Why does the negative sign arise in this thermodynamic relation?Why is the derivative of the Fermi-Dirac...

Is "conspicuously missing" or "conspicuously" the subject of this sentence?

What are some noteworthy "mic-drop" moments in math?

They call me Inspector Morse

Why was Goose renamed from Chewie for the Captain Marvel film?

Could you please stop shuffling the deck and play already?

Why is computing ridge regression with a Cholesky decomposition much quicker than using SVD?

Signed and unsigned numbers

Motivation for Zeta Function of an Algebraic Variety

Why does liquid water form when we exhale on a mirror?

What was the Kree's motivation in Captain Marvel?

Is "history" a male-biased word ("his+story")?

Doesn't allowing a user mode program to access kernel space memory and execute the IN and OUT instructions defeat the purpose of having CPU modes?

How do I express some one as a black person?

Why does Captain Marvel assume the people on this planet know this?

Why would one plane in this picture not have gear down yet?

Difference on montgomery curve equation between EFD and RFC7748

How can The Temple of Elementary Evil reliably protect itself against kinetic bombardment?

Virginia employer terminated employee and wants signing bonus returned

Fixing conmutation for high voltage switching with power mosfet

Is it necessary to separate DC power cables and data cables?

How to draw cubes in a 3 dimensional plane

Why does the negative sign arise in this thermodynamic relation?

PTIJ: Should I kill my computer after installing software?

What's wrong with this bogus proof?



Why does the negative sign arise in this thermodynamic relation?


Why is the derivative of the Fermi-Dirac distribution negative?Partial derivatives vs total derivatives in thermodynamicsWhy does the material derivative and transport theorem look different?Partial Derivatives Relation on Thermodynamics and minus signExplain me the sign in imageFourier Heat Conduction Law - why is temperature gradient negative?What is the significance of the temperature derivative of the isentropic bulk modulus?Entropy and heat capacity at constant volumeWhy does the internal energy's total differential behave like this?How to know the dependances of thermodynamic variables













1












$begingroup$


I can't understand why $left(frac{partial P}{partial V} right)_T=-left(frac{partial P}{partial T} right)_Vleft(frac{partial T}{partial V}right)_P$. Why does the negative sign arise? I can easily write $left(frac{partial P}{partial V}right)_T=left(frac{partial P}{partial T}right)_Vleft(frac{partial T}{partial V}right)_P$ from the rule of partial derivative, but what's the negative sign for?






thermodynamics differentiation







share|cite|improve this question









New contributor




Srijan Ghosh is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.







$endgroup$








  • 1




    $begingroup$
    Your second formula is easily written but it is wrong. The first formula is right and to find out why try en.wikipedia.org/wiki/Triple_product_rule
    $endgroup$
    – Andrew Steane
    4 hours ago
















1












$begingroup$


I can't understand why $left(frac{partial P}{partial V} right)_T=-left(frac{partial P}{partial T} right)_Vleft(frac{partial T}{partial V}right)_P$. Why does the negative sign arise? I can easily write $left(frac{partial P}{partial V}right)_T=left(frac{partial P}{partial T}right)_Vleft(frac{partial T}{partial V}right)_P$ from the rule of partial derivative, but what's the negative sign for?






thermodynamics differentiation







share|cite|improve this question









New contributor




Srijan Ghosh is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.







$endgroup$








  • 1




    $begingroup$
    Your second formula is easily written but it is wrong. The first formula is right and to find out why try en.wikipedia.org/wiki/Triple_product_rule
    $endgroup$
    – Andrew Steane
    4 hours ago














1












1








1





$begingroup$


I can't understand why $left(frac{partial P}{partial V} right)_T=-left(frac{partial P}{partial T} right)_Vleft(frac{partial T}{partial V}right)_P$. Why does the negative sign arise? I can easily write $left(frac{partial P}{partial V}right)_T=left(frac{partial P}{partial T}right)_Vleft(frac{partial T}{partial V}right)_P$ from the rule of partial derivative, but what's the negative sign for?






thermodynamics differentiation







share|cite|improve this question









New contributor




Srijan Ghosh is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.







