# Thermal expansion

1. May 18, 2017

### Alex126

1. The problem statement, all variables and given/known data
A one-liter pot is completely filled with oil. Heat is applied to the pot&oil and the temperature rises from 15°C to 190°C. How much oil is spilled over?

The linear coefficient of thermal expansion for oil is 0.68*10-3; the one for the pot is 2.4*10-5

2. Relevant equations
Linear expansion = starting length * coefficient α * ΔTemperature
Volume expansion = starting volume * coefficient β * ΔT

Coefficient β = 3*α

3. The attempt at a solution
Since we're talking of a pot, and oil in the pot, I thought that we'd be dealing with volume expansion here. So I simply used the formulas, and got the wrong result (0.344 Liters).

Just as an attempt, I then tried doing the exercise with the linear expansion, and got the right (apparently, according to the book) result (0.11 Liters).

What's up with that? Shouldn't it be volume expansion here? The process I thought to be correct was as follows:

V = starting volume (1L)

Oil spilled = [Final oil volume] - [Final pot volume]
Final oil volume = V + volume expansion oil
Final pot volume = V + volume expansion pot
=> oil spilled = volume expansion oil - volume expansion pot

Volume expansion oil/pot = V * βoil/pot * (190-15)
β = 3α

So:
Volume expansion oil = 1*3*0.68*10-3*175 = 0.357
Volume expansion pot = 1*3*2.4*10-5*175 = 0.0126

=> oil spilled = 0.357-0.0126 = 0.344

If I were to "force" the right result (0.11), I would have to use a formula that reads this:

volume expansion = V * linear expansion coefficient * ΔT

Which doesn't make sense to me. So am I missing something, or am I right and the book authors made a mistake and the right answer is 0.344 after all? (Or maybe the error was in the text when they said "linear coefficient" when they actually meant "volume coefficient")

2. May 18, 2017

### Staff: Mentor

I think that's the error.

Your thinking is correct. (Look up the coefficient of expansion for oil and check.)

3. May 19, 2017

### Alex126

Alright, thanks.