One mole of an ideal gas at an initial temperature of $T\, K$ does $6\, R\, joules$ of work adiabatically. If the ratio of specific heats of this gas at constant pressure and at constant volume is $\frac{5}{3}$ , the final temperature of gas will be

Check the statement are trrue or false :

$1.$ The change in internal energy $\Delta U = 0$ in a cyclic process.

$2.$ In an adiabatic process temperature remains constant.

$3.$ The internal energy of a system during isothermal process decreases.

Air is filled in a motor tube at ${27^o}C$ and at a pressure of $8$ atmospheres. The tube suddenly bursts, then temperature of air is $[{\rm{Given}}\,\,\gamma \,{\rm{of}}\,{\rm{air}} = \,1.5]$

A tyre filled with air $({27^o}C,$ and $2$ atm) bursts, then what is temperature of air ……. $^oC$ $(\gamma = 1.5)$

In adiabatic expansion