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LCSphysicist
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The question is simply why i can't use ∂U/∂V = -P?
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Thermodynamics: internal energy and pressure
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SUMMARY
The discussion centers on the relationship between internal energy (U), volume (V), and pressure (P) in thermodynamics, specifically addressing the equation ∂U/∂V = -P. It is established that for this equation to hold true, temperature (T) must be held constant, leading to the correct formulation: (∂U/∂V)_T = -P + T(∂P/∂T)_V. Participants emphasize the significance of recognizing which variables are constant when taking partial derivatives, highlighting a common misconception among beginners in thermodynamics.
PREREQUISITES- Understanding of thermodynamic principles, specifically internal energy and pressure.
- Familiarity with partial derivatives and their application in thermodynamics.
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Students of thermodynamics, physics enthusiasts, and professionals in engineering fields who seek a deeper understanding of the relationships between internal energy, pressure, and volume in thermodynamic systems.
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?
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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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