At the top of a mountain, a thermometer reads `7^(@)C` and a barometer reads 70 cm of Hg. At the bottom of the mountain, they read `27^(@)C` and 76 cm of Hg respectively. Compare the density of air at the top with that at the bottom of the mountain.

Explanation

At the top of the mountain,
Pressure `P_(1)` = 70 cm of Hg
Temperature `T_(1)` = 7 + 273 = 280 K
Density of the air = `d_(1)`
At the bottom of the mountain,
Pressure `P_(2)` = 76 cm of Hg
Temperature `T_(2)` = 27 + 273 = 300 K
Density of the air = `d_(2)`
From the gas equation,
`P_(1)/(d_(1)T_(1))=P_(2)/(d_(2)T_(2))(or)d_(1)/d_(2)=P_(1)/T_(1)xxT_(2)/P_(2)=70/280xx300/76=0.9868`.