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  • At the top of a mountain, a thermometer reads  and a barometer reads 70 cm of mercury. At the

At the top of a mountain, a thermometer reads 7^{o}C and a barometer reads 70 cm of mercury. At the bottom of the mountain they read 27^{o}C and 76 cm of mercury respectively. The ratio of density of air at the top to that at the bottom of the mountain is

Option: 1

\frac{22}{28}


Option: 2

\frac{14}{18}


Option: 3

\frac{32}{34}

 


Option: 4

\frac{75}{76}


Answers (1)

best_answer

Answer (4)

\frac{P_{1}V_{1}}{T_{1}}=\frac{P_{2}V_{2}}{T_{2}}\Rightarrow \frac{P_{1}M}{\rho_{1} T_{1}}=\frac{P_{2}M}{\rho_{2} T_{2}}\Rightarrow \frac{P_{1}}{\rho _{1}T_{1}}=\frac{P_{2}}{\rho _{2}T_{2}}

\therefore \frac{P_{1}}{P_{2}}=\frac{P_{1}}{P_{2}}.\frac{T_{2}}{T_{1}}=\frac{70}{76}\times\frac{(273+27)}{(273+7)}=\frac{70}{76}\times\frac{300}{280}

=\frac{75}{76}

 

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Rishi

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