120 ml of ethyl alcohol is heated from -15°C to 30 °C in a glass flask with a linear expansion coefficient of 90 x 10-6/°C. During the process, 6 ml of ethyl alcohol overflows because the flask was completely filled at -15°C. Calculate: a) The apparent cubic expansion coefficient of the ethyl alcohol
To calculate the apparent cubic expansion coefficient of ethyl alcohol, we first need to calculate the volume expansion of the liquid and the volume expansion of the flask separately.
1. Volume expansion of ethyl alcohol:
Given:
Initial volume of ethyl alcohol, V1 = 120 ml
Final volume of ethyl alcohol, V2 = 120 ml + 6 ml = 126 ml
Therefore, the change in volume of ethyl alcohol, ΔV = V2 - V1 = 126 ml - 120 ml = 6 ml
2. Volume expansion of the flask:
Given:
Linear expansion coefficient of the flask, α = 90 x 10^-6°C
Initial temperature, Ti = -15°C
Final temperature, Tf = 30°C
The change in temperature, ΔT = Tf - Ti = 30°C - (-15°C) = 45°C
Using the linear expansion coefficient, the change in length of the flask, ΔL = α * Li * ΔT, where Li is the initial length of the flask.
The change in volume of the flask, ΔV_flask = A_initial * ΔL = A_initial * α * Li * ΔT
The change in volume of the ethyl alcohol, ΔV_alcohol = 6 ml
Since the total volume change is due to the change in both the substance and the container, we have:
ΔV_alcohol + ΔV_flask = 0
6 + A_initial * α * Li * ΔT = 0
A_initial * α * Li * ΔT = -6
Now, we can calculate the apparent cubic expansion coefficient (β) of ethyl alcohol using the relation:
β = 3 * α
Substitute the values of α and solve for β.