1. Identify compound $P$ from the nitration behavior

A compound which on nitration with dilute $HNO_3$ gives two isomers that can be separated by steam distillation, where one shows intramolecular hydrogen bonding and the other intermolecular hydrogen bonding, is phenol.

On mononitration of phenol, we get:

• $o$-nitrophenol: shows intramolecular H-bonding
• $p$-nitrophenol: shows intermolecular H-bonding

These can be separated by steam distillation because $o$-nitrophenol is steam volatile.

So, $P = \text{phenol}$

2. Reaction of phenol with concentrated $HNO_3$

Phenol with concentrated nitric acid gives 2,4,6-trinitrophenol, commonly called picric acid.

The reaction is: $\text{Phenol} \xrightarrow[\text{conc.}]{HNO_3} \text{2,4,6-trinitrophenol}$

This is a yellow compound and a strong acid, matching the description of compound $C$.

3. Count oxygen atoms in compound $C$

Picric acid = 2,4,6-trinitrophenol

Its structure contains:

• one phenolic $-OH$ group $\Rightarrow 1$ oxygen
• three nitro groups $(-NO_2)$, each containing $2$ oxygen atoms

So total oxygen atoms: $1 + 3 \times 2 = 7$

4. Final answer

The number of oxygen atoms in compound $C$ is: $\boxed{7}$