# What is the fractional decrease in pressure when a...

What is the fractional decrease in pressure when a barometer is raised 35 m to the top of a building? (Assume that the density of air is constant over that distance.)

1. we know that,

change in pressure , ?P = ?gh

where,
? = density of medium = 1.184 kg/m3 (for airat 250 C)
g = acc due to gravity = 9.8 m/s2
h = height change = 35 m

=> ?P = 1.184*9.8*35 = 406.112Pa

1 atm = 101325 Pa
=> 1 Pa = 1/101325 atm
=> 406.112 Pa = 406.112/101325 = 0.004atm   (approx)
2. The variation of Pressure with allitude is given by theequation
P = Poe - ( ?og /Po)h
The constant ( ?og / Po) = (1.29kg/m3*9.8m/s2) / ( 1.013*105N/ m2)
= 1.25*10-4 / m
Therefore,               P = 1.004*105 N/m2
The fractional decrease P -Po = 442N/m2
3. We know that the pressure is the weight ofthe column of height h of air (having density ?) per unitof area or P=W/A
W= mg ( assuming these 35 m are close tothe Earths surface)
m = ?V
V= h A
Puting it together we have
P=W/A= mg/A = ?Vg/A= g? h A/ A
P= g?h
or the change in pressure?P=P=g?h
?P= 9.81 x ? x 35 =343?
the density of air at see level can varybased on themperature from 1.4 - 1.15 kg/m3 (temperaturerange from -25 to +35 deg C) http://en.wikipedia.org/wiki/Density .
4. The fractional decrease in pressure = ?gh =1.15kg/m3*9.8*35 = 389.4*10-5 Pa