- #1

Ignitia

- 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

- Relevant 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/(v-b)]-[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 Newton-Rapson.

**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__