The fundamental equation - Intensive forms and state functions

6 important questions on The fundamental equation - Intensive forms and state functions

How is the intensive quantity of internal energy defined?

By deviding the extensive variable E by the number of atoms, moles or even the volume

How to find the fundamental derivative of e = e(s,v) using the partial derivatives?

Since
By first taking the s derivative:

Then the v derivative:

We find that we can write

How is the chemical potential be expressed in partial derivatives in the intensive form of the energy function?

By taking the fundamental internal energy equation and dividing by N. After rearranging this gives an expression for the chemical potential.
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How many pieces of intensive information are needed to completely specify the thermodynamic state?

For a single component system 2 pieces of information need to be given to completely specify the thermodynamic state of the system. For each component extra an additional piece of information needs to be known

What are conjugate variable pairs?

A conjugate variable pair consists of the partial derivative and its conjugate for example:


What are state functions?

State functions are completely determined by the thermodynamic state of the system. The history of the system is of no influence on the state function.

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