An ideal gas is allowed to expand both reversibly and irreversibly in an isolated system If ${\text{T}}_{\text{i}}$ is the initial temperature and ${\text{T}}_{\text{f}}$ is the final temperature, which of the following statements is correct

In isolated system the expansion of gas is carried out adiabatically. Since heat exchange between system and surrounding is not possible i.e. $\mathrm{q}= 0$ and secondary ${\text{W}}_{\text{rev}}$ is always greater than ${\text{W}}_{\text{irr}}$ therefore for reversible process there must be comparatively higher decreases in internal energy i.e .. $△\mathrm{U}$for reversible process will be more negative. Hence final temperature in reversible process will be smaller than irreversible process. 

$\therefore {\left({\mathrm{T}}_{\text{t}}\right)}_{\text{irrev }}>{\left({\text{T}}_{\text{f}}\right)}_{\text{rev. }}$