The $SI$ unit of universal gas constant is

An ideal gas at temperature $T$, pressure $p$ occupies a volume $V$. If its temperature is halved and pressure doubled, what is its new volume?

$A$ gas is contained in a $5 \, L$ vessel at a pressure of $0.8 \, m$. It is connected to another evacuated vessel of $3 \, L$ capacity. What will be the resultant pressure in $m$ (at constant temperature)?

$A$ vessel that can withstand a pressure of $100 \,atm$ is filled with hydrogen at $27^{\circ} C$ up to a pressure of $20 \,atm$. If the vessel is heated, then the temperature at which it explodes is (in $\,K$)

For an ideal gas,the density of the gas is $\varrho_0$ when temperature and pressure of the gas are $T_0$ and $P_0$ respectively. When the temperature of the gas is $2 T_0$,its pressure becomes $3 P_0$. The new density will be

What is the universal gas constant? Write its value and unit.