At the top of the mountain, the thermometer reads `0^(@)C` and the barometer reads `710 mm Hg`. At the bottom of the mountain the temperature is `30^(@)C` and the pressure is `760 mm Hg`. The ratio of the density of air at the top with that at the bottom is

Options

A. `1 : 1.04`
B. `1.04 : 1`
C. `1.5 : 1`
D. `1 : 1`

Answer

B

Explanation

`PV = nRT rArr PV = (w)/(M) RT`
`w =` mass of the gas, `M =` molar mass of the gas
`PM = (w)/(V) RT rArr PM = dRT`
`d =` density of the gas
`d = (PM)/(RT)`
`(d_(1))/(d_(2)) = (P_(1))/(T_(1)) xx (T_(2))/(T) P_(2)`
(M and R are constants)
`:gt (d_(1))/(d_(2)) = (710)/(273) xx (303)/(750) = (1.04)/(1)`