$endgroup$




I can't understand why $left(frac{partial P}{partial V} right)_T=-left(frac{partial P}{partial T} right)_Vleft(frac{partial T}{partial V}right)_P$. Why does the negative sign arise? I can easily write $left(frac{partial P}{partial V}right)_T=left(frac{partial P}{partial T}right)_Vleft(frac{partial T}{partial V}right)_P$ from the rule of partial derivative, but what's the negative sign for?






thermodynamics differentiation




thermodynamics differentiation






share|cite|improve this question









New contributor




Srijan Ghosh is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











share|cite|improve this question









New contributor




Srijan Ghosh is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









share|cite|improve this question




share|cite|improve this question








edited 4 hours ago









ACuriousMind♦

72.5k18126318




72.5k18126318






New contributor




Srijan Ghosh is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









asked 4 hours ago









Srijan GhoshSrijan Ghosh

83




83




New contributor




Srijan Ghosh is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.





New contributor





Srijan Ghosh is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.






Srijan Ghosh is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.








  • 1




    $begingroup$
    Your second formula is easily written but it is wrong. The first formula is right and to find out why try en.wikipedia.org/wiki/Triple_product_rule
    $endgroup$
    – Andrew Steane
    4 hours ago














  • 1




    $begingroup$
    Your second formula is easily written but it is wrong. The first formula is right and to find out why try en.wikipedia.org/wiki/Triple_product_rule
    $endgroup$
    – Andrew Steane
    4 hours ago








1




1




$begingroup$
Your second formula is easily written but it is wrong. The first formula is right and to find out why try en.wikipedia.org/wiki/Triple_product_rule
$endgroup$
– Andrew Steane
4 hours ago




$begingroup$
Your second formula is easily written but it is wrong. The first formula is right and to find out why try en.wikipedia.org/wiki/Triple_product_rule
$endgroup$
– Andrew Steane
4 hours ago










2 Answers
2






active

oldest

votes


















2












$begingroup$

This is not a simple application of partial derivatives, since the variables that are being held constant vary here, but an instance of the triple product rule, which says that for any three quantities $x,y,z$ depending on each other, the relation
$$ left(frac{partial x}{partial y}right)_zleft(frac{partial y}{partial z} right)_xleft(frac{partial z}{partial x}right)_y = -1$$
holds.






share|cite|improve this answer









$endgroup$





















    2












    $begingroup$

    This all starts from the basic relationship $$dP=left(frac{partial P}{partial T}right)_VdT+left(frac{partial P}{partial V}right)_TdV$$Since, at constant pressure, dP=0, if we solve for dT/dV at constant pressure, we obtain:
    $$left(frac{partial T}{partial V}right)_P=-frac{left(frac{partial P}{partial V}right)_T}{left(frac{partial P}{partial T}right)_V}$$






    share|cite|improve this answer









    $endgroup$













      Your Answer





      StackExchange.ifUsing("editor", function () {
      return StackExchange.using("mathjaxEditing", function () {
      StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
      StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
      });
      });
      }, "mathjax-editing");

      StackExchange.ready(function() {
      var channelOptions = {
      tags: "".split(" "),
      id: "151"
      };
      initTagRenderer("".split(" "), "".split(" "), channelOptions);

      StackExchange.using("externalEditor", function() {
      // Have to fire editor after snippets, if snippets enabled
      if (StackExchange.settings.snippets.snippetsEnabled) {
      StackExchange.using("snippets", function() {
      createEditor();
      });
      }
      else {
      createEditor();
      }
      });

      function createEditor() {
      StackExchange.prepareEditor({
      heartbeatType: 'answer',
      autoActivateHeartbeat: false,
      convertImagesToLinks: false,
      noModals: true,
      showLowRepImageUploadWarning: true,
      reputationToPostImages: null,
      bindNavPrevention: true,
      postfix: "",
      imageUploader: {
      brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
      contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
      allowUrls: true
      },
      noCode: true, onDemand: true,
      discardSelector: ".discard-answer"
      ,immediatelyShowMarkdownHelp:true
      });


      }
      });






      Srijan Ghosh is a new contributor. Be nice, and check out our Code of Conduct.










