Question

If the gas inside the flask is cooled so that its pressure is reduced from 797.3 torr to a value of 715.7 torr what will be the height of the mercury in the open arm? 49.0 mm 95.6 mm 144.6 mm 120.1 mm

Answer 1

1 mm = 1 torr
Hence, we will consider presssure in mm Hg units.

$797.3 = Patm + (136.4-103.8) \\ 797.3 = Patm + 32.6 \\ Patm = 797.3 - 32.6 \\ Patm = 764.7 mm$

The sum of the heights in two arms $= 136.4 + 103.8 = 240.2$ mm

Now pressure is reduced to 715.7 mm
$715.7 = Patm + \text {height difference} \\ 715.7 = 764.7 + \text {height difference} \\ \text {height difference} = 715.7-764.7 = -49$
The height of mercury in the open ended arm $= \dfrac {240.5}{2}- \dfrac {49}{2} = 95.8$ mm

Hence the second option 95.6 mm is correct answer.