A mercury thermometer has a glass bulb of interior volume $0.100 \mathrm {~cm} ^ { 3 } \text { at } 10 ^ { \circ } \mathrm { C }$ The glass capillary tube above the bulb has an inner cross-sectional area of $0.012 \mathrm {~mm} ^ { 2 }$. The coefficient of volume expansion of mercury is $1.8 \times 10 ^ { - 4 } K ^ { - 1 }$. If the expansion of the glass is negligible, how much will the mercury rise in the capillary tube when the temperature rises from $5 ^ { \circ } \mathrm { C } \text { to } 35 ^ { \circ } \mathrm { C }$ if the bulb was full at $5 ^ { \circ } \mathrm { C } ?$?
A) 4.5 mm
B) 0.45 mm
C) 45 cm
D) 45 mm

Question

A mercury thermometer has a glass bulb of interior volume $0.100 \mathrm {~cm} ^ { 3 } \text { at } 10 ^ { \circ } \mathrm { C }$ The glass capillary  tube above the bulb has an inner cross-sectional area of $0.012 \mathrm {~mm} ^ { 2 }$. The coefficient of volume expansion of mercury is $1.8 \times 10 ^ { - 4 } K ^ { - 1 }$. If the expansion of the glass is negligible, how much will the mercury rise in the capillary tube when the temperature rises from $5 ^ { \circ } \mathrm { C } \text { to } 35 ^ { \circ } \mathrm { C }$ if the bulb was full at $5 ^ { \circ } \mathrm { C } ?$?
A) 4.5 mm
B) 0.45 mm
C) 45 cm
D) 45 mm

Quizplus · Accepted Answer

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

A Mercury Thermometer Has a Glass Bulb of Interior Volume 0.100 cm3 at 10∘C0.100 \mathrm {~cm} ^ { 3 } \text { at } 10 ^ { \circ } \mathrm { C }0.100 cm3 at 10∘C

A Mercury Thermometer Has a Glass Bulb of Interior Volume $0.100 \mathrm {~cm} ^ { 3 } \text { at } 10 ^ { \circ } \mathrm { C }$