Which of the following is true in the case of an adiabatic process, where $\gamma = C_p / C_V$?

For an adiabatic expansion of an ideal gas,the fractional change in its pressure is equal to (where $\gamma$ is the ratio of specific heats):

$A$ rigid diatomic ideal gas undergoes an adiabatic process at room temperature. The relation between temperature and volume for the process is $TV^x =$ constant,then $x$ is

$A$ litre of dry air at $STP$ expands adiabatically to a volume of $3$ litres. If $\gamma=1.40,$ the work done by air is $(3^{1.4}=4.6555)$. [Take air to be an ideal gas] (in $; J$)

The pressure $P_{1}$ and density $d_{1}$ of a diatomic gas $\left(\gamma = \frac{7}{5}\right)$ change suddenly to $P_{2} (> P_{1})$ and $d_{2}$ respectively during an adiabatic process. The temperature of the gas increases and becomes $......$ times its initial temperature. (Given $\frac{d_{2}}{d_{1}} = 32$)

The internal energy of the gas increases in: