$A$ vacuum vessel of volume $1 \, dm^3$ is evacuated at a constant temperature of $-23 \, ^\circ C$ until the pressure drops to $7.6 \times 10^{-5} \, torr$. What is the number of molecules remaining in the vessel?

What is the number of molecules in $0.082 \ L$ of an ideal gas kept at a temperature of $400 \ K$ and a pressure of $10 \ atm$?

Consider the figure provided. $1 \ mol$ of an ideal gas is kept in a cylinder,fitted with a piston,at the position $A$,at $18^{\circ} C$. If the piston is moved to position $B$,keeping the temperature unchanged,then '$x$' $L \ atm$ work is done in this reversible process. $x=$ . . . . . . $L \ atm$. (nearest integer) [Given : Absolute temperature $=^{\circ} C + 273.15$,$R=0.08206 \ L \ atm \ mol^{-1} \ K^{-1}$]

The variation of volume of an ideal gas with its number of moles $(n)$ is obtained as a graph at $300 \ K$ and $1 \ atm$ pressure. What is the slope of the graph?

$A$ certain mass of a gas occupies a volume of $2 \,L$ at $STP$. To what temperature must the gas be heated to double its volume, keeping the pressure constant?

One litre of a gas weighs $2 \ g$ at $300 \ K$ and $1 \ atm$ pressure. If the pressure is made $0.75 \ atm$,at which of the following temperatures will one litre of the same gas weigh $1 \ g$?