An ideal gas of density $\rho_1=0.2 \ kg \ m^{-3}$ 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
  The pressure of the gas at the upper end of the chimney is $150 \ Pa$.
• B
  The velocity of the gas at the lower end of the chimney is $40 \ ms^{-1}$ and at the upper end is $20 \ ms^{-1}$.
• C
  The height of the chimney is $360 \ m$.
• D
  The density of the gas at the upper end is $0.1 \ kg \ m^{-3}$.