Properties of Matter

An ideal gas of density ρ=0.2‌kg‌m−3 enters a chimney of height h at the rate of α=0.8‌kg‌s−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 A1=0.1m2 and the upper end is A2=0.4m2. The pressure and the temperature of the gas at the lower end are 600‌Pa and 300K, respectively, while its temperature at the upper end is 150K. The chimney is heat insulated so that the gas undergoes adiabatic expansion. Take g=10ms−2 and the ratio of specific heats of the gas γ=2. Ignore atmospheric pressure.