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

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

1. A The pressure of the gas at the upper end of the chimney is $300 \mathrm{Pa}$.
2. B The velocity of the gas at the lower end of the chimney is $40 \mathrm{m} {\mathrm{s}}^{-1}$ and at the upper end is $20 \mathrm{m} {\mathrm{s}}^{-1}$.
3. C The height of the chimney is $590 \mathrm{m}$.
4. D The density of the gas at the upper end is $0.05 \mathrm{kg} {\mathrm{m}}^{-3}$.