If $P, V, M, T,$ and $R$ represent pressure,volume,molar mass,temperature,and gas constant respectively,then the density of an ideal gas is given by:

One mole of an ideal gas at $300 \ K$ is expanded isothermally from $1 \ L$ to $10 \ L$ volume. $\Delta U$ for this process is $....... \ J$ (Use $R = 8.314 \ J \ K^{-1} \ mol^{-1}$)

At constant pressure,the volume of a gas is $300 \ mL$. If the temperature is changed from $27 \ ^oC$ to $-3 \ ^oC$,what will be the final volume in $mL$?

$A$ container is divided into two equal parts $A$ and $B$ containing $H_2$ and $O_2$ respectively,each at $1 \ atm$ pressure. If the wall separating the two sections is removed,what happens to the pressure?

$A$ vessel of volume $24.6 \ L$ contains $1.5 \ moles$ of $H_2$ and $2.5 \ moles$ of $N_2$ at $300 \ K$. Calculate the partial pressure of $N_2$ in the vessel. (in $atm$)

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 $12.2 \ K$? $(R = 0.082 \ L \ atm \ mol^{-1} \ K^{-1})$.