Gibbs free energy partial derivative

In summary, The conversation discusses the method for finding the partial derivative of g with respect to T at constant P. It is determined that the correct method involves taking the derivative of g with respect to T while keeping P constant. The method of finding the derivative of g with respect to T at constant P by using the partial derivative formula is not accurate as it assumes that u, v, and s are constant, which they are not.
  • #1
spaghetti3451
1,344
33
g = u + Pv - Ts

To find the partial derivative of g with respect to T at constant P, we do the following.

dg = du + vdP + Pdv - Tds - sdT and du = Tds - Pdv.

Therefore, dg = vdP - sdT.

At constant pressure, dg = - sdT.
Therefore, the partial derivative is - s.

I think we could have found this result equally well by just taking the derivative of g with respect to T keeping P constant. u, v and s are constant, so the answer is - s.

Which method do you think is the right one?
 
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  • #2
The method you've detailed above is the right one. It's not true where you say that u, v and s are constant -- they're not.
 
  • #3
Just to confirm: Are you saying that the first method is correct and the second is not?

Why are u, v and s not constant?
 

What is Gibbs free energy partial derivative?

Gibbs free energy partial derivative is a mathematical concept that measures the change in Gibbs free energy with respect to changes in a specific variable. It is denoted by ∂G/∂x, where G represents Gibbs free energy and x represents the variable.

Why is Gibbs free energy partial derivative important?

Gibbs free energy partial derivative is important because it helps in determining the direction and extent of a chemical reaction. It can also be used to calculate the equilibrium constant of a reaction, which provides information about the spontaneity of the reaction.

How is Gibbs free energy partial derivative calculated?

Gibbs free energy partial derivative is calculated using the equation ∂G/∂x = ∂H/∂x - T∂S/∂x, where H is the enthalpy, T is the temperature, and S is the entropy. This equation is derived from the fundamental relationship of thermodynamics, dG = dH - TdS.

What is the physical meaning of Gibbs free energy partial derivative?

The physical meaning of Gibbs free energy partial derivative is the change in Gibbs free energy per unit change in the specified variable. This provides information about how the Gibbs free energy of a system will change as a result of changes in the variable.

What are some practical applications of Gibbs free energy partial derivative?

Gibbs free energy partial derivative is used in various fields, such as chemistry, biology, and engineering. It is useful in predicting the spontaneity and direction of chemical reactions, determining the equilibrium constant of a reaction, and analyzing thermodynamic processes. It is also used in the design and optimization of chemical processes and in the study of biological systems.

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