 where,

For our control volume we obtain

This may be simplified as

Expanding and simplifying in the limit to first order, we get

If we confine to ideal gases, formula_25 , so

Above equation relates the differential changes in velocity and temperature.We can derive a relation between formula_27 and formula_2 using formula_29.Differentiating (and dividing the left hand side by formula_2 and the right by formula_31 ),

Using equation 1.6

Hence,

Combining (1.4) and (1.7)

We generally apply the above equation to negative formula_37, let formula_38.