Fundamental equation (thermodynamics) from Euler's equation

In summary, the fundamental equation in thermodynamics is a mathematical representation of the relationship between the thermodynamic properties of a system. It was first introduced by the Swiss mathematician Leonhard Euler in the 18th century and includes variables such as temperature, pressure, volume, entropy, and internal energy. It is derived using calculus and the laws of thermodynamics and serves as the foundation for solving problems in engineering, physics, and chemistry.
  • #1
VVS2000
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by substituting all values in the euler equation you get most of the terms in the fundamental equation but not (N/No)^-(c+1)
How do you get this term?
 
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  • #2
VVS2000 said:
Summary:: So in the fundamental equation, there's this one term which doesn't seem like it should be there but it is.

View attachment 259073View attachment 259074View attachment 259075
by substituting all values in the euler equation you get most of the terms in the fundamental equation but not (N/No)^-(c+1)
How do you get this term?
Your notebook is unreadable.
 

1. What is the fundamental equation of thermodynamics?

The fundamental equation of thermodynamics is a mathematical expression that relates the various thermodynamic properties of a system. It is based on the first law of thermodynamics, which states that energy cannot be created or destroyed, only transferred or converted.

2. What is Euler's equation in thermodynamics?

Euler's equation is a specific form of the fundamental equation of thermodynamics that is used to describe the behavior of an ideal gas. It relates the internal energy, pressure, and volume of a gas at a constant temperature.

3. How is Euler's equation derived?

Euler's equation is derived from the first and second laws of thermodynamics, along with the ideal gas law. It is a result of applying the laws of conservation of energy and mass to a closed system.

4. What is the significance of Euler's equation in thermodynamics?

Euler's equation is significant because it provides a mathematical framework for understanding the behavior of ideal gases. It is also used in the study of fluid dynamics and other areas of physics.

5. Can Euler's equation be applied to real-world systems?

While Euler's equation is derived from ideal gas behavior, it can be applied to real-world systems as an approximation. However, in order to accurately describe the behavior of more complex systems, modifications must be made to account for non-ideal behavior.

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