Question

At the top of a mountain a thermometer reads $7^{\circ }$ and barometer reads 70 cm of Hg. At the bottom of the mountain they read ${27}^{\circ }$ and 76 cm of Hg respectively. Compare the density of the air at the top with that at the bottom.

• A. 0.7867
• B. 0.5894
• C. 0.9868
• D. 0.3658

Answer 1

The correct option is C 0.9868

According to gas equation PV = nRT
$PV=\frac{m}{M}RT[asn=\frac{m}{M}]or\frac{P}{\rho T}=MR[as\frac{m}{V}=\rho ]$
Now as M and R are same for top and bottom
${\left(\frac{P}{\rho T}\right)}_T={\left(\frac{P}{\rho T}\right)}_{B}i.e.\frac{{\rho }_T}{{\rho }_B}=\frac{P_T}{P_B}\times \frac{T_B}{T_T}So\frac{{\rho }_T}{{\rho }_B}=\frac{70}{76}\times \frac{300}{280}=\frac{75}{76}=0.9868$