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:

Estimate the total number of air molecules (inclusive of oxygen,nitrogen,water vapour,and other constituents) in a room of capacity $25.0 \; m^{3}$ at a temperature of $27^{\circ} C$ and $1 \; atm$ pressure.

At $10^{\circ} C$,the value of the density of a fixed mass of an ideal gas divided by its pressure is $x$. At $110^{\circ} C$,this ratio is:

$A$ tyre kept outside in sunlight bursts after some time because of:

For a gas,as shown in the $P-T$ graph,the densities at points $A$ and $B$ are $\varrho_0$ and $\frac{4}{3} \varrho_0$ respectively. The value of $Y$ on the pressure $(P)$ axis is

There are two vessels filled with an ideal gas where the volume of one is double the volume of the other. The large vessel contains the gas at $8 \ kPa$ at $1000 \ K$,while the smaller vessel contains the gas at $7 \ kPa$ at $500 \ K$. If the vessels are connected to each other by a thin tube allowing the gas to flow and the temperature of both vessels is maintained at $600 \ K$,at steady state the pressure in the vessels will be (in $kPa$).