$$\Delta h = \alpha L \Delta T$$
where:
* \(\Delta h\) is the change in the height of the mercury column
* \(\alpha\) is the coefficient of linear expansion of glass
* \(L\) is the original length of the mercury column
* \(\Delta T\) is the change in temperature
For mercury in a glass capillary, the coefficient of linear expansion is approximately:
$$\alpha = 9.0\times10^{-6} \text{ K}^{-1}$$
A typical original length of the mercury column might be:
$$L = 10 \text{ cm}$$
The change in temperature is given as:
$$\Delta T = 25.0^\circ\text{C} - 0.0^\circ\text{C} = 25.0^\circ\text{C}$$
Substituting these values into the formula, we get:
$$\Delta h = (9.0\times10^{-6} \text{ K}^{-1})(10^{-2} m)(25.0 K)$$
$$= 0.00225m = 2.25 \text{ mm}$$
Therefore, the mercury rises by approximately 2.25 mm in the capillary when the temperature changes from 0.0 to 25.0°C.