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## Homework Statement

The 4 fundamental equations of thermodynamics are:

*dE = TdS - PdV*

dH = TdS + VdP

dG = VdP - SdT

dA = - PdV - SdT

dH = TdS + VdP

dG = VdP - SdT

dA = - PdV - SdT

Supose a gas obeys the equation of state

P = [itex]\frac{nRT}{V}[/itex] - [itex]\frac{an^{2}}{V^{2}}[/itex]

Use one of the fundamental equations to find the change in Helmholtz energy (A) when one mole of gas expands isothermally from 20 L to 40 L at 300 K. Let a = 0.1 Pa m

^{6}mol

^{-2}. (1 L = 10

^{-3}m

^{3}).

## Homework Equations

Well the four fundamental equations should be a given. In particular, the fourth one for Helmholtz energy dA.

## The Attempt at a Solution

Well I tried integrating the fourth fundamental equation

[itex]\int[/itex]dA = -[itex]\int[/itex]PdV -[itex]\int[/itex]SdT

And since the process is isothermal, the last term is zero, and the Helmholtz energy is just the product of the pressure P and the change in volume ΔV.

But how would I obtain the pressure P? My first guess would be to plug in the known values into the equation of state:

P = [itex]\frac{nRT}{V}[/itex] - [itex]\frac{an^{2}}{V^{2}}[/itex]

I'm letting R = 8.314 [itex]\frac{Pa m^{3}}{K mol}[/itex] since that would lead to a dimensionally correct answer in Pa.

**My problem is what to plug in for volume considering I have two values.**