During an all-night cram session, a student heats up a 0.420 liter (0.420 x 10- 3 m3) glass (Pyrex) beaker of cold coffee. Initially, the temperature is 19.4 °C, and the beaker is filled to the brim. A short time later when the student returns, the temperature has risen to 98.3 °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?
i keep solving it and getting 6.96 E-6
To determine 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 when heated.
First, let's find the initial volume of the coffee. The given volume of the beaker is 0.420 liters, which is equivalent to 0.420 x 10^(-3) m^3.
Next, we need to calculate the change in temperature:
ΔT = Final temperature - Initial temperature
= 98.3 °C - 19.4 °C
= 78.9 °C
The coefficient of volume expansion for water is approximately 2.1 x 10^(-4) °C^(-1). Since the coffee's coefficient of volume expansion is the same as water, we can use this value.
Using the formula for thermal expansion of a substance:
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
Substituting the values into the formula:
ΔV = (0.420 x 10^(-3) m^3) * (2.1 x 10^(-4) °C^(-1)) * (78.9 °C)
= 0.00696861 m^3
So, the amount of coffee that has spilled out of the beaker is approximately 0.00696861 cubic meters, which can be rounded to 6.97 x 10^(-3) m^3 or 6.97 cm^3.