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 76 cm of mercury. The contact angle of mercury with glass is 135^ and the surface tension of mercury is 0.465 N/m . The density of mercury is 13600 kg/m ^3 .

Step-by-step solution

The atmospheric pressure corresponds to a mercury column of height h₀ = 76 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 = 2T r g Substituting the given values: T = 0.465 N/m = 135^ 135^ = - 1 2 -0.707 r = 1.0 mm = 10⁻³ m = 13600 kg/m ^3 g = 9.8 m/s ^2 h_c = 2 0.465 (-0.707) 10⁻³ 13600 9.8 h_c = - 0.6575 133.28 -0.00493 m = -0.493 cm -0.5 cm The actual height of the mercury column in the barometer is: h = h₀ + h_c =