A barometer is constructed using a tube of radius 1.0 mm . Assuming the surface of the mercury in the tube has a spherical shape, determine the height raised in the barometer tube if the atmospheric pressure is equal to

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Quantrex Academy · Accepted Answer

Correct answer: B. 75.5 cm

The atmospheric pressure corresponds to a mercury column of height

h_0 = 76 \text{ cm}

.

Due to surface tension, the mercury level in the tube experiences a capillary depression. The capillary rise (or depression) is given by:

h_c = \dfrac{2T \cos \theta}{r \rho g}

Substituting the given values:

T = 0.465 \text{ N/m}

\theta = 135^{}^{{}^{\circ}} \Rightarrow \cos 135^{}^{{}^{\circ}} = -\dfrac{1}{\sqrt{2}} \approx -0.707

r = 1.0 \text{ mm} = 10^{-3} \text{ m}

\rho = 13600 \text{ kg/m}^3

g = 9.8 \text{ m/s}^2

h_c = \dfrac{2 \times 0.465 \times (-0.707)}{10^{-3} \times 13600 \times 9.8}

h_c = -\dfrac{0.6575}{133.28} \approx -0.00493 \text{ m} = -0.493 \text{ cm} \approx -0.5 \text{ cm}

The actual height of the mercury column in the barometer is:

h = h_0 + h_c = 76 \text{ cm} - 0.5 \text{ cm} = 75.5 \text{ cm}

A barometer is constructed using a tube of radius 1.0 mm . Assuming...

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