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Chemical EngineeringQ&A Library5.8. Using the extensivity property of the entropy, find the fundamental equation for the intensive quantity s = S/N in both differential and integrated forms.This problem is from a book "Thermodynamics and Statistical Mechanics An Integrated Approach by M. Scott Shell"Question

Asked Feb 28, 2019

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5.8. Using the extensivity property of the entropy, find the fundamental equation for the intensive quantity s = S/N in both differential and integrated forms.

This problem is from a book "Thermodynamics and Statistical Mechanics An Integrated Approach by M. Scott Shell"

Step 1

For entropy ‘S’, the extensive property in its differential form of fundamental equation is:

Step 2

Now, take partial derivative of (1) keeping two variables constant at one time as shown below.

Step 3

All the independent variables are extensive properties. These are *S, E, V, *and* N*. All the derivatives of equations (2), (3) and (4) are intensive properties.

So, according to the Euler’s theo...

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