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In Homework 08 we found the Legendre Transform on the internal energy with respect to entropy and number of moles (.e., 0G(T,V, 4) = U*[S
In Homework 08 we found the Legendre Transform on the internal energy with respect to entropy and number of moles (.e., 0G(T,V, 4) = U*[S T,N u]) was (U G = U-S (as)v,N - N en sy G = U ST Nu and we called this the 'Grand Canonical potential. One can write = dU SdT TdS Ndu udN dU = TDS PdV + udN dog = -PdV SDT Ndu (1) d MSEG 211 - Spring 2022 The Grand Canonical ensemble is described by the Grand Canonical partition function E(T,V, u), which is analogous to 2(U,V,N) in the Boltzmann equation. Furthermore, it can be shown that the Grand Canonical potential is related to the Grand Canonical partition function through the following relationship: g = -kpT in E (2) Using relationship (1) and (2) write an expression of P, S, and N in terms of the Grand Canonical partition function. In Homework 08 we found the Legendre Transform on the internal energy with respect to entropy and number of moles (.e., 0G(T,V, 4) = U*[S T,N u]) was (U G = U-S (as)v,N - N en sy G = U ST Nu and we called this the 'Grand Canonical potential. One can write = dU SdT TdS Ndu udN dU = TDS PdV + udN dog = -PdV SDT Ndu (1) d MSEG 211 - Spring 2022 The Grand Canonical ensemble is described by the Grand Canonical partition function E(T,V, u), which is analogous to 2(U,V,N) in the Boltzmann equation. Furthermore, it can be shown that the Grand Canonical potential is related to the Grand Canonical partition function through the following relationship: g = -kpT in E (2) Using relationship (1) and (2) write an expression of P, S, and N in terms of the Grand Canonical partition function
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