- #1
LCSphysicist
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- Homework Statement
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The question is simply why i can't use ∂U/∂V = -P?
(
Thermodynamics: internal energy and pressure
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Homework Help Overview
The discussion revolves around the relationship between internal energy and pressure in thermodynamics, specifically focusing on the use of partial derivatives in this context.
Discussion Character
- Conceptual clarification, Assumption checking
Approaches and Questions Raised
- Participants explore the conditions under which the equation ∂U/∂V = -P is valid, questioning which variables need to be held constant during differentiation.
Discussion Status
Some participants have offered insights into the correct formulation involving temperature and pressure, while others reflect on their initial misunderstandings regarding the treatment of variables in partial derivatives. The discussion appears to be productive, with various interpretations being explored.
Contextual Notes
There is an acknowledgment of the complexity involved in thermodynamic relationships and the importance of understanding the implications of holding certain variables constant when taking partial derivatives.
The question is simply why i can't use ∂U/∂V = -P?
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- #2
TSny
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When taking partial derivatives, it is important to know what variables are being kept constant.LCSphysicist said:
In order for ##P = -\large \frac{\partial U}{\partial V}## to be true, what variables are to be kept constant?
- #3
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You should be using: $$\left(\frac{\partial U}{\partial V}\right)_T=-P+T\left(\frac{\partial P}{\partial T}\right)_V$$
- #4
LCSphysicist
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Yes, when i started thermodynamics i wrongly ignored this terms aside thinking they would be constant anyway as we are dealing with partial derivatives... Now i am doing more advanced i am seeing the importance and the lacune!
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