$A$ gas has pressure $P$ and volume $V$. If the gas is compressed adiabatically to $\frac{1}{32}$ of its initial volume,what will be the new pressure? (Given: $(32)^{1.4} = 128$)

The temperature of a hypothetical gas increases to $\sqrt{2}$ times when compressed adiabatically to half the volume. Its equation can be written as

$A$ gas is compressed adiabatically. Which one of the following statements is $NOT$ true?

$Assertion :$ Adiabatic expansion is always accompanied by fall in temperature.
$Reason :$ In adiabatic process, volume is inversely proportional to temperature.

Five moles of Hydrogen gas initially at $STP$ is compressed adiabatically so that its temperature becomes $673 \, K$. The increase in internal energy of the gas is $(R=8.3 \, J \, mol^{-1} \, K^{-1}, \gamma=1.4$ for diatomic gas$)$ (in $kJ$)

We consider a thermodynamic system. If $\Delta U$ represents the increase in its internal energy and $W$ the work done by the system,which of the following statements is true?