A faulty barometer contains certain amount of air and saturated water vapor. It reads 74.0 cm when the atmospheric pressure is 76.0 cm of mercury and reads 72.10 cm when the atmospheric pressure is 74.0 cm of mercury. Saturation vapor pressure at the air temperature = 1.0 cm of mercury. Find the length of the barometer tube above the mercury level in the reservoir.

Let the length of barometer be x cm.


Let the curved surface area of barometer tube be A


Given


Saturation vapor pressure (SVP) = 1.0 cm of mercury


In first case length of mercury column is 74cm.


Length of air above mercury = x-74


Volume of air column V1= (x-74)A


In first case atmospheric pressure is 76 cm of Hg.


Let pressure of air column be P1 in first case.


Then,


Atmospheric pressure= SVP+ P1+mercury column height


76=1+P+74


P1=1 …. (1)


In second case,


Length of mercury column is 72.10cm.


Length of air above mercury = x-72.10


Volume of air column V2= (x-72.1)A


Atmospheric pressure is 74 cm of Hg.


Let pressure of air column be P2.


Atmospheric pressure= SVP+ P2 +mercury column height


74=1+P2+72.1


74=P2+73.1


P2=74-73.1=0.9


P2=0.9 …. (2)


Since temperature has not changed, we can apply Boyle’s law which states that PV=constant, if temperature is constant, for both the cases



P1V1=P2V2


1(x-74)A=0.9(x-72.1)A


(x-74)A=0.9(x-72.1)A


0.1x=9.11


x=91.1cm


Therefore, length of barometer tube is 91.1cm.


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