Which one of the following represents correctly the variation of volume $(V)$ of an ideal gas with temperature $(T)$ under constant pressure conditions?

$A$ cylindrical tube of cross-sectional area $A$ has two airtight,frictionless pistons at its two ends. The pistons are tied with a straight piece of metallic wire. The tube contains a gas at atmospheric pressure $P_0$ and temperature $T_0$. If the temperature of the gas is doubled,then the tension in the wire is:

Estimate the total number of air molecules (inclusive of oxygen,nitrogen,water vapour,and other constituents) in a room of capacity $25.0 \; m^{3}$ at a temperature of $27^{\circ} C$ and $1 \; atm$ pressure.

Which of the following shows the correct relationship between the pressure $P$ and density $\rho$ of an ideal gas at constant temperature?

The $PV$ versus $T$ graph for equal masses of $H_2, He$,and $O_2$ is shown in the figure. Choose the correct alternative:

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: