Question

A mercury thermometer is constructed as shown in the diagram. The capillary tube has a diameter of $0.004 \, cm$ , and the bulb has a diameter of $0.250 \, cm$ . Neglecting the expansion of the glass, find the change in height of the mercury column with a temperature change of $30.0 \,{}^\circ C$ .

• A. $\text{3.55 cm}$
• B. $\text{2.60 cm}$
• C. $\text{4.50 cm}$
• D. $\text{3.33 cm}$

Answer 1

Answer: (A)

For an easy-to-read thermometer, the column should rise by a few centimetres.
We use the definition of the coefficient of expansion of the glass, the volume of liquid in the capillary will be $\Delta V=A\Delta h$ , where $A$ is the cross-sectional area of the capillary. Let $V_{i}$ represent the volume of the bulb.
$\Delta V=V_{i}\gamma \Delta T$
$\Delta h=\left(\frac{V_{i}}{A}\right)\gamma \Delta T=\left[\frac{\frac{4}{3} \pi R_{b u l b}^{3}}{\pi R_{c a p}^{2}}\right]\gamma \Delta T$
$\Delta h=\frac{4}{3}\frac{(0.125 \text{cm})^{3}}{(0.002 {cm})^{2}}(\text{1.82} \times 1 0^{- 4} {/^\circ } {C})(\text{30.0})^{^\circ } {C})=3.55{cm}$
This is a practical thermometer. Glass expands so little as compared to mercury that only the third digit of the answer would be affected by including the expansion of the glass in our analysis.