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An ideal gas is trapped inside a test tube of cross-sectional area $20 \times 10^{-6} \,\,m^2$ as shown in the figure. The gas occupies a height $L_1$ at the bottom of the tube and is separated from air at atmospheric pressure by a mercury column of mass $0.002\,\, kg$. If the tube is quickly turned isothermally, upside down so that $L_2$ mercury column encloses the gas from below. The gas now occupies height $L_1$ in the tube. The ratio $L_1$ is [Take atmospheric pressure $= 10^5 Nm^{-2}]$
Let $\bar v,\;{v_{rms}}$ and ${v_p}$ respectively denote the mean speed, root mean square speed and most probable speed of the molecules in an ideal monoatomic gas at absolute temperature $T.$ The mass of a molecule is $m.$ Then
An ideal gas has an initial pressure of $3$ pressure units and an initial volume of $4$ volume units. The table gives the final pressure and volume of the gas (in those same units) in four, processes. Which processes start and end on the same isotherm
$\begin{array}{|c|c|c|c|c|} \hline & A & B & C & D \\ \hline P & 5 & 4 & 12 & 6 \\ \hline V & 7 & 6 & 1 & 3 \\ \hline \end{array}$
When temperature of an ideal gas is increased from $27^\circ C$ to $227^\circ C$, its $r.m.s.$ speed changed from $400\, metre/sec$ to ${V_s}.$ The ${V_s}$ is ........ $metre/sec$
An ideal gas initially at pressure $1$ bar is being compressed from $30 \,m ^{3}$ to $10\, m ^{3}$ volume and its temperature decreases from $320\, K$ to $280\, K$. then find final pressure of gas (in bar)