Partial Differential - Thermodynamics

In summary, the individual is new to the platform and seeking help with a physics problem involving the partial derivatives of energy and pressure. They are not well-versed in physics and are struggling to solve the problem. The equation is represented in Latex format with a bar over E and p, indicating that it is an average.
  • #1
Rdgmol
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0
Hello guys!
I'm new here, so sorry if I'm posting on wrong place or wrong way.

I just need help to solve a problem:
(∂E/∂V)β, N + β(∂p/∂β)N, V = - p

PS: There is a bar over E and over p (this in both sides) - meaning that is an average.

I don't know how to start, so any help will be amazing.
I'm not a physicist, so I'm having a bad time trying to solve this.

Thank you very much!

Equation latex
\left(\frac{\partial \overline{E}}{\partial V}\right)_{\beta, N} + \beta \left(\frac{\partial \overline{p}}{\partial \beta}\right)_{N, V} = - \overline{p}
 
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  • #2
Rdgmol said:
Equation latex
\left(\frac{\partial \overline{E}}{\partial V}\right)_{\beta, N} + \beta \left(\frac{\partial \overline{p}}{\partial \beta}\right)_{N, V} = - \overline{p}

FYI in this forum

If you put your Latex code between double #'s you get your equation in line with the
text ##\left(\frac{\partial \overline{E}}{\partial V}\right)_{\beta, N} + \beta \left(\frac{\partial \overline{p}}{\partial \beta}\right)_{N, V} = - \overline{p}##

if you put your Latex code between double $'s you get your equation alone and centered

$$\left(\frac{\partial \overline{E}}{\partial V}\right)_{\beta, N} + \beta \left(\frac{\partial \overline{p}}{\partial \beta}\right)_{N, V} = - \overline{p}$$
 
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Likes Rdgmol

1. What is a partial differential equation?

A partial differential equation (PDE) is a mathematical equation that involves multiple variables and their partial derivatives. It describes the relationship between these variables and can be used to model various physical phenomena, including thermodynamic processes.

2. How is thermodynamics related to partial differential equations?

Thermodynamics is the branch of physics that deals with the relationships between energy, heat, and work. Many thermodynamic processes can be described using partial differential equations, which help to understand and predict the behavior of thermodynamic systems.

3. What is the role of boundary conditions in partial differential equations for thermodynamics?

Boundary conditions are specific conditions that are applied at the boundaries of a thermodynamic system in order to fully define the behavior of the system. These conditions are necessary in solving partial differential equations for thermodynamics, as they provide the necessary information to determine the solution.

4. Can partial differential equations be solved analytically?

In most cases, partial differential equations for thermodynamics cannot be solved analytically. This means that there is no exact mathematical solution and numerical methods must be used to approximate the solution. However, there are some special cases where analytical solutions are possible.

5. How are partial differential equations used in thermodynamic research and engineering?

Partial differential equations are used extensively in thermodynamic research and engineering to model and understand various processes, such as heat transfer, fluid flow, and chemical reactions. They are also used in the design and optimization of thermodynamic systems, such as engines and power plants.

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