Which of the following graphs represents the variation of $\beta = -(dV/dP)$ with pressure $P$ for an ideal gas kept at a constant temperature?

If the collision frequency of hydrogen molecules in a closed chamber at $27^{\circ} C$ is $Z$,then the collision frequency of the same system at $127^{\circ} C$ is :

Which graph represents the molar heat capacity at constant volume $(C_V)$ for a monoatomic gas?

For the equation $\beta = - \frac{1}{V} \left( \frac{dV}{dP} \right)$, identify the correct graph of $\beta$ versus $P$ for an ideal gas at constant temperature.

Three vessels of equal capacity have gases at the same temperature and pressure. The first vessel contains neon (monatomic),the second contains chlorine (diatomic),and the third contains uranium hexafluoride (polyatomic). Do the vessels contain equal number of respective molecules? Is the root mean square speed of molecules the same in the three cases? If not,in which case is $v_{rms}$ the largest?

An ideal gas at pressure $P$ and temperature $T$ is expanding such that $PT^3 = \text{constant}$. The coefficient of volume expansion of the gas is . . . . . . .