Statistical Mechanics problem from RK Pathria

[Sudeb Sarkar]

How does the equation with partial derivative evolve into the next equation which also involves ln?
How do we get the logarithmic part?
E(0) = const = E1 +E2
where E1 and E2 are the energies of two separate systems in equilibrium and E(0) is the energy of the conjugate system where the two systems can exchange energy (only) with each other.

The Attempt at a Solution

The book used is RK Pathria's Statistical Mechanics, article 1.2

 

[TSny]

Welcome to PF!

Note that $\frac{1}{y} \frac{ \partial {y}}{\partial x} = \frac{ \partial \; {\ln y}}{\partial x}$

Looking at the equation before the equation with the logs, can you rearrange it so that you get terms of the form $\frac{1}{y} \frac{ \partial {y}}{\partial x}$?

 

[Sudeb Sarkar]

Welcome to PF!

Note that $\frac{1}{y} \frac{ \partial {y}}{\partial x} = \frac{ \partial \; {\ln y}}{\partial x}$

Looking at the equation before the equation with the logs, can you rearrange it so that you get terms of the form $\frac{1}{y} \frac{ \partial {y}}{\partial x}$?

Thank you. I didn't know about that relation.