Oxidation of Alcohols

An alcohol can be oxidised to a carbonyl compound only if the carbon bearing the –OH group has at least one hydrogen atom.
2-hydroxy propane is propan-2-ol, $CH_3CH(OH)CH_3$, a secondary alcohol. Its carbinol carbon has one H, so it is oxidised to the ketone acetone:
$CH_3CH(OH)CH_3 \xrightarrow{[O]} CH_3COCH_3 + H_2O$
2-methyl-2-hydroxy propane is tert-butyl alcohol, $(CH_3)_3C-OH$. It has no H on the carbinol carbon, so it is not oxidised to a carbonyl compound (under strong conditions it breaks down instead).
In phenol and o-nitrophenol, the –OH is attached to an aromatic ring carbon that has no H; they cannot form a corresponding carbonyl compound.
So 2-hydroxy propane can be oxidised to the corresponding carbonyl compound (acetone).

n-Propyl alcohol, $CH_3CH_2CH_2OH$, is a primary alcohol. On oxidation with acidified potassium dichromate it gives propanal and then propanoic acid (an acid with the same number of carbons).
Isopropyl alcohol, $(CH_3)_2CHOH$, is a secondary alcohol. On oxidation it gives acetone (a ketone), which is not oxidised further easily.
The products can be told apart: the aldehyde/acid gives positive Tollens' or Fehling's tests, while acetone does not (but gives the iodoform test).
$PCl_5$ reacts with both alcohols in the same way, giving HCl fumes, so it cannot distinguish them; reduction and ozonolysis are not relevant.
So they can be distinguished by oxidation with potassium dichromate.