophisticated to recognize alternate legitimate routes.but used an equating of double partial derivatives that wasn't shown in the method you used
I would have to look at your derivation to see its relationship to the method I presented. However when I employed the Maxwell-Euler relation ∂S/∂V =∂P/∂T it was actually using the mixed partial double derivative for the Helmholz Free Energy State function A: -∂S/∂V=∂2A/(∂V∂T)=∂2A/(∂T∂V)=-∂P/∂T This may be related to the double partial method from the text, but the text may not yet have wanted to employ the Helmholz Free Energy A=U-TS dA=-SdT - PdV (pretty soon we are going to see the meaning and utility of the state function A, but defining A 'early' makes these entropy calculations and derivations much more straight forward !!)