The slopes of isothermal and adiabatic curves are related as

Monoatomic, diatomic and triatomic gases whose initial volume and pressure are same, are compressed till their volume becomes half the initial volume.

An ideal gas of density $\rho=0.2 kg m ^{-3}$ enters a chimney of height $h$ at the rate of $\alpha=0.8 kg s ^{-1}$ from its lower end, and escapes through the upper end as shown in the figure. The cross-sectional area of the lower end is $A_1=0.1 m ^2$ and the upper end is $A_2=0.4 m ^2$. The pressure and the temperature of the gas at the lower end are $600 Pa$ and $300 K$, respectively, while its temperature at the upper end is $150 K$. The chimney is heat insulated so that the gas undergoes adiabatic expansion. Take $g=10 ms ^{-2}$ and the ratio of specific heats of the gas $\gamma=2$. Ignore atmospheric pressure.

Which of the following statement($s$) is(are) correct?

A gas is compressed adiabatically till its temperature is doubled. The ratio of its final volume to initial volume will be

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