The volume versus temperature graph of $1 \ mole$ of an ideal gas is given below. The pressure of the gas (in $atm$) at $X, Y$ and $Z$,respectively,are

Which of the following laws is followed by a hot air balloon used for sports and meteorology?

$A$ bulb of $1 \, L$ capacity contains $5 \, g$ of ethane. If the pressure increases to $10 \, atm$,what will be the temperature in $^oC$ at which the bulb will burst?

$A$ closed tank has two compartments $A$ and $B$,both filled with oxygen (assumed to be ideal gas). The partition separating the two compartments is fixed and is a perfect heat insulator (Figure $1$). If the old partition is replaced by a new partition which can slide and conduct heat but does $NOT$ allow the gas to leak across (Figure $2$),the volume (in $m^3$) of the compartment $A$ after the system attains equilibrium is. . . . . . . .

Match the following gas laws with their respective equations.

If $2$ moles of an ideal gas at $546 \ K$ has a volume of $44.8 \ L$,then what will be its pressure (in $atm$)? $(R=0.082 \ L \ atm \ K^{-1} \ mol^{-1})$