Register to reply

Determining an expression for an entropy equation

by Benzoate
Tags: determining, entropy, equation, expression
Share this thread:
Benzoate
#1
Mar11-08, 06:58 AM
P: 569
1. The problem statement, all variables and given/known data

Calculate the entropy of mixing for a system of two monatomic ideal gases, A and B ,whose relative proportion is arbitrary. Let N be the total number of molecules and let x be the fraction of these that are of species B. You should find
delta(S) mixing=-Nk[x ln x +(1-x) ln (1-x)

2. Relevant equations

delta (S(total))=delta(S(A)) + delta(S(B))=2Nk ln 2
S=Nk[ln((V/N)(((4*pi*m*U)/3Nh^2)^(3/2))+2.5]


3. The attempt at a solution

according to my thermal physics text, delta(S(A))=Nk ln 2 . The problem says that in species B , x is just a fraction of N. Then , I think I would have to conclude that delta(S(B))=x/N*(k)*ln(2).

so would my expressison be :delta(S(mixing))=delta(S(A))+delta(S(B))=Nk ln 2+ xk/N*(ln(2))
Phys.Org News Partner Science news on Phys.org
Experts defend operational earthquake forecasting, counter critiques
EU urged to convert TV frequencies to mobile broadband
Sierra Nevada freshwater runoff could drop 26 percent by 2100
Mapes
#2
Mar11-08, 08:27 AM
Sci Advisor
HW Helper
PF Gold
Mapes's Avatar
P: 2,532
You can't apply [itex]\Delta S_A=Nk\ln 2[/itex] to the general problem; that's the increase in entropy for a single gas expanding into twice its original volume. If [itex]x[/itex] can vary, there's no reason to assume the volume doubles.

Also, remember that as [itex]x[/itex] increases, there are no longer [itex]N[/itex] molecules of gas A but rather [itex](1-x)N[/itex].

One common way to show your desired relation is to assume that each gas expands from its original volume into the total volume and to use the Maxwell relation


[tex]\left(\frac{\partial S}{\partial V}\right)_T=\left(\frac{\partial P}{\partial T}\right)_V=\frac{nR}{V}\quad[/tex]

[tex]dS=\frac{nR}{V}\,dV[/tex]

to calculate the change in entropy.


Register to reply

Related Discussions
Is the Entropy of the Universe Zero? Entropy as Entanglement) Quantum Physics 10
Determining uncertanity from the wave equation Quantum Physics 3
Determining the Line of Symmetry of a Reciprocal Equation. Precalculus Mathematics Homework 1
Determining an Equation of Motion Introductory Physics Homework 3
Finding an expression for charge (Q) given an I-V equation Engineering, Comp Sci, & Technology Homework 1