Consider two containers $A$ and $B$ containing monoatomic gases at the same Pressure $(P)$, Volume $(V)$ and Temperature $(T)$. The gas in $A$ is compressed isothermally to $\frac{1}{8}$ of its original volume while the gas $B$ is compressed adiabatically to $\frac{1}{8}$ of its original volume. The ratio of final pressure of gas in $B$ to that of gas in $A$ is ………..

Three samples of the same gas $A, B$ and $C(\gamma = 3/2)$ have initially equal volume. Now the volume of each sample is doubled. The process is adiabatic for $A$ isobaric for $B $ and isothermal for $C$. If the final pressures are equal for all three samples, the ratio of their initial pressures are

During an adiabatic compression, $830\, J$ of work is done on $2\, moles$ of a diatomic ideal gas to reduce its volume by $50\%$. The change in its temperahture is nearly….. $K$ $(R\, = 8.3\, J\,K^{-1}\, mol^{-1} )$

If $\gamma $ denotes the ratio of two specific heats of a gas, the ratio of slopes of adiabatic and isothermal $PV$ curves at their point of intersection is

$P-V$ plots for two gases during adiabatic process are shown in the figure. Plots $1$ and $2$ should correspond respectively to