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A vertical cylinder of height 100cm contains air at a constant temperature and its top is closed by a frictionless piston at atmospheric pressure (76 cm of Hg) as shown figure - a. If mercury is slowly poured on the piston, due to its weight air is compressed. Find the maximum height of the mercury column which can be put on the piston.

Answer» <html><body><p></p><a href="https://interviewquestions.tuteehub.com/tag/solution-25781" style="font-weight:bold;" target="_blank" title="Click to know more about SOLUTION">SOLUTION</a> :When <a href="https://interviewquestions.tuteehub.com/tag/mercury-558950" style="font-weight:bold;" target="_blank" title="Click to know more about MERCURY">MERCURY</a> is poured on the top of the piston, due to increase in pressure, the volume of air will <a href="https://interviewquestions.tuteehub.com/tag/decrease-946104" style="font-weight:bold;" target="_blank" title="Click to know more about DECREASE">DECREASE</a>. <br/> If final mercury column of height x is poured on the piston then gas pressure in <a href="https://interviewquestions.tuteehub.com/tag/equilibrium-974342" style="font-weight:bold;" target="_blank" title="Click to know more about EQUILIBRIUM">EQUILIBRIUM</a> can be given as `P_(f)=(76+x)` cm of Hg <br/> As atmospheric pressure is equivalent to the pressure due to a mercury column of height 76 cm. If A be the area of cross section of cylinder then we have according to Boyle.s <a href="https://interviewquestions.tuteehub.com/tag/law-184" style="font-weight:bold;" target="_blank" title="Click to know more about LAW">LAW</a> <br/> `P_(1)V_(1)=P_(2)V_(2)" or "(76 cm)(100A)=(76+x)(100-x)A" (or) "7600=7600+24x-x^(2)" (or) "x=24cm`</body></html>


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