An insulated cylindrical vessel is fitted with an insulated piston of negligible weight and negligible thickness at the midpoint of the vessel. The cylinder contains a gas at $0^{\circ} C$. When the gas is heated to $100^{\circ} C$, the piston moves through a length of $5 \, cm$. The length of the cylindrical vessel in $cm$ is:

The expansion of an ideal gas of mass $m$ at a constant pressure $P$ is given by the straight line $D$. Then the expansion of the same ideal gas of mass $2m$ at a pressure $P/2$ is given by the straight line

In the relation $n = \frac{PV}{RT}$,what does $n$ represent?

Which of the following graphs represents the behavior of an ideal gas? Symbols have their usual meaning.

The volume occupied by the molecules contained in $4.5 \, kg$ of water at $STP$,if the intermolecular forces vanish away,is ........ $m^{3}$.

An ideal gas undergoes a process maintaining the relation between pressure $(P)$ and volume $(V)$ as $P = P_o(1 + (\frac{V_o}{V})^2)^{-1}$, where $P_o$ and $V_o$ are constants. If two samples $A$ and $B$ (two moles each) with initial volumes $V_o$ and $3V_o$ respectively undergo the above-mentioned process, calculate the difference in the temperatures of these samples, $T_B - T_A$, assuming the process is evaluated at their initial states. ($R$ = gas constant)