Answer
$$3.5 \space cm$$
Work Step by Step
1. When the temperature raises, the mercury volume changes, but the mass is constant. Calculate the volume at 0.0 and 25.0 $^oC$ . $$3.380 \space g \times \frac{1 \space cm^3}{13.596 \space g} = 0.2486\space cm^3$$ $$3.380 \space g \times \frac{1 \space cm^3}{13.534 \space g} = 0.2497 \space cm^3$$ - Now, calculate the change in volume: $$\Delta H = 0.2497 \space cm^3 - 0.2486 \space cm^3 = 0.0011 \space cm^3$$ 2. The volume of a cylinder (the shape of the capillary) is: $V = \pi r^2 h$, since $\pi$ and the radius are constant: $\Delta V = \pi r^2 \Delta h$. Solving for $\Delta h:$ $$\Delta h = \frac{\Delta V}{\pi r^2} $$ $$r = \frac d 2 = \frac{0.200 \space mm}{2} \times \frac{1 \space cm}{10 \space mm} = 0.0100 \space cm$$ $$\Delta h = \frac{0.0011 \space cm^3}{\pi (0.0100 \space cm)^2} = 3.5 \space cm$$
