Thermal Expansion Ethanol Problem

[Fizzicist]

Homework Statement

You pour 108 cm^3 of ethanol, at a temperature of -10.0 degrees C, into a graduated cylinder initially at 20.0 degrees C, filling it to the very top. The cylinder is made of glass with a specific heat of 840 J/(kg *K) and a coefficient of volume expansion of 1.2 *10^-5 K^-1; its mass is 0.110 kg. The mass of the ethanol is 0.0873 kg.

A. What will be the final temperature of the ethanol, once thermal equilibrium is reached?

(Answer: -.892 degrees C)

B. How much ethanol will overflow the cylinder before thermal equilibrium is reached?

Homework Equations

Equation for volumetric expansion:

$$\Delta$$V = $$\beta$$ V0 ($$\Delta$$T)

The Attempt at a Solution

I honestly think this question (part B) is flawed. How could you solve this without knowing V0, the initial volume of the cylinder? And even if you did know the volume of the cylinder, you still wouldn't be able to determine the volume capacity it is able to hold (the ratio of volume capacity to volume of the cylinder varies). Is this even possible?

 

[mgb_phys]

You can do part 'a' easily.

B, You can't know how much it will overflow without knowing the volume of the cylinder.
But I think you are meant to assume that 108cc of cold ethanol will fill the cylinder to the top and it overflows when it warms - so just work out how much the ethanol expands

 

[Fizzicist]

B, You can't know how much it will overflow without knowing the volume of the cylinder.
But I think you are meant to assume that 108cc of cold ethanol will fill the cylinder to the top and it overflows when it warms - so just work out how much the ethanol expands

Yeah. That seems reasonable...

I didn't like the way this question was asked. It made it sound as if you were supposed account for the contraction of the cylinder because it gave you the coefficient of volumetric expansion for the glass.

 

[mgb_phys]

Yes - especially because you would need to know the shape of the cylinder!
The volume expansion of the glass isn't the volume expansion of the cylinder.
If you had a thin-walled spherical container and the glass expanded would the volume inside get bigger or would the wall just get thicker and expand outward?

 

[james brug]

How did you find part A?

Yeah. That seems reasonable...

I didn't like the way this question was asked. It made it sound as if you were supposed account for the contraction of the cylinder because it gave you the coefficient of volumetric expansion for the glass.

?

You are supposed to account for the contraction of the cylinder.

 

[Fizzicist]

?

You are supposed to account for the contraction of the cylinder.

TY, but I figured this out about a year ago.