Two different masses $m$ and $3m$ of an ideal gas are heated separately in a vessel of constant volume. The pressure $P$ versus absolute temperature $T$ graphs for these two cases are shown in the figure. The ratio of the slopes of curves $B$ to $A$ is

The molecular weights of $O_2$ and $N_2$ are $32$ and $28$ respectively. At $15^{\circ}C$,the pressure of $1 \, g$ of $O_2$ will be the same as that of $1 \, g$ of $N_2$ in the same bottle at the temperature of ...... $^{\circ}C$.

An insulated cylindrical vessel is fitted with an insulated piston of negligible weight and negligible thickness at the midpoint of the vessel. The cylinder contains a gas at $0^{\circ} C$. When the gas is heated to $100^{\circ} C$, the piston moves through a length of $5 \, cm$. The length of the cylindrical vessel in $cm$ is:

For a monoatomic gas at constant pressure,the $V \rightarrow T$ graph is . . . . . .

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:

The following graph represents the $T-V$ curves of an ideal gas (where $T$ is the temperature and $V$ is the volume) at three pressures $P_1, P_2$ and $P_3$ compared with those of Charles's law represented as dotted lines. Then the correct relation is: