Question

At the top of the mountain the temperature is $-13^{\circ} C$ and the barometer reads $68\, cm$ of $Hg$. At the bottom the temperature is $27^{\circ} C$ and the barometer reads $70\, cm$ of $Hg$. What is the ratio of the densities of the air at the mountain to that at the sea level ?

• A. $1.03$
• B. $1.12$
• C. $1.15$
• D. $1.24$

Answer 1

Answer: (B)

We use $P=\frac{\rho R T}{M}$
$\Rightarrow \frac{P_{1}}{P_{2}}=\frac{\rho_{1}}{P_{2}} \times \frac{T_{1}}{T_{2}}$
$\Rightarrow \frac{68}{70}=\frac{\rho_{1}}{\rho_{2}}\left(\frac{260}{300}\right)$
$\Rightarrow \frac{\rho_{1}}{\rho_{2}}=1.12$