An ideal gas of density $\rho = 0.2\,\text{kg m}^{-3}$ enters a chimney of height $h$ at the rate of $\alpha = 0.8\,\text{kg s}^{-1}$ from its lower end, and escapes through the upper end as shown in the figure. The cross-sectional area of the lower end is $A_{1} = 0.1\,\text{m}^{2}$ 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 $g = 10\,\text{m s}^{-2}$ 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 $300\,\text{Pa}$.
2. B The velocity of the gas at the lower end of the chimney is $40\,\text{m s}^{-1}$ and at the upper end is $20\,\text{m s}^{-1}$.
3. C The height of the chimney is $590\,\text{m}$.
4. D The density of the gas at the upper end is $0.05\,\text{kg m}^{-3}$.

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Answers: B. The velocity of the gas at the lower end of the chimney is $40\,\text{m s}^{-1}$ and at the upper end is $20\,\text{m s}^{-1}$.

Thermodynamics An ideal gas of density $\rho = 0.2\,\text{kg m}^{-3}$ enters a chimney of height $h$ at the rate of $\alpha = 0.8\,\text{kg s}^{-1}$ from its lower end, and escapes through the upper end as shown in the figure. The cross-sectional area of the lower end is $A_{1} = 0.1\,\text{m}^{2}$ 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 $g = 10\,\text{m s}^{-2}$ and the ratio of specific heats of the gas $\gamma = 2$. Ignore atmospheric pressure. Which of the following statement(s) is(are) correct? Watch this solved on the board The full walkthrough, written out a line at a time with narration explaining each step as it appears. Pause anywhere and ask why a line is there. Free to watch

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