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