Volumetric Expansion of Liquids

[chunkytuna21]

A thermometer has a quartz body within which is sealed a total volume of 0.400 cm3 of mercury. The stem contains a cylindrical hole with a bore diameter of 0.10 mm. How far does the mercury column extend in the process of rising from 10°C to 94°C? Neglect any change in volume of the quartz.


delta V= B*V0*delta T


I thought this problem would be pretty simple. I have the equation from my textbook along with the value for B so I just plugged them in: delta V= (182*10^-6)(0.400cm3)(84)= 0.0061152. Now, this is where I'm stuck. This isn't the answer and I don't know what to do with this number. I'm starting to think this isn't even the right equation. Does the 10mm come into the problem somewhere?

 

[kuruman]

Yes the 10 mm is crucial. You have calculated the change in volume. You need the change in height. Assuming that the cross-sectional area remains the same, how much extra height does this change in volume result in?

 

[chunkytuna21]

How do I solve for the extra height? Is there an equation for that?

 

[ideasrule]

Imagine watching a thermometer as the temperature rises from 10 to 94 degrees. The mercury rises, and you can imagine the extra mercury as being held within a cylinder. You've calculated the cylinder's volume, and you have its diameter, so how do you calculate height?

 

[chunkytuna21]

V= (Pi)(R^2)(l), solving for l. Right?

 

[ideasrule]

Yup, exactly.

 

[chunkytuna21]

Thanks. Now, I just have to go back and rework my math. I'm still getting the wrong answer.

 

[ideasrule]

I'm getting an unrealistic answer. Are you sure the numbers you gave are right? 0.4 cm^3 seems like a lot of mercury for a thermometer.

 

[chunkytuna21]

The question is right. I copied and pasted it exactly. Plus, I'm looking at it on webassign right now. I think it's my calculated change in volume. Delta T would be 84 because that's the change in temperature and B is given in a chart in my textbook and V0 would have to be the initial volume of 0.400cm3. So, I really don't know what's wrong. I would convert from cm to m, but they want the answer in cm. Unless it's the wrong equation.

 

[PhaseShifter]

I'm getting a reasonable number. Check your unit conversion on that diameter again.

 

[PhaseShifter]

I'm getting an unrealistic answer. Are you sure the numbers you gave are right? 0.4 cm^3 seems like a lot of mercury for a thermometer.

Not really. You should see the ones used for calorimetry.

 

[chunkytuna21]

When you say a reasonable number, are we talking about a small decimal number or a number in the thousands? Because everytime I work the problem out, I get one or the other.

 

[PhaseShifter]

I'm getting a number in the dozens.
How many cm in 0.10 mm? (looks like you changed it from 0.10mm to 10mm in the middle of your original post, so I suspect you're using the wrong number)

 

[chunkytuna21]

I finally got it. Thanks for all the help everyone.