![]() The tendency of the total entropy to increase therefore means that the grand free energy tends to decrease (since dStotal is positive, dΦ must be negative in order to make −dΦ/T positive). The total entropy of the system plus reservoir (expressed in terms of system variables) is then dStotal = − 1 T (dU − TdS − µdN) = − 1 T dΦ. Assuming V fixed, apply the thermodynamic identity to dSR (solve the ex- pression for dUR in terms of dSR), and use the fact that dUR = −dU and dNR = −dN to write dSR in terms of system variables. b) As was done for F and G in chapter 5.2 in Schroeder, express an infinitesimal change in the total entropy Stotal as a sum of changes in the entropy S of the 1 system and the entropy SR of the reservoir it is in contact with: dStotal = dS + dSR. T, V or µ is obtained by holding the two other quantities fixed:( ∂Φ ∂T ) V,µ = −S, ( ∂Φ ∂V ) T,µ = −P, ( ∂Φ ∂µ ) T,V = −N. Inserting the thermodynamic identity for dU gives dΦ = −PdV − SdT −Ndµ. ![]() Download Schroeder Solutions for Introduction to Thermal Physics and more Thermal Physics Exercises in PDF only on Docsity!Solutions to exercises week 45 FYS2160 Kristian Bjørke, Knut Oddvar Høie Vadla NovemSchroeder 5.23 a) Writing Φ = U −TS−µN in terms of infinitesimal changes of the quantities involved: dΦ = dU − TdS − SdT − µdN −Ndµ.
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