The $S.I.$ unit of the gas constant $R$ is:

For an ideal gas,the compressibility factor $(Z)$ is

The volume-temperature graph of a given mass of an ideal gas at constant pressure is shown below. What is the correct order of pressures?

Pay load is defined as the difference between the mass of displaced air and the mass of the balloon. Calculate the pay load when a balloon of radius $10 \, m$,mass $100 \, kg$ is filled with helium at $1.66 \, bar$ at $27^{\circ} C$. (Density of air $= 1.2 \, kg \, m^{-3}$ and $R = 0.083 \, bar \, dm^{3} \, K^{-1} \, mol^{-1}$).

For $1 \ mol$ of an ideal gas,an isochore is obtained. The slope of the isochore is $0.082 \ atm \ K^{-1}$. What will be its pressure (in $atm$) when the temperature is $12.2 \ K$? $(R = 0.082 \ L \ atm \ mol^{-1} \ K^{-1})$.

$1 \ L$ closed flask contains a mixture of $4 \ g$ of methane and $4.4 \ g$ of carbon dioxide. The pressure inside the flask at $27^{\circ} C$ is [Assume ideal behaviour of gases] (in $atm$)