First slide

Pressure in a fluid-mechanical properties of fluids

Question

Mercury Over a Piston: A vertical cylinder of height 100 cm contains air at a constant temperature and its top is closed by a frictionless piston at atmospheric pressure which is 76 cm of Hg column height. If mercury is slowly poured over the top of piston, find the maximum height of mercury column that can be put over piston.

Moderate

A

36 cm
B

24 cm
C

12 cm
D

38 cm

Solution

If Hg is poured on piston up to a depth x,
the gas pressure will be
$P_{g} = (76 + x) cm of Hg$
As gas temperature is constant, we can use by gas law
$P_{1} V_{1} = P_{2} V_{2}$
$76 \times 100 = (76 + x) (100 - x)$
$7600 = 7600 + 24 x - x^{2}$
$x = 24 cm$

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