Question

A barometer tube contains some air above mercury and its length is $90cm$ . On some hot days when temperature is $50^{\circ }C$ and true atmospheric pressure is $75cm$ of $Hg,$ the reading of the mercury level is $74.8cm.$ If the reading is observed to be $75.1cm$ on some another day when temperature is $25^{\circ }C,$ then the true pressure on that day will be ------- $cm$ of $Hg$ . Give answer in nearest integer.

Answer 1

Answer: 76

$P_1=75-74.8=0.2cm$ of $Hg$
The length of barometer tube above mercury level is equivalent to volume of air in the tube in both cases.
$\therefore V_1=90-74.8=15.2$ and $V_2=14.9$
From equation of state, $\frac{P_1{V}_1}{T_1}=\frac{P_2{V}_2}{T_2}$
$(\because$ number of moles of gas is constant in the barometer tube)
$\therefore \frac{0.2\times 15.2}{(50+273)}=\frac{P_2\times 14.9}{(25+273)}$
$\therefore P_2=\frac{298\times 0.2\times 15.2}{323\times 14.9}=\frac{298\times 152\times 0.2}{323\times 149}$
$=\frac{2\times 8\times 0.2}{17}$
$=\frac{3.2}{17}$
$\therefore P_2=0.188=0.19$
$\therefore P^{{}^{\prime }}=75.4+0.19\approx 75.59$ of $Hg$