Question about the derivative of Gibbs Energy

[yungwun22]

Homework Statement

There is a formula which says the change (delta) of volume of a mixture is equal to the partial derivative of delta G with respect to pressure at constant temperature. I don't understand how there can be a derivative and the delta used at the same time on G. I thought that derivatives were used for infinitesimal changes and that delta was used for larger ones.

Homework Equations

The Attempt at a Solution

 

[Mapes]

Perhaps the delta signifies not the finite difference between values of G at different pressure or volume (which, as you said, would be improper to combine with differentials), but the finite difference between values of G for two separate phases of the same material.

 

[Blueshift5]

The derivative of Gibbs Energy, also known as the Helmholtz free energy, is a fundamental concept in thermodynamics that helps us understand the relationship between a system's energy, temperature, and pressure. The formula you mentioned, which states that the change in volume of a mixture is equal to the partial derivative of delta G with respect to pressure at constant temperature, is known as the Maxwell relation. This relation is derived from the fundamental thermodynamic equations and is used to calculate the change in volume of a system under certain conditions.

The use of "delta" in this context simply indicates a change in a variable, in this case, the change in Gibbs Energy. This change can be infinitesimal or larger, depending on the specific situation. The fact that we are using a derivative and "delta" at the same time does not contradict the concept of derivatives being used for infinitesimal changes. In fact, the derivative itself is an infinitesimal change in one variable with respect to another.

To better understand the concept, it may be helpful to think of "delta" as a shorthand notation for "change in". So the formula can be rephrased as "the change in volume is equal to the change in Gibbs Energy with respect to pressure at constant temperature". This makes it clearer that the derivative is being used to calculate the change in volume, just as it is used to calculate infinitesimal changes in other contexts.

I hope this explanation helps clarify your confusion about the use of derivatives and "delta" in the formula for the change in volume of a mixture. Keep in mind that thermodynamics can be a complex topic and it's normal to have questions and seek clarification. I encourage you to continue exploring and learning about this fascinating field of science.