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Question
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° and surface tension of mercury = 0.465 N m−1. Density of mercury = 13600 kg m−3.
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Solution
Given:
Radius of tube r = 1.0 mm
Atmospheric pressure = 76 cm of Hg
Contact angle of mercury with glass θ = 135°
Surface tension of mercury T = 0.465 N/m
Density of mercury = 13600 kg m−3
Let h be the rise in level in the baromet
\[\text{ h } = \frac{2T\cos\theta}{r\rho g}\]
\[ = \frac{2 \times 465 \times \left( 1/\sqrt{2} \right)}{{10}^{- 3} \times 13600 \times 10} = 0 . 0048 \text{ m}\]
\[ = 0 . 48 \text{ cm}\]
∴ Net rise in level in the barometer tube = H − h
= 76 − 0.48
= 75.52 cm
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