A glass flask has a volume of 500 mL at a temperature of $20 ^ { \circ } \mathrm { C }$ The flask contains 492 mL of mercury at an equilibrium temperature of $20 ^ { \circ } \mathrm { C }$ The temperature is raised until the mercury reaches the 500 mL reference mark. At what temperature does this occur? The coefficients of volume expansion of mercury and glass are $18 \times 10 ^ { - 5 } \mathrm {~K} ^ { - 1 }$ (mercury) and $2.0 \times 10 ^ { - 5 } \mathrm {~K} ^ { - 1 } \text { (glass) }$
A) $110 ^ { \circ } \mathrm { C }$
B) $100 ^ { \circ } \mathrm { C }$
C) $140 ^ { \circ } \mathrm { C }$
D) $130 ^ { \circ } \mathrm { C }$
E) $120 ^ { \circ } \mathrm { C }$

Question

A glass flask has a volume of  500 mL at a temperature of $20 ^ { \circ } \mathrm { C }$ The flask contains  492 mL of mercury at an equilibrium temperature of $20 ^ { \circ } \mathrm { C }$ The temperature is raised until the mercury reaches the  500 mL reference mark. At what temperature does this occur? The coefficients of volume expansion of mercury and glass are $18 \times 10 ^ { - 5 } \mathrm {~K} ^ { - 1 }$ (mercury) and $2.0 \times 10 ^ { - 5 } \mathrm {~K} ^ { - 1 } \text { (glass) }$
A) $110 ^ { \circ } \mathrm { C }$
B) $100 ^ { \circ } \mathrm { C }$
C) $140 ^ { \circ } \mathrm { C }$
D) $130 ^ { \circ } \mathrm { C }$
E) $120 ^ { \circ } \mathrm { C }$

Quizplus · Accepted Answer

The volume expansion for both the mercury and the glass flask can be described by 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. The goal is for the mercury to expand by 8 mL (from 492 mL to 500 mL) while the flask also expands. The effective volume expansion needed for mercury to fill the flask to 500 mL must account for the expansion of the flask itself. Setting up the equation for mercury and glass and solving for $\Delta T$ gives a temperature increase that, when added to the initial 20°C, results in a final temperature of approximately 120°C.

A Glass Flask Has a Volume of 500 ML 20∘C20 ^ { \circ } \mathrm { C }20∘C

A Glass Flask Has a Volume of 500 ML $20 ^ { \circ } \mathrm { C }$