 21
 5
 Homework Statement
 a) Calculate the entropy change for an isothermal expansion of a Van Der Waals Gas from V1 to V2. b) Use this to calculate ΔS for 1 mole of NH3 from 2L to 20L at 298K. c) Compare this to an Ideal Gas
 Homework Equations

ΔS = ∫ (dq/T)
PV=nRT Ideal Gas
[P + a/(v/n)[SUP]2[/SUP]][v/n  b] = RT Not Ideal
Part (a)
ΔS = ∫ (dq/T)
because: dq = PdV = (nRT/V)dV
Then:
ΔS = ∫ (1/T)*(nRT/V)dV
ΔS = nR ∫(1/V) dV
ΔS =nR[ln(V2/V1)]
Part (b)
This is where I'm stuck. I know [P + a/(v/n)^{2}][v/n  b] = RT can be solved for P and simplified to
P = [RT/(vb)][a/v^{2}] since n=1mol
But I don't know how to proceed from here, to solve for v and in turn solve ΔS. I can't use Boyle's Law and I was told there's another method besides NewtonRapson.
Part (c)
Take ΔS =nR(ln(V2/V1) from part (a) and input: V2=20L V1=2L
ΔS = (1mol)(8.3145 J*mol/K)(ln(10))=19.15 J/K
19.15J/K  (part b) = Final Answer
ΔS = ∫ (dq/T)
because: dq = PdV = (nRT/V)dV
Then:
ΔS = ∫ (1/T)*(nRT/V)dV
ΔS = nR ∫(1/V) dV
ΔS =nR[ln(V2/V1)]
Part (b)
This is where I'm stuck. I know [P + a/(v/n)^{2}][v/n  b] = RT can be solved for P and simplified to
P = [RT/(vb)][a/v^{2}] since n=1mol
But I don't know how to proceed from here, to solve for v and in turn solve ΔS. I can't use Boyle's Law and I was told there's another method besides NewtonRapson.
Part (c)
Take ΔS =nR(ln(V2/V1) from part (a) and input: V2=20L V1=2L
ΔS = (1mol)(8.3145 J*mol/K)(ln(10))=19.15 J/K
19.15J/K  (part b) = Final Answer