During an all-night cram session, a student heats up a one-half liter (0.50 10-3 m3) glass (Pyrex) beaker of cold coffee. Initially, the temperature is 19°C, and the beaker is filled to the brim. A short time later when the student returns, the temperature has risen to 90°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?
Wouldn't you use the volume coefficent of water, and compute the new volume? I will be happy to critique your work.
you have to find the deltaV for the water, then the deltaV for the pyrex beaker, then subtract the two.
Yes, to solve this problem, we will need to use the coefficient of volume expansion of water, since the volume expansion of coffee is assumed to be the same as that of water.
To find the volume of spilled coffee, we can start by calculating the change in volume of the coffee due to its temperature increase. We can use the formula:
ΔV = β * V * ΔT
Where:
ΔV is the change in volume
β is the coefficient of volume expansion of water (and coffee)
V is the initial volume of the coffee
ΔT is the change in temperature
First, let's convert the initial volume of the coffee from liters to cubic meters:
V_initial = 0.50 * 10^-3 m^3
Next, we can calculate the change in volume using the coefficient of volume expansion of water (assumed to be the same as that of coffee) and the temperature change:
ΔT = (90 - 19) °C = 71 °C
Substituting the values into the formula, we have:
ΔV = β * V_initial * ΔT
Now, we need to find the coefficient of volume expansion of water. The coefficient of volume expansion of water, β_water, is approximately 0.000207°C^(-1). Since coffee's coefficient of volume expansion is assumed to be the same, we can use this value.
Calculating the change in volume:
ΔV = 0.000207 °C^(-1) * 0.50 * 10^-3 m^3 * 71 °C
Evaluating the expression, we find:
ΔV ≈ 7.315 * 10^(-9) m^3
Therefore, approximately 7.315 * 10^(-9) cubic meters of coffee has spilled out of the beaker.