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At the top of the mountain, the thermome...

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

A

`1 : 1.04`

B

`1.04 : 1`

C

`1.5 : 1`

D

`1 : 1`

Text Solution

Verified by Experts

The correct Answer is:
B
`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)`
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