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?

$A$ gas expands adiabatically at constant pressure such that its temperature $T \propto \frac{1}{\sqrt{V}}$. The value of $C_P/C_V$ for the gas is:

$A$ monoatomic ideal gas, initially at temperature $T_{1}$, is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature $T_{2}$ by releasing the piston suddenly. If $l_{1}$ and $l_{2}$ are the lengths of the gas column before and after the expansion respectively, then the value of $\frac{T_{1}}{T_{2}}$ will be

$Assertion:$ In adiabatic compression,the internal energy and temperature of the system decrease.
$Reason:$ Adiabatic compression is a slow process.

Helium at $27^oC$ has a volume of $8$ litres. It is suddenly compressed to a volume of $1$ litre. The temperature of the gas will be ....... $^oC$ $[\gamma = 5/3]$

Compressed air in the tube of a bicycle wheel at normal temperature suddenly starts coming out from a puncture. The air inside: