$A$ diatomic gas undergoes adiabatic change. Its pressure $P$ and temperature $T$ are related as $P \propto T^{x}$ where the value of $x$ is

One mole of an ideal gas is taken through an adiabatic process where the temperature rises from $27^{\circ}C$ to $37^{\circ}C$. If the ideal gas is composed of polyatomic molecules that have $4$ vibrational modes,which of the following is true?

An ideal gas at $127^{\circ} C$ is compressed suddenly to $\frac{8}{27}$ of its initial volume. If $\gamma=\frac{5}{3}$ for the ideal gas, then the rise in its temperature is: (in $K$)

$A$ gas at initial temperature $T$ undergoes sudden expansion from volume $V$ to $2 \, V$. Then,

In an adiabatic change,the pressure $P$ and temperature $T$ of a diatomic gas are related by the relation $P \propto T^C$,where $C$ is equal to:

$A$ tyre pumped to a pressure of $2 \text{ atm}$ suddenly bursts. If the temperature of air before expansion is $T$, then the air temperature after the tyre bursts is (Assume the expansion is adiabatic and adiabatic constant $\gamma = \frac{3}{2}$).