Answer :

Given


Height of vertical cylinder=100cm=1m


Pressure P1=75cm of Hg=0.75m of Hg


1mm of Hg = hg Pa


Where h= height of mercury column =1mm=0.001m


= density of mercury


g= acceleration due to gravity


So,


P1= 0.75m of Hg= 0.75g Pa


Let h be height of mercury above the piston. When mercury is poured over piston the piston will move down and gas inside vessel will get compressed.


So, let the pressure of gas when mercury is poured be P2


So,


P2=P1+hg=0.75g+ hg


Let the circular area of cylinder be A.


Then, volume of gas before mercury was poured V1=Aheight of cylinder


V1=A1=A


Height of cylinder when mercury was poured =(1-h) m


Volume of gas after mercury was poured V2=A(1-h)


Since it is given in question that temperature has not being changed so we can apply Boyle’s law which states that PV=constant, if temperature is constant.



P1V1=P2V2


0.75gA=0.75g+ hg A(1-h)


Taking gA common from both side of equation we get


0.75=(0.75+h) (1-h)


0.75=0.75+h-0.75h-h2


h2-0.25h=0


h-0.25=0h=0.25m


The maximum height of the mercury column that can be put on the piston is 25cm.


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