A given ideal gas with $\gamma  = \frac{{{C_p}}}{{{C_v}}} = 1.5$ at a temperature $T$. If the gas is compressed adiabatically to one-fourth of its initial volume, the final temperature will be ….. $T$

A cylinder with a movable piston contains $3$ moles of hydrogen at standard temperature and pressure. The walls of the cylinder are made of a heat insulator, and the piston is insulated by having a pile of sand on it. By what factor does the pressure of the gas increase if the gas is compressed to half its original volume ?

This question has Statement $1$ and Statement $2.$ Of the four choices given after the Statements, choose the one that best describes the two Statements.
Statement $1:$ In an adiabatic process, change in internal energy of a gas is equal to work done on/by the gas in the process.

Statement $2 :$ The temperature of a gas remains constant in an adiabatic process.

In adiabatic expansion

A motor-car tyre has a pressure of $2\, atm$ at $27\,^oC$. It suddenly burst's. If $\left( {\frac{{{C_p}}}{{{C_v}}}} \right) = 1.4$ for air, find the resulting temperatures (Given $4^{1/7} = 1.219$)