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- https://phys.libretexts.org/Courses/Georgia_State_University/GSU-TM-Introductory_Physics_II_(1112)/zz%3A_Back_Matter/10%3A_13.1%3A_Appendix_J-_Physics_Formulas_(Wevers)/1.08%3A_ThermodynamicsClassical thermodynamics and its statistical basis
- https://phys.libretexts.org/Learning_Objects/A_Physics_Formulary/Physics/08%3A_ThermodynamicsClassical thermodynamics and its statistical basis
- https://phys.libretexts.org/Bookshelves/Thermodynamics_and_Statistical_Mechanics/Thermodynamics_and_Statistical_Mechanics_(Nair)/06%3A_Thermodynamic_Relations_and_Processes/6.01%3A_Maxwell_RelationsThis page shows the derivation of the four Maxwell relations from the basic relations given for a system with one constituent with a fixed number of particles, from equation 5.1.10, the first law, and...This page shows the derivation of the four Maxwell relations from the basic relations given for a system with one constituent with a fixed number of particles, from equation 5.1.10, the first law, and the second law.
- https://phys.libretexts.org/Bookshelves/Thermodynamics_and_Statistical_Mechanics/Book%3A_Thermodynamics_and_Statistical_Mechanics_(Arovas)/02%3A_Thermodynamics/2.08%3A_Maxwell_RelationsIn general, we have \[\begin{aligned} \hbox{\tt THIS}&\hbox{\tt\ SPACE AVAILABLE}& dE&=T\,dS + y\,dX + \mu\,dN \vph\\ F&=E-TS & dF &= -S\,dT+ y\,dX + \mu\,dN \vph\\ \CH&=E-yX & d\CH &= T\,dS - X\,dy +...In general, we have \[\begin{aligned} \hbox{\tt THIS}&\hbox{\tt\ SPACE AVAILABLE}& dE&=T\,dS + y\,dX + \mu\,dN \vph\\ F&=E-TS & dF &= -S\,dT+ y\,dX + \mu\,dN \vph\\ \CH&=E-yX & d\CH &= T\,dS - X\,dy + \mu\,dN \vph\\ G &= E - TS - yX & dG &= -S\,dT -X\,dy + \mu\,dN \vph\\ \Omega &= E - TS - \mu N & d\Omega &= -S\,dT+y\,dX -N\,d\mu\ .\end{aligned}\] Generalizing \((-p,V)\to (y,X)\), we also obtain, mutatis mutandis, the following Maxwell relations: \[\begin{aligned} \pabc{T}{X}{S,N}&=\pabc{y}{S}{…
- https://phys.libretexts.org/Bookshelves/Thermodynamics_and_Statistical_Mechanics/Heat_and_Thermodynamics_(Tatum)/12%3A_Free_Energy/12.05%3A_Summary_the_Maxwell_Relations_and_the_Gibbs-Helmholtz_Relations\[\left(\frac{\partial U}{\partial S}\right)_{V}=T \quad\left(\frac{\partial U}{\partial V}\right)_{S}=-P\] \[\left(\frac{\partial H}{\partial S}\right)_{P}=T \quad\left(\frac{\partial H}{\partial P}\...\[\left(\frac{\partial U}{\partial S}\right)_{V}=T \quad\left(\frac{\partial U}{\partial V}\right)_{S}=-P\] \[\left(\frac{\partial H}{\partial S}\right)_{P}=T \quad\left(\frac{\partial H}{\partial P}\right)_{S}=V\] \[\left(\frac{\partial A}{\partial T}\right)_{V}=-S \quad\left(\frac{\partial A}{\partial V}\right)_{T}=-P\] \[\left(\frac{\partial G}{\partial T}\right)_{P}=-S \qquad\left(\frac{\partial G}{\partial P}\right)_{T}=V\]
