The bulb of a thermometer holds 0.40 cm³ of mercury, and its capillary tube has a cross-section of…

Step 1. Per kelvin. $\dfrac{1.8 \times 10^{-4}\ \text{K}^{-1} \times 0.40\ \text{cm}^3}{4.0 \times 10^{-4}\ \text{cm}^2} = 0.18\ \text{cm/K}$.

Step 2. Scale. $100\ \text{K} \times 0.18\ \text{cm/K} = 18\ \text{cm}$.

Step 3. With the glass. $(1.8 \times 10^{-4} - 2.7 \times 10^{-5})\ \text{K}^{-1} \times \dfrac{0.40\ \text{cm}^3}{4.0 \times 10^{-4}\ \text{cm}^2} = 0.153\ \text{cm/K}$.