During an all-night cram session, a student heats up a 0.332 liter (0.332 x 10- 3 m3) glass (Pyrex) beaker of cold coffee. Initially, the temperature is 19.0 °C, and the beaker is filled to the brim. A short time later when the student returns, the temperature has risen to 95.8 °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?
I keep getting the answer 5.354e-06 m3
To find the amount of coffee that has spilled out of the beaker, we need to calculate the change in volume of the coffee due to its expansion.
To do this, we can use the formula for volume expansion:
ΔV = V0 * β * ΔT
Where:
ΔV is the change in volume
V0 is the initial volume
β is the coefficient of volume expansion
ΔT is the change in temperature
In this case, the coffee is behaving like water, so we can use the coefficient of volume expansion for water, which is approximately 3.0 x 10^-4 °C^-1.
The initial volume of the coffee is 0.332 x 10^-3 m^3, the change in temperature is 95.8 °C - 19.0 °C = 76.8 °C, and the coefficient of volume expansion is 3.0 x 10^-4 °C^-1.
Now let's plug these values into the formula:
ΔV = (0.332 x 10^-3 m^3) * (3.0 x 10^-4 °C^-1) * (76.8 °C)
Calculating this expression will give us the change in volume.
ΔV = 0.323328 x 10^-7 m^3
Thus, the amount of coffee that has spilled out of the beaker is approximately 0.323328 x 10^-7 m^3 or 3.23328 x 10^-9 m^3.
So, it seems there was an error in your calculation. The correct answer is approximately 3.23328 x 10^-9 m^3 or 3.23 x 10^-9 m^3.