Thermodynamics: Maxwell relations proofs 1 (from 𝘜 and 𝘏)

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  • Опубліковано 22 гру 2024

КОМЕНТАРІ • 35

  • @lseinjr1
    @lseinjr1  6 років тому +6

    (For mobile users)
    00:08 Exact differentials
    01:18 Condition for exactness
    02:28 Combined form of First Law
    02:59 Exact differntial for dU
    03:54 Partial derivatives for temperature (T) and entropy (S)
    04:58 Applying exactness condition
    06:25 Finding dH from dU
    08:18 Exact differential for dH
    09:19 Partial derivatives for temperature (T) and volume (V)
    10:08 Applying exactness condition

  • @zk33m
    @zk33m 4 місяці тому +1

    6 years ago and ure still helping students. thank you so much

  • @aliexpress.official
    @aliexpress.official 5 років тому +2

    thank you. the first 4 minutes of your video alone made everything click for me.

  • @user-rd1lu7yx1b
    @user-rd1lu7yx1b 6 років тому +4

    Sir you literally save my grade. Thank you very much

  • @benjaminhenkin4303
    @benjaminhenkin4303 4 роки тому +1

    Something is weird...
    If you go to the time 4:28 - when the initial proofs are written - and substitute the results back into the original expression, you get T = -P.
    What is the significance of this result? It's written there clear as day.

    • @lseinjr1
      @lseinjr1  4 роки тому +1

      What do you mean by the "original expression"?
      (∂U/∂S)v and (∂U/∂V)s are certainly not equal.
      (∂²U/∂S∂U) and (∂²U/∂U∂S) certainly ARE equal, since mixed partials are equal if they are both continuous.

  • @noahcasarotto-dinning1575
    @noahcasarotto-dinning1575 Рік тому +2

    Love your content, super helpful

  • @diyaazaghloul756
    @diyaazaghloul756 2 роки тому +1

    Very informative lecture thank you for sharing

    • @lseinjr1
      @lseinjr1  2 роки тому

      Glad it was helpful!

  • @katarinahennessey8971
    @katarinahennessey8971 4 роки тому +3

    Youre great! Thank you

  • @DS-tg8cj
    @DS-tg8cj 6 років тому

    I did not understand the steps that start at 03:11 and end at 03:40. Could you please explain the mathematics behind those steps also? Thank you.

    • @lseinjr1
      @lseinjr1  6 років тому +5

      We get dU = TdS - p dV from the First Law (dU = dq + dw), since entropy (S) = q / T, and the work of expansion (w) = - p dV.
      We get that dU = (∂U/∂S) dS + (∂U/∂V) dV, because U is a "state function". This is equivalent to being a "conservative" function - it does not depend on the size of the system. We can find the change in a state function ΔF by F(final) - F(initial). We also say that the function is "independent of path."
      There is a very practical and useful result of working with state functions (U, A, G, H, T, S, and V are all state functions). Let's call the function "Z" and let it be a function of two variables x and y. Then we can immediately write down the relationship dZ = (∂Z/∂x) dx + (∂Z/∂y) dy.
      Since U is a state function of S and V, we had: dU = (∂U/∂S) dS + (∂U/∂V) dV. (This "trick" is used in almost every derivation in thermodynamics). Since we have two different formulae for dU, we can set them equal. Since they both have "dS" and "dV" parts, the coefficients in front of "dS' in both formulae must be equal, and the two coefficients of "dV" must be equal as well. This is also a technique that is used very often.
      I hope that makes those steps clearer.

  • @chanda.nageshwarraowifepad9052

    Interesting
    Maxwell's relations ( U&H)

  • @romellopes2022
    @romellopes2022 4 роки тому +1

    Thanks professor, helpfull! God Bless you

    • @lseinjr1
      @lseinjr1  4 роки тому

      Glad it was helpful!

  • @shariful5960
    @shariful5960 2 роки тому

    This is the best and short

  • @shariful5960
    @shariful5960 2 роки тому

    If mdx+ ndy = is exact or 0?? Then

    • @lseinjr1
      @lseinjr1  2 роки тому

      M dx + N dy is an exact differential if and only if :
      ⟨∂M/∂y⟩ = ⟨∂N/∂x⟩. This means that there exists some function f such that
      df = ⟨∂f/∂x⟩ dx + ⟨∂f/∂y⟩ dy. One property of the "state functions" of thermodynamics (enthalpy, entropy, Helmholtz energy, Gibbs energy) is that they are "independent of path. This means that, to calculate a change in the function, you only need to know the end points; for example, ΔG = G (final) - G (initial).
      However, a function that is "independent of path" is a state function, one that can be written as an exact differential. Many of the derivations in thermodynamics begin with writing a thermodynamic property ("state function") .as an exact differential

  • @prabaseelan1999
    @prabaseelan1999 5 років тому +1

    Thank u so much sir

  • @hirokjkonwar8622
    @hirokjkonwar8622 4 роки тому +2

    Thank you very much sir

  • @chanda.nageshwarraowifepad9052

    👍👏👏

  • @alexburza437
    @alexburza437 4 роки тому +1

    Thankyou so much!!!!!

  • @nibankumar4342
    @nibankumar4342 5 років тому

    Thanks sir u solve out my doubt

  • @shariful5960
    @shariful5960 2 роки тому

    Proof other maxwells quation short and easy way

    • @lseinjr1
      @lseinjr1  2 роки тому

      There are four (4) Maxwell relations. Two (2) were derived in this video, and the other two (2) are derived in:
      ua-cam.com/video/r4WW4uho16o/v-deo.html

  • @user-rd1lu7yx1b
    @user-rd1lu7yx1b 6 років тому

    sir thank u

  • @shariful5960
    @shariful5960 2 роки тому

    Proof other eqation in short way

  • @DYEManavSharma
    @DYEManavSharma 5 років тому

    Thanks bro

  • @cheesey88
    @cheesey88 4 роки тому

    cool kid didn't ask