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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
- Thread starter LCSphysicist
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In summary, when taking partial derivatives, it is important to keep in mind which variables are being held constant. This is especially crucial in equations involving thermodynamics, such as the one presented in the conversation where the use of partial derivatives is necessary. The equation in question, ##P = -\large \frac{\partial U}{\partial V}##, is only valid when the variables T and V are kept constant. It is important to not overlook this fact, as it can lead to errors and misunderstandings in more advanced concepts of thermodynamics.
The question is simply why i can't use ∂U/∂V = -P?
(
- #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: $$\left(\frac{\partial U}{\partial V}\right)_T=-P+T\left(\frac{\partial P}{\partial T}\right)_V$$
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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!
1. What is internal energy in thermodynamics?
Internal energy in thermodynamics refers to the total energy contained within a system, including the kinetic and potential energy of its particles. It is a measure of the system's microscopic energy and is affected by factors such as temperature, pressure, and composition.
2. How is internal energy related to temperature?
Internal energy and temperature are directly proportional to each other. As the temperature of a system increases, so does its internal energy, and vice versa. This relationship is described by the equation E = mc2, where E is the internal energy, m is the mass of the system, and c is the speed of light.
3. What is the difference between internal energy and enthalpy?
Internal energy and enthalpy are both measures of energy in a system, but they differ in how they take into account the energy required to maintain a constant pressure. Enthalpy includes this energy, while internal energy does not. In other words, enthalpy takes into account the work done by the system on its surroundings, while internal energy does not.
4. How does pressure affect the internal energy of a system?
Pressure can affect the internal energy of a system in two ways. First, an increase in pressure can cause the particles in the system to move closer together, resulting in an increase in the system's internal energy. Second, changing the pressure of a system can also change its temperature, which in turn affects its internal energy.
5. Can internal energy be created or destroyed?
According to the first law of thermodynamics, energy cannot be created or destroyed, only transferred or converted from one form to another. This means that the internal energy of a system can change, but it cannot be created or destroyed. It is always conserved in a closed system.
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