The height to which water will rise in the capillary tube is approximately \(0.014 \, \text{m}\) or \(1.4 \, \text{cm}\).
The height (\(h\)) to which water will rise in a capillary tube can be calculated using the Jurin's Law equation:
\[ h = \frac{2T \cos \theta}{r\rho g} \]
where:
- \( T \) is the surface tension of water,
- \( \theta \) is the contact angle between water and the glass,
- \( r \) is the radius of the capillary tube,
- \( \rho \) is the density of water,
- \( g \) is the acceleration due to gravity.
Assuming a full capillary rise (\( \cos \theta \approx 1 \)), the equation simplifies to:
\[ h = \frac{2T}{r\rho g} \]
Given:
- \( T = 71.99 \, \text{mN/m} \),
- \( r = 0.75 \, \text{mm} \) (convert to meters),
- \( \rho = 1.0 \, \text{g/cm}^3 \) (convert to kg/m\(^3\)),
- \( g = 9.8 \, \text{m/s}^2 \).
Convert the units and substitute the values into the formula:
\[ h = \frac{2 \times 71.99 \times 10^{-3}}{0.75 \times 10^{-3} \times 1.0 \times 10^3 \times 9.8} \]
\[ h \approx 0.014 \, \text{m} \]
The height to which water will rise in the capillary tube is approximately \(0.014 \, \text{m}\) or \(1.4 \, \text{cm}\).