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

$P_{1}=75-74.8=0.2cm$ 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, $\frac{P_{1} V_{1}}{T_{1}}=\frac{P_{2} V_{2}}{T_{2}}$
$\left(\right.\because $ number of moles of gas is constant in the barometer tube)
$\therefore \frac{0 . 2 \times 15 . 2}{\left(\right. 50 + 273 \left.\right)}=\frac{P_{2} \times 14 . 9}{\left(\right. 25 + 273 \left.\right)}$
$\therefore P_{2}=\frac{298 \times 0 . 2 \times 15 . 2}{323 \times 14 . 9}=\frac{298 \times 152 \times 0 . 2}{323 \times 149}$
$=\frac{2 \times 8 \times 0 . 2}{17}$
$=\frac{3 . 2}{17}$
$\therefore P_{2}=0.188=0.19$
$\therefore P^{'}=75.4+0.19\approx75.59$ of $Hg$