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Answer :
The diameter of the capillary is approximately 0.657 mm.
1. Calculate the mass of the mercury: Mass of tube after adding mercury - Mass of tube before adding mercury = 3.421g - 3.263g = 0.158g.
2. Convert the mass of the mercury to volume using the density: Volume = Mass / Density = 0.158g / 13.546 g/cm^3 = 0.0116 cm^3.
3. Calculate the radius of the capillary: Volume = π(radius)^2(length), where the length is given as 26.78 mm = 2.678 cm. Rearranging the formula, we get (radius)^2 = Volume / (π * length) = 0.0116 cm^3 / (π * 2.678 cm) = 0.00108 cm^2.
4. Take the square root of the radius to get the diameter: Diameter = 2 * radius = 2 * √(0.00108 cm^2) = 0.0657 cm.
5. Convert the diameter to millimeters: Diameter in millimeters = 0.0657 cm * 10 mm/cm = 0.657 mm.
Therefore, the diameter of the capillary is approximately 0.657 mm.
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The diameter of the capillary is approximately 0.42 mm.
Calculation of Capillary Diameter
To determine the diameter of a capillary, we can use the formula for the volume of a cylinder:
V = πr²h
Given:
Mass of tube before adding mercury: 3.263 g
Mass of tube after adding mercury: 3.421 g
Length of capillary filled with mercury: 26.78 mm
Density of mercury: 13.546 g/cm³
To calculate the volume of the mercury-filled capillary, we can subtract the mass of the empty tube from the mass of the tube with mercury:
Δmass = 3.421 g - 3.263 g = 0.158 g
Next, we convert the mass difference to volume using the density of mercury:
V = Δmass / density = 0.158 g / 13.546 g/cm³ = 0.01166 cm³
Finally, we can rearrange the volume formula to solve for the radius (which is half the diameter) of the capillary:
r = sqrt(V / (πh)) = sqrt(0.01166 cm³ / (π * 26.78 mm))
Convert mm to cm: 26.78 mm = 2.678 cm
r = sqrt(0.01166 cm³ / (π * 2.678 cm)) = 0.042 cm
Convert cm to mm: 0.042 cm = 0.42 mm
Therefore, the diameter of the capillary is approximately 0.42 mm.
