- #1
Youngster
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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
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 m6 mol-2. (1 L = 10-3 m3).
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.