The relationship between pressure and the density of a gas expressed by Boyle's law,$P = K\rho$,holds true:

$A$ cylinder contains hydrogen gas at a pressure of $249\; kPa$ and temperature $27^{\circ} C$. Its density is $............. kg/m^{3}$ $(R = 8.3\; J\; mol^{-1} K^{-1})$.

When the pressure of a gas is increased by $0.4\%$,its temperature increases by $1\,^{\circ}\text{C}$. What is the initial temperature of the gas?

Air is pumped into an automobile tube up to a pressure of $200\, kPa$ in the morning when the air temperature is $22^{\circ}C$. During the day,the temperature rises to $42^{\circ}C$ and the tube expands by $2\%$. The pressure of the air in the tube at this temperature will be approximately ...... $kPa$.

In the given pressure $(P)$ - absolute temperature $(T)$ graph of an ideal gas,the relation between volumes $V_1, V_2, V_3$ and $V_4$ is

Two bulbs of identical volumes connected by a small capillary are initially filled with an ideal gas at temperature $T$. Bulb $2$ is heated to maintain a temperature $2 T$,while bulb $1$ remains at temperature $T$. Assume throughout that the heat conduction by the capillary is negligible. Then,the ratio of final mass of the gas in bulb $2$ to the initial mass of the gas in the same bulb is close to