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147.5 ml of ethyl alcohol (coefficient of volume expansion = 1120 x 10-6K-1) at a temperature of 273.1 K is measured into a 150.0 ml glass beaker (whose coefficient of volumeexpansion is negligible by comparison). To what temperature does the beaker have to be warmed for it to be completely full (i.e. for the volume of the alcohol to reach 150.0 ml)?

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boffeemadrid

Answer:

288.2 K

Explanation:

[tex]\beta[/tex] = Volumetric expansion coefficient = [tex]1120\times 10^{-6}\ /K[/tex]

[tex]T_i[/tex] = Initial temperature = 273.1 K

[tex]T_f[/tex] = Final temperature

[tex]v_0[/tex] = Original volume = 150 mL

Change in volume is given by

[tex]\Delta v=\beta v_0(T_f-T_i)\\\Rightarrow T_f=\frac{\Delta v}{\beta v_0}+T_i\\\Rightarrow T_f=\frac{150-147.5}{1120\times 10^{-6}\times 147.5}+273.1\\\Rightarrow T_f=288.2\ K[/tex]

The temperature of the ethyl alcohol should be 288.2 K to reach 150 mL

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