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 5.35e-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 the change in temperature.
The volume of the coffee can be calculated using the formula:
V = V_initial * (1 + β * ΔT)
Where:
V is the final volume of the coffee
V_initial is the initial volume of the coffee
β is the coefficient of volume expansion of coffee (which is the same as water)
ΔT is the change in temperature
Given:
V_initial = 0.332 x 10^-3 m^3 (the initial volume of the coffee)
ΔT = (95.8 °C - 19.0 °C) = 76.8 °C (the change in temperature)
Now, we need to find the coefficient of volume expansion of the coffee (β). Since the problem states that it is the same as that of water, we can use the coefficient of volume expansion for water, which is approximately 3.7 x 10^-4 per °C.
Substituting the given values into the formula, we get:
V = (0.332 x 10^-3 m^3) * (1 + 3.7 x 10^-4 per °C * 76.8 °C)
Calculating the value, we find:
V ≈ 0.332 x 10^-3 m^3 * (1 + 0.028416)
V ≈ 0.332 x 10^-3 m^3 * 1.028416
V ≈ 0.341678912 x 10^-3 m^3
Therefore, the amount of coffee that has spilled out of the beaker is approximately:
0.341678912 x 10^-3 m^3 - 0.332 x 10^-3 m^3 = 0.009678912 x 10^-3 m^3
Converting to scientific notation, we get:
0.009678912 x 10^-3 m^3 ≈ 9.678912 x 10^-6 m^3 ≈ 9.68 x 10^-6 m^3
Hence, the amount of coffee that has spilled out of the beaker is approximately 9.68 x 10^-6 m^3 or 9.68 μm^3 (cubic meters).