Question

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

Answer 1

r = 1.0mm

p = 76 cm

$\theta ={135}^{\circ },$ T = 0.465 N/m

$h=\frac{2Tcos\theta }{r\rho g}$

= $\frac{2\times 465\times \left(\frac{1}{\sqrt{2}}\right)}{{10}^{-3}\times 13600\times 10}$ = 0.0048 m

= 0.48 cm

= capillary fault due to surface tension

So, Height rased in barometer tube

= H - h = 76 - 0.48 = 75.52 cm