Fundamental equation (thermodynamics) from Euler's equation

[VVS2000]

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?

 

[Chestermiller]

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.