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 actual cubic expansion coefficient of the ethyl alcohol.
To find the actual cubic expansion coefficient of ethyl alcohol, we can use the relationship between linear expansion coefficient and cubic expansion coefficient.
The relationship between linear expansion coefficient (α) and cubic expansion coefficient (γ) is given by:
γ = 3α
Given that the linear expansion coefficient of the glass flask is 90 x 10^-6/°C, we can find the linear expansion coefficient of ethyl alcohol:
α = (6 ml / 120 ml) / (30°C - (-15°C))
α = 6 / 120 / 45
α = 1 / 800
Now, we can find the actual cubic expansion coefficient of ethyl alcohol:
γ = 3α
γ = 3 * (1 / 800)
γ = 3 / 800
Therefore, the actual cubic expansion coefficient of ethyl alcohol is 3/800 or 0.00375.