Question

During an all-night cram session, a student heats up a 0.577 liter (0.577 x 10- 3 m3) glass (pyrex) beaker of cold coffee. initially, the temperature is 15.8 °c, and the beaker is filled to the brim. a short time later when the student returns, the temperature has risen to 91.3 °c. the coefficient of volume expansion of coffee is the same as that of water. how much coffee (in cubic meters) has spilled out of the beaker

Answer 1

Here coffee is filled into a glass cup and when it is heated expansion of coffee as well as glass occurs

we will find the change in volume of glass cup and change in the volume of coffee.

volume expansion is calculated by

$\Delta V = V_o \gamma \Delta T$

for pyrex glass we have

$\gamma = 4 * 10^{-6}$

now by the formula

$\Delta V = 4* 10^{-6} * 0.577 * (91.3 - 15.8)$

$\Delta V = 0.174 mL$

Now for the expansion of coffee

$\gamma = 2.14 * 10^{-4}$

now the expansion of coffee will be

$\Delta V = 2.14 * 10^{-4}* 0.577* (91.3 - 15.8)$

$\Delta V = 9.32 mL$

now the coffee that will spill out of the cup will be

$\Delta V = 9.32 mL - 0.174 mL$

$\Delta V = 9.15 mL$

so 9.15 mL coffee will spill out of the cup