The pressure $(P)$ and temperature $(T)$ relationship of an ideal gas obeys the equation $PT^2 = \text{constant}$. The volume expansion coefficient of the gas will be:

$A$ gas of mass $m$ undergoes expansion at a constant pressure $P$,resulting in graph $D$. Which graph will be obtained if the same gas of mass $2m$ undergoes expansion at a pressure of $P/2$?

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

$A$ thin tube sealed at both ends is $100 \ cm$ long. It lies horizontally, the middle $20 \ cm$ containing mercury and two equal ends containing air at standard atmospheric pressure. If the tube is now turned to a vertical position, by what amount will the mercury be displaced? (Given: cross-section of the tube can be assumed to be uniform) ........ $cm$

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 ...... $kPa$.

$A$ gas is contained in a closed vessel. The initial temperature of the gas is $100^{\circ} C$. If the pressure of the gas is increased by $4 \%$,what is the increase in the temperature of the gas (in $^{\circ} C$)?