Explain why the pressure inside a tyre increases when a vehicle moves for a long period of time.

An engineer is given a fixed volume $V_m$ of metal with which to construct a spherical pressure vessel. Assuming the vessel has thin walls and is pressurized to its bursting point,the amount of gas the vessel can contain,$n$ (in moles),depends only on $V_m$ $(m^3)$,the temperature $T$ $(K)$,the ideal gas constant $R$ $(J/(K \cdot mol))$,and the tensile strength of the metal $\sigma$ $(N/m^2)$. Which of the following gives $n$ in terms of these parameters?

For three low density gases $A, B, C$,pressure versus temperature graphs are plotted while keeping them at constant volume,as shown in the figure. The temperature corresponding to the point '$K$' is $...........\,{}^{\circ}\,C$.

$A$ 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 $P/2$?

What will be the volume occupied by $4.5 \, kg$ of water at $STP$ if the intermolecular forces are neglected?

The expansion of an ideal gas of mass $m$ at a constant pressure $P$ is given by the straight line $B$ in the $V-T$ graph. Then the expansion of the same ideal gas of mass $2m$ at a pressure $2P$ is given by the straight line: