The volume of a gas at pressure $21 \times 10^4 \ N/m^2$ and temperature $27^\circ C$ is $83 \ L$. If $R = 8.3 \ J/mol/K$,then the quantity of gas in $gm-mole$ will be:

What is $1$ mole? Write two different methods to represent a mole.

The $P-T$ diagram of an ideal gas having three different densities $\rho_1, \rho_2, \rho_3$ (in three different cases) is shown in the figure. Which of the following is correct?

The pressure $P$,volume $V$,and temperature $T$ of a gas in jar $A$ are given. The gas in another jar $B$ is at pressure $2P$,volume $V/4$,and temperature $T/4$. What is the ratio of the number of molecules in jar $A$ to jar $B$?

$A$ vessel with an open mouth contains air at $60^{\circ}C$. When the vessel is heated up to temperature $T$,one-fourth of the air goes out. The value of $T$ is ..... $^{\circ}C$

What is the nature of the $P$ versus $1/V$ graph at a constant temperature?