Answer :
Using the cylinder volume formula, the volume of water is found to be 6.28 x 10^-9 m^3, the height of water is assumed to be up to the tube's length at 0.2 m, the mass is calculated to be 6.28 grams, and the density of water is a known constant at 1 g/cm^3 or 1000 kg/m^3.
To determine the characteristics of water in a capillary tube, we use principles from physics related to capillary action and fluid mechanics. Given the length of the capillary tube is 20 cm and the internal diameter is 0.2 mm, we'll calculate the asked quantities. However, we cannot calculate the final height of water in this tube without knowing its capillary rise, which depends on the adhesive force between water and the tube's material. So, if we assume the question implies the water rises to the top of the tube:
- Volume of water: The volume of a cylinder is given by
V =
π r2 h, where r is radius and h is height. Since the diameter is 0.2 mm, the radius is 0.1 mm or 0.0001 m. Thus, V = 3.14 * (0.0001 m)2 * 0.2 m = 6.28 * 10-9 m3. - Height of water: If the water rises to the top of the tube, the height is 20 cm or 0.2 meters.
- Mass of water: To calculate mass, we use the density of water, ρ = 1 g/cm3, and the volume we calculated earlier. Mass m = ρ V, so m = 1 g/cm3 * 6.28 cm3 (since 1 m3 = 106 cm3) = 6.28 grams.
- The density of water is known to be 1 g/cm3 or 1000 kg/m3 at room temperature.
These calculations are based on assumptions and the given data, but the capillary rise should be measured or specified for accuracy about the height of water.
