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

Answer» <html><body><p></p>Solution :When mercury is poured on the top of the piston, due to increase in pressure, the volume of air wiU decrease according to Boyle.s law. If <a href="https://interviewquestions.tuteehub.com/tag/final-461168" style="font-weight:bold;" target="_blank" title="Click to know more about FINAL">FINAL</a> mercury column of height <a href="https://interviewquestions.tuteehub.com/tag/x-746616" style="font-weight:bold;" target="_blank" title="Click to know more about X">X</a> is poured on the <a href="https://interviewquestions.tuteehub.com/tag/pistion-2929643" style="font-weight:bold;" target="_blank" title="Click to know more about PISTION">PISTION</a> then <a href="https://interviewquestions.tuteehub.com/tag/gas-1003521" style="font-weight:bold;" target="_blank" title="Click to know more about GAS">GAS</a> pressure in equilibrium can be given as `P_(f) = (76 + x) ` <a href="https://interviewquestions.tuteehub.com/tag/cm-919986" style="font-weight:bold;" target="_blank" title="Click to know more about CM">CM</a> of Hg <br/> As at1nospheric pressure is equivalent to the pressure due to a mercury column of height 76cm. If A be the area of cross secion of cylinder then we have according to Boyle.s law `P_(1) V_(1) = P_(2) V_(2) ` or <br/> `(76) (100 A) = (76 + x) (100 - x) A ` or <br/> `7600 = 7600 + 24 x - x^(2) " or " x = 24 ` cm .</body></html>


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