A glass thermometer using a thin column of ethyl alcohol at room temperature $(293.0 \mathrm{~K})$ is cooled. When the temperature reaches $273.0 \mathrm{~K}$ the column of alcohol is $15.50 \mathrm{~cm}$ high. How tall was it when the temperature was $293.0 \mathrm{~K}$ ? The coefficient of volume expansion of ethyl alcohol is $1,120 \times 10^{-6} \mathrm{~K}^{-1}$.
A) $15.85 \mathrm{~cm}$
B) Cannot answer without knowing the diameter of the column
C) $15.68 \mathrm{~cm}$
D) $15.62 \mathrm{~cm}$

Question

Quizplus · Accepted Answer

The change in height is given by:$$\Delta h = h_i \beta \Delta T$$where $h_i$ is the initial height, $\beta$ is the coefficient of volume expansion, and $\Delta T$ is the change in temperature.Substituting the given values, we get:$$\Delta h = (15.50 \mathrm{~cm})(1,120 \times 10^{-6} \mathrm{~K}^{-1})(293.0 \mathrm{~K} - 273.0 \mathrm{~K}) = 0.35 \mathrm{~cm}$$Therefore, the initial height was:$$h_i = 15.50 \mathrm{~cm} + 0.35 \mathrm{~cm} = 15.85 \mathrm{~cm}$$

A Glass Thermometer Using a Thin Column of Ethyl Alcohol (293.0 K)(293.0 \mathrm{~K})(293.0 K)

A Glass Thermometer Using a Thin Column of Ethyl Alcohol $(293.0 \mathrm{~K})$