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An open pipe made of glass is immersed in mercury in such a way that a length of $8cm$ extends above the mercury level. The open end of the tube is then closed and sealed and the tube is raised verticllay up by additional $46cm.$ What will be the length of the air column above mercury in the tube now $?$

$($ Atom pressure $=76cm$ of $Hg)$
Option: 1
$16cm$

Option: 2
$22cm$

Option: 3
$38cm$

Option: 4
$6cm$

Answers (1)

best_answer

Let $a=$ cross-sectional area of the pipe in $cm^2$

So, initially volume of air above mercury $V_1=8a\:cm^3$ and pressure $P_1=76cm\:Hg$

When the top of the pipe is $(46+8)\:or\:54cm$ higher than the outer mercury level, let $x=$ rise of mercury level inside of the pipe.

Then volume of air inside the pipe, $V_2=(54-x)a\:cm^3$ and pressure $P_2=(76-x)cm\:Hg$

$From\: Boyle\: law \:P_1 V_1=P_2 V_2\: or, 76 \times 8 a=(76-x)(54-x) a\: or, 608=4104-130 x+x^2\: or\:, x^2-130 x+3496=0\: or, \:(x-38)(x-92)=0.\: So,\: x=38 \mathrm{~cm} \:or,\: x=92 \mathrm{~cm}$

The chemically meaningfull soluntion is $x=38\:cm.$

Therefore, the length of the air column in the pipe above mercury $=54-38=16\:cm.$

Posted by

Gaurav

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