      draft saved

      draft discarded


















      StackExchange.ready(
      function () {
      StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fphysics.stackexchange.com%2fquestions%2f465965%2fwhy-does-the-negative-sign-arise-in-this-thermodynamic-relation%23new-answer', 'question_page');
      }
      );

      Post as a guest















      Required, but never shown

























      2 Answers
      2






      active

      oldest

      votes








      2 Answers
      2






      active

      oldest

      votes









      active

      oldest

      votes






      active

      oldest

      votes









      2












      $begingroup$

      This is not a simple application of partial derivatives, since the variables that are being held constant vary here, but an instance of the triple product rule, which says that for any three quantities $x,y,z$ depending on each other, the relation
      $$ left(frac{partial x}{partial y}right)_zleft(frac{partial y}{partial z} right)_xleft(frac{partial z}{partial x}right)_y = -1$$
      holds.






      share|cite|improve this answer









      $endgroup$


















        2












        $begingroup$

        This is not a simple application of partial derivatives, since the variables that are being held constant vary here, but an instance of the triple product rule, which says that for any three quantities $x,y,z$ depending on each other, the relation
        $$ left(frac{partial x}{partial y}right)_zleft(frac{partial y}{partial z} right)_xleft(frac{partial z}{partial x}right)_y = -1$$
        holds.






        share|cite|improve this answer









        $endgroup$
















          2












          2








          2





          $begingroup$

          This is not a simple application of partial derivatives, since the variables that are being held constant vary here, but an instance of the triple product rule, which says that for any three quantities $x,y,z$ depending on each other, the relation
          $$ left(frac{partial x}{partial y}right)_zleft(frac{partial y}{partial z} right)_xleft(frac{partial z}{partial x}right)_y = -1$$
          holds.






          share|cite|improve this answer









          $endgroup$



          This is not a simple application of partial derivatives, since the variables that are being held constant vary here, but an instance of the triple product rule, which says that for any three quantities $x,y,z$ depending on each other, the relation
          $$ left(frac{partial x}{partial y}right)_zleft(frac{partial y}{partial z} right)_xleft(frac{partial z}{partial x}right)_y = -1$$
          holds.







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered 4 hours ago









          ACuriousMind♦ACuriousMind

          72.5k18126318




          72.5k18126318























              2












              $begingroup$

              This all starts from the basic relationship $$dP=left(frac{partial P}{partial T}right)_VdT+left(frac{partial P}{partial V}right)_TdV$$Since, at constant pressure, dP=0, if we solve for dT/dV at constant pressure, we obtain:
              $$left(frac{partial T}{partial V}right)_P=-frac{left(frac{partial P}{partial V}right)_T}{left(frac{partial P}{partial T}right)_V}$$






              share|cite|improve this answer









              $endgroup$


















                2












                $begingroup$

                This all starts from the basic relationship $$dP=left(frac{partial P}{partial T}right)_VdT+left(frac{partial P}{partial V}right)_TdV$$Since, at constant pressure, dP=0, if we solve for dT/dV at constant pressure, we obtain:
                $$left(frac{partial T}{partial V}right)_P=-frac{left(frac{partial P}{partial V}right)_T}{left(frac{partial P}{partial T}right)_V}$$






                share|cite|improve this answer









                $endgroup$
















                  2












                  2








                  2





                  $begingroup$

                  This all starts from the basic relationship $$dP=left(frac{partial P}{partial T}right)_VdT+left(frac{partial P}{partial V}right)_TdV$$Since, at constant pressure, dP=0, if we solve for dT/dV at constant pressure, we obtain:
                  $$left(frac{partial T}{partial V}right)_P=-frac{left(frac{partial P}{partial V}right)_T}{left(frac{partial P}{partial T}right)_V}$$






                  share|cite|improve this answer









                  $endgroup$



                  This all starts from the basic relationship $$dP=left(frac{partial P}{partial T}right)_VdT+left(frac{partial P}{partial V}right)_TdV$$Since, at constant pressure, dP=0, if we solve for dT/dV at constant pressure, we obtain:
                  $$left(frac{partial T}{partial V}right)_P=-frac{left(frac{partial P}{partial V}right)_T}{left(frac{partial P}{partial T}right)_V}$$







                  share|cite|improve this answer












                  share|cite|improve this answer



                  share|cite|improve this answer










                  answered 3 hours ago









                  Chester MillerChester Miller

                  15.3k2824




                  15.3k2824






















                      Srijan Ghosh is a new contributor. Be nice, and check out our Code of Conduct.










                      draft saved

                      draft discarded


















                      Srijan Ghosh is a new contributor. Be nice, and check out our Code of Conduct.













