A mercury thermometer has a glass bulb of interior volume 0.100 cm³ at 10°C.The glass capillary tube above the bulb has an inner cross-sectional area of 0.012 mm².The coefficient of volume expansion of mercury is 1.8 × 10^-4 K^-1.If the expansion of the glass is negligible,how much will the mercury rise in the capillary tube when the temperature rises from 5°C to 35°C if the bulb was full at 5°C? A)0.45 mm B)4.5 mm C)45 mm D)45 cm

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Quizplus · Accepted Answer

The volume expansion of mercury can be calculated using the formula $\Delta V = V_0 \beta \Delta T$, where $\Delta V$ is the change in volume, $V_0$ is the initial volume, $\beta$ is the coefficient of volume expansion, and $\Delta T$ is the change in temperature. Given that $V_0 = 0.100 \, \text{cm}^3 = 100 \, \text{mm}^3$, $\beta = 1.8 \times 10^{-4} \, \text{K}^{-1}$, and $\Delta T = 35°C - 5°C = 30°C$, we find:$\Delta V = 100 \, \text{mm}^3 \times 1.8 \times 10^{-4} \, \text{K}^{-1} \times 30 \, \text{K} = 0.54 \, \text{mm}^3$.The height $h$ that the mercury rises in the capillary tube is given by $\Delta V = A \cdot h$, where $A = 0.012 \, \text{mm}^2$ is the cross-sectional area of the tube. Solving for $h$, we get:$h = \frac{\Delta V}{A} = \frac{0.54 \, \text{mm}^3}{0.012 \, \text{mm}^2} = 45 \, \text{mm}$.Therefore, the mercury will rise 45 mm in the capillary tube.

A Mercury Thermometer Has a Glass Bulb of Interior Volume