Exploring the Total Derivative of Gibbs Free Energy in a Closed System"

In summary, the conversation discusses finding the total derivative of the Gibbs free energy with respect to volume, temperature, amount of substance, and surface in a closed system where the temperature is constant. The question arises of how the total derivative changes in this scenario, with the assumption that volume and surface may not be constant.
  • #1
Lindsayyyy
219
0
Hi everyone

Homework Statement



Let's say I want to do the totale drivative of the Gibbs free energy in dependent of: volume, temperature, amount of substance and surface. And let's say afterwards we have a closed system where the temperature is constant. How does the total derivative change?



Homework Equations


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The Attempt at a Solution



I guess I know that the amount of substance doesn't change in a closed system, so my dn=0 and this part gets lost, also dT=0. But I'm not sure about the surface, does that change aswell? I think the Volume can't be disregarded.

Thanks for your help
 
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  • #2
If all you are given is that the temperature is constant, I would see no reason to assume that volume or "surface" are constant.

(What, exactly, do you mean by "surface"? All other variables you mention are numbers.)
 

1. What is the total derivative of Gibbs Free Energy?

The total derivative of Gibbs Free Energy is a mathematical concept that describes the change in Gibbs Free Energy with respect to changes in temperature, pressure, and composition in a closed system. It is an important tool in thermodynamics for predicting how a system will behave under different conditions.

2. Why is exploring the total derivative of Gibbs Free Energy important?

Exploring the total derivative of Gibbs Free Energy allows us to understand and predict the behavior of a closed system under different conditions. This is crucial in many fields, including chemistry, physics, and engineering, as it allows us to design and optimize systems for specific purposes.

3. How is the total derivative of Gibbs Free Energy calculated?

The total derivative of Gibbs Free Energy can be calculated using the partial derivatives of Gibbs Free Energy with respect to temperature, pressure, and composition. It is typically represented by the symbol dG and is expressed as:

dG = ∂G/∂T dT + ∂G/∂P dP + ∂G/∂ni dni

4. What information can we obtain from the total derivative of Gibbs Free Energy?

The total derivative of Gibbs Free Energy provides us with information about how the Gibbs Free Energy of a system will change when one of its variables (temperature, pressure, or composition) is altered. It can also help us determine the equilibrium state of a closed system under different conditions.

5. Are there any limitations to the total derivative of Gibbs Free Energy?

While the total derivative of Gibbs Free Energy is a useful tool, it does have some limitations. It assumes that the system is in equilibrium and that all changes are infinitesimal. It also does not account for external factors, such as non-ideal behavior or chemical reactions, which may affect the system's behavior.

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