Which of the following statement(s) are incorrect?

Combustion of hydrocarbon is always an exothermic process, so if the process is occurring in an adiabatic rigid container temperature must increase.

$\Rightarrow 2{\mathrm{CH}}_3\mathrm{COOH}⟶{\left({\mathrm{CH}}_3\mathrm{COOH}\right)}_2$

Entropy decreases as number of moles decreases.

$\Rightarrow$ In adiabatic process, between any two states there can be only one path. 

$\mathrm{R}\to \mathrm{P}$ at constant T

$\Rightarrow$ In case of free expansion ${\mathrm{P}}_{\text{ext }}=0$

$\mathrm{\Delta U}=(\mathrm{U}{)}_{\mathrm{P}}-(\mathrm{U}{)}_{\mathrm{R}}\ne 0$
$\therefore \mathrm{w}=0$ even if there is change in volume.