                      Srijan Ghosh is a new contributor. Be nice, and check out our Code of Conduct.












                      Srijan Ghosh is a new contributor. Be nice, and check out our Code of Conduct.
















                      Thanks for contributing an answer to Physics Stack Exchange!


                      • Please be sure to answer the question. Provide details and share your research!

                      But avoid …



                      • Asking for help, clarification, or responding to other answers.

                      • Making statements based on opinion; back them up with references or personal experience.


                      Use MathJax to format equations. MathJax reference.


                      To learn more, see our tips on writing great answers.




                      draft saved


                      draft discarded














                      StackExchange.ready(
                      function () {
                      StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fphysics.stackexchange.com%2fquestions%2f465965%2fwhy-does-the-negative-sign-arise-in-this-thermodynamic-relation%23new-answer', 'question_page');
                      }
                      );

                      Post as a guest















                      Required, but never shown





















































                      Required, but never shown














                      Required, but never shown












                      Required, but never shown







                      Required, but never shown

































                      Required, but never shown














                      Required, but never shown












                      Required, but never shown







                      Required, but never shown







                      -

                      Popular posts from this blog

                      Anexo:Material bélico de la Fuerza Aérea de Chile Índice Aeronaves Defensa...

                      Image
                      Fuerza Aérea de Chile materialFuerza Aérea de ChileJDAMAdvanced HawkTA-50Alenia Aermacchi M-346FLIRHydrahttp://www.infodefensa.com/latam/2014/02/26/noticia-fuerza-aerea-chile-interesada-a400m.htmlhttps://www.scramble.nl/index.php?option=com_mildb&view=search Aquí esta todo el material bélico de la Fuerza Aérea de Chile. Índice 1 Aeronaves 2 Defensa Antiaérea 3 Armamento 4 Material de reserva 5 Véase también 6 Referencias Aeronaves Aeronave Origen Tipo Versiones en servicio Total [ 1 ] ​ Fotos Aeronaves de la FACH (225) Lockheed Martin F-16 Estados Unidos   Estados Unidos   Países Bajos Caza Polivalente -AIM120/AAM Derby/JDAM/WCMD -Serán modernizados con radares AESA, <br>Se sumarán unidades adicionales 11A 7B 6C 4D 46 Northrop F-5E Tigre III Estados Unidos   Estados Unidos Caza Polivalente -Sistema de guerra electrónica mejorado -Equipado con el misil AAM Derby y casco Dash II...
                      Read more

                      Always On Availability groups resolving state after failover - Remote harden of transaction...

                      Image
                      Should corporate security training be tailored based on a users' job role? Does human life have innate value over that of other animals? Limit involving inverse functions Father gets chickenpox, but doesn't infect his two children. How is this possible? Is it possible to re-order a List of continous entries? Who, if anyone, was the first astronaut to return to earth in a different vessel? The totem pole can be grouped into Identical projects by students at two different colleges: still plagiarism? Sci fi book, man buys a beat up spaceship and intervenes in a civil war on a planet and eventually becomes a space cop How to not...
                      Read more

                      update json value to null Announcing the arrival of Valued Associate #679: Cesar Manara ...

                      Image
                      Seeking colloquialism for “just because” Sci-Fi book where patients in a coma ward all live in a subconscious world linked together Understanding Ceva's Theorem Dating a Former Employee How to find out what spells would be useless to a blind NPC spellcaster? Why am I getting the error "non-boolean type specified in a context where a condition is expected" for this request? Why are both D and D# fitting into my E minor key? Do I really need recursive chmod to restrict access to a folder? How to override model in magento2? How do I stop a creek from eroding my steep embankment? Wit...
                      Read more