Thermal Expansion: Volume vs. Linear - 0.11L Spilled

In summary, a one liter pot is completely filled with oil and is heated to 190 degrees Celsius. The linear coefficient of thermal expansion for oil is 0.68*10-3, while the coefficient for the pot is 2.4*10-5. When solving for how much oil was spilled over, the author think that it would be volume expansion, but it is actually linear expansion. The error is in the text when it says "linear coefficient" when it should have said "volume coefficient".
  • #1
Alex126
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5

Homework Statement


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

Homework Equations


Linear expansion = starting length * coefficient α * ΔTemperature
Volume expansion = starting volume * coefficient β * ΔT

Coefficient β = 3*α

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")
 
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  • #2
Alex126 said:
(Or maybe the error was in the text when they said "linear coefficient" when they actually meant "volume coefficient")
I think that's the error.

Your thinking is correct. (Look up the coefficient of expansion for oil and check.)
 
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Likes Alex126
  • #3
Alright, thanks.
 

1. What is thermal expansion?

Thermal expansion is the tendency of matter to increase in volume or linear size when heated and decrease in volume or linear size when cooled.

2. How does thermal expansion affect volume and linear size?

Thermal expansion affects both volume and linear size, but in different ways. When heated, most materials expand in all directions, increasing both volume and linear size. However, some materials, such as water, have a unique property where they expand when heated but contract when cooled, leading to a decrease in volume. Linear expansion refers to the increase in length or width of an object when heated, while volume expansion refers to the increase in all three dimensions (length, width, and height).

3. What is the difference between volume and linear expansion?

The main difference between volume and linear expansion is the direction in which the material expands. Volume expansion refers to the increase in all three dimensions of an object, while linear expansion only refers to the increase in one or two dimensions (length, width, or height).

4. How is thermal expansion measured?

Thermal expansion is typically measured using a coefficient of thermal expansion (CTE), which is a measure of how much a material expands or contracts per unit of temperature change. The CTE can be expressed as a linear or volume expansion coefficient, depending on the type of expansion being measured.

5. What is the significance of the "0.11L spilled" in the question?

The "0.11L spilled" refers to the amount of liquid that has spilled and is affected by thermal expansion. This information is important in understanding the potential impact of thermal expansion on the spilled liquid, as well as any containers or surrounding materials that may also be affected.

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