Answer :

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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