$A$ fixed mass of gas at constant pressure occupies a volume $V$. The gas undergoes a rise in temperature so that the r.m.s. velocity of the molecules is doubled. The new volume will be

At which temperature will the speed of sound in hydrogen be the same as the speed of sound in oxygen at $100\,^{\circ}C$?

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.

An ideal gas of molar mass $M$ is contained in a vertical tube of height $H$,closed at both ends. The tube is accelerating vertically upwards with acceleration $g$. Then,the ratio of pressure at the bottom $(P_B)$ and the midpoint $(P_m)$ of the tube will be:

$A$ monoatomic gas of mass $4.0 \, g$ is kept in an insulated container. The container is moving with a velocity of $30 \, m/s$. If the container is suddenly stopped,then the change in temperature of the gas (where $R$ is the gas constant) is given by $\frac{x}{3R}$. The value of $x$ is ..........

Nitrogen gas is filled in an insulated container. If $\alpha$ fraction of moles dissociates without exchange of any energy,then the fractional change in its temperature is ..............