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ICSE Class 9 Answered

Assuming the density of air to be 1.295kg/m^3, find the fall in barometric height in mm of Hg at a height of 107 m above the sea level. Take density of mercury = 13.6 x 10^3 kg/m^3.
Asked by dr_pradip27121972 | 01 Feb, 2018, 03:19: PM
answered-by-expert Expert Answer
Pressure P and density ρ are related by
 
P = ρ (R/M)T, where R is Gas constant (8.314 J/(mol.K) ) , M is molar mass ( for air 0.028964 kg/mole) and T is temperature in K.
 
Given air density is very high, normally air density at sea level at temp 15ºC (288 K) is 1.225 kg/m3.
 
Pressure is temperature dependent but Temperature is not given in the problem.
 
Hence to know the pressure at 107m above sea level, we need to know the exact air density and temperature at that point.
 
By knowing the proper values of density and temperature, pressure is calculated using the formula P = ρ (R/M) T.
 
To get barometer height we use the relation P = ρmgh, where ρm is density of mercury, g is acceleration due to gravity and h is height of mercury in barometer. Here it is to be noted g also varies with altitude and we have to take it account the variation of g at the height 107 m above sea level.
 

 
 

Answered by Thiyagarajan K | 02 Feb, 2018, 02:58: PM

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