A barometer is constructed with its tube having radius $1.0$ mm. Assume that the surface of mercury in the tube is spherical in shape. If the atmospheric pressure is equal to $76$ cm of mercury, what will be the height raised in the barometer tube? The contact angle of mercury with glass $= 135^{o}$ and surface tension of mercury $= 0.465$ N $m^{- 1}$ . Density of mercury $= 13600$ kg $m^{- 3}$ .

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Solution

$h = 2 t c o s θ / ρ g r$
$T i s s u r f a c e t e n s i o n T = 0.465 N / m$
$θ c o n t a c t a n g l e 135^{0}$
$ρ d e n s i t y 13600 k g / m^{3}$
$g g r a v i t a t i o n a l 9.8 m / s^{2}$
$r r a d i u s 0.001 m$
$h = (2 \times 0.465 \times c o s 135) / (13600 \times 9.8 \times 0.001)$
$h ⇝ 0.005 m = 75.5 c m$

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h=2tcosθ/ρgrTissurfacetensionT=0.465N/mθcontactangle1350ρdensity13600kg/m3ggravitational9.8m/s2rradius0.001mh=(2×0.465×cos135)/(13600×9.8×0.001)h⇝0.005m=75.5cm