Question

1. Meaning of \"Extensive\" (20 pts): Consider the Helmholz Free energy $F(N, V, T)$. The fact that $F$ is extensive can be expressed mathematically as, $F(\lambda N, \lambda V, T) = \lambda F(N, V, T)$ (1) From this show that $G = F + PV = N \frac{\partial F}{\partial N}_{V, T} = \mu N$ (2) Hint: Take derivative with respect to $\lambda$ on both sides of equation (1).

          1. Meaning of \"Extensive\" (20 pts): Consider the Helmholz Free energy $F(N, V, T)$. The fact that $F$ is extensive can be expressed mathematically as,
$F(\lambda N, \lambda V, T) = \lambda F(N, V, T)$ (1)
From this show that
$G = F + PV = N \frac{\partial F}{\partial N}_{V, T} = \mu N$ (2)
Hint: Take derivative with respect to $\lambda$ on both sides of equation (1).

1. Meaning of Ëxtensive(̈20 pts): Consider the Helmholz Free energy F(N, V, T). The fact that F is extensive can be expressed mathematically as,
F(λ N, λ V, T) = λ F(N, V, T) (1)
From this show that
G = F + PV = N (∂ F)/(∂ N)V, T = μ N (2)
Hint: Take derivative with respect to λ on both sides of equation (1).

Added by Colin A.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Penny Riley

05/11/2023

Step 1

∂/∂N [F(XN,XV,T)] = ∂/∂N [XF(N,V,T)] Show more…

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Texts: 1. Meaning of "Extensive" (20 pts): Consider the Helmholtz Free energy F(N,V,T). The fact that F is extensive can be expressed mathematically as, F(XN,XV,T)=XF(N,V,T) (1) From this, show that ∂G/∂N=F+PV=N (2) Hint: Take the derivative with respect to N on both sides of equation (1)