Easy question but I get a crazy answer

1. Aug 13, 2008

sai2020

The question is

Mercury has a thermal expansion coefficient (volume) of about 1/5500 perKelvin. Estimate the inner diameter of the thermometer tube.

Here's my attempt.

L $$\approx$$ 30cm
V = 2*pi*r^2*L
Change in volume at 0 C and 110 C approximately equal to V

=> 110/5500 = r^2(3*pi/5)
=> r = sqrt(1/30*pi) $$\approx$$ 0.10m

I am well known to make crazy errors but I can't find out where that is over here

2. Aug 13, 2008

Topher925

Theres not enough information to determine an actual value for the diameter. You give no initial volume (Vo) and I dont know if you need to consider the expanding glass container as well. Given the assumptions that the volume at 0 C is unknown and the expansion of glass is negligible, I got a solution of

d = 0.2899*sqrt(Vo)

3. Aug 13, 2008

Cvan

Recheck how you determine the volume of a cylinder.
Where does (3*pi/5) come from?
What are your justifications for those assumptions in the problem? There's insufficient data to complete it with the question you provided.
Make sure you don't fluke up on units.
Remember that 100 cm^2 =/= 1 m^2. 100^2 cm^2 = 1 m^2

4. Aug 13, 2008

Andy Resnick

Another clue: the point of a decent thermometer is to provide sufficient changes in length to read (say) a quarter-degree change in temperature.

5. Aug 13, 2008

sai2020

It comes from

L = 30*10^-2 = 0.3m
V = r^2(2*pi*L) = r^2(3*pi/5)

The *Hint* says the initial volume is 1mm^3. and I think the glass expansion can be neglected cos this is an introductory thermal course and this is the first tutorial.

Can you please tell me how you got to that.

Last edited: Aug 13, 2008
6. Aug 14, 2008

Topher925

*I made a mistake in my first post, that should be the radius, r not the diameter, d

I just used the equation

dV = B*dT*Vo

where:
dV = change in volume (0.03 x pi x r^2)
B = expansion coefficient (18x10^-5/C)
dT = change in temp (110C)
Vo = initial volume (1mm^3)

Plug all that in and solve for r and you get r = 0.2899*sqrt(Vo).

7. Aug 15, 2008

sai2020

OH!! My definition of B was wrong.. Thanks a lot..