# Gibbs free energy

#### koomanchoo

would anyone happen to know what the expression for an isothermal change in Gibbs free energy for a liquid is when the pressure changes from pi to pf. Also an expression for when its a perfect gas?
i cant seem to figure them out.. and how would they be deduced?
i've come across one equation: Gf=Gi +nrtln(pf/pi) <- that i think may be for perfect gas. but i'm still unsure abotu the first expression.
thanks for any help.

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#### Iraides Belandria

For a pure sustance the variation of the Gibbs free energy, dG, is equal to
dG= VdP-SdT
where V,P,S,T are volume, pressure, entropy and temperature, respectively. At constant T, above equation becomes
dG= VdP
For an ideal gas PV= nRT, then
dG= nRT dP/P
Integrating at constant T between Pi and Pf
Gf=Gi + nRT Ln ( Pf/Pi)

Where Gf and Gi are the Gibbs free energy at T and Pf , and at T and Pi, respectively. You can assume any value for Gi .

for a liquid you may use a convenient equation of state valid for the liquid phase. If the liquid is incomprensible V is almost independent of pressure, then
Gf=Gi + V(Pf-Pi)

#### dextercioby

Homework Helper
And one more thing,it's called Gibbs potential or free enthalpy."Free energy" is the name for Helhmoltz potential customarily denoted by "F".

Daniel.

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