During an all-night cram session, a student heats up a 0.451 liter (0.451 x 10- 3 m3) glass (Pyrex) beaker of cold coffee. Initially, the temperature is 19.5 °C, and the beaker is filled to the brim. A short time later when the student returns, the temperature has risen to 96.3 °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 know that the amount of coffee that spills out you calculate the volume change of the beaker, but how do i solve it.
Set up your equation:
coefficient of expansion = (1/V) x (change in volume)/(change in temp)
So, you know everything and can plug them in: you now the coefficient of expansion, you know the initial volume, you know the change in temperature, so yo can calculate the change in volume.
what is the variable 1/v?
To calculate the change in volume of the beaker, we can use the formula:
coefficient of expansion = (1 / V) * (change in volume) / (change in temperature)
We know that the coefficient of volume expansion for both coffee and water is the same, so we can use the same coefficient for our calculation.
Let's plug in the given values into the equation:
coefficient of expansion = (1 / V) * (change in volume) / (change in temperature)
The initial volume, V, of the beaker is given as 0.451 x 10^ -3 m^3.
The change in temperature is (96.3 °C - 19.5 °C) = 76.8 °C.
Plugging in the values, we get:
coefficient of expansion = (1 / 0.451 x 10^ -3) * (change in volume) / 76.8 °C
Now, we need to rearrange the equation to solve for the change in volume:
(change in volume) = coefficient of expansion * V * (change in temperature)
Substituting the values:
(change in volume) = coefficient of expansion * (0.451 x 10^ -3 m^3) * 76.8 °C
Now, all we need to do is calculate the change in volume.
To solve this problem, we can use the formula for the coefficient of volume expansion:
coefficient of expansion = (1/V) x (change in volume)/(change in temperature)
In this case, the coefficient of volume expansion is the same for coffee and water, so we can use the value for water (which is approximately 0.00021 per °C) as a close approximation.
Given:
Initial volume, V0 = 0.451 x 10^(-3) m^3
Initial temperature, T0 = 19.5 °C
Final temperature, Tf = 96.3 °C
First, calculate the change in temperature:
Change in temperature, ΔT = Tf - T0
Next, calculate the change in volume using the formula:
Change in volume, ΔV = coefficient of expansion x V0 x ΔT
Substitute the values into the formula:
coefficient of expansion = 0.00021 per °C
V0 = 0.451 x 10^(-3) m^3
ΔT = (96.3 - 19.5) °C
Now, solve for the change in volume:
ΔV = 0.00021 x 0.451 x 10^(-3) x (96.3 - 19.5)
Calculate the value, keeping in mind the units:
ΔV ≈ 8.26 x 10^(-6) m^3
Therefore, the volume of coffee that has spilled out of the beaker is approximately 8.26 x 10^(-6) cubic meters.