At $0\,^{\circ}\text{C}$,the value of the density of a fixed mass of an ideal gas divided by its pressure is $x$. At $100\,^{\circ}\text{C}$,this quotient is:

The state of an ideal gas was changed isobarically. The graph depicts three such isobaric lines. Which of the following is true about the pressures of the gas?

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?

Air is filled in a bottle at atmospheric pressure and it is corked at $35^{\circ}C$. If the cork can come out at $3$ atmospheric pressure,then up to what temperature should the bottle be heated in order to remove the cork? (in $^{\circ}C$)

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

$S.I.$ unit of universal gas constant is