How Does Temperature Affect the Movement of Mercury in a Thermometer?

[Kingrly]

Homework Statement

(a) The tube of a mercury thermometer (made of Pyrex glass) has an inside diameter of 0.140 mm. The bulb has a volume of 0.275 cm³. How far will the thread of mercury move when the temperature changes from 10.5 degrees Celsius to 33.0 degrees Celsius?

(b) Determine a formula for the change in length of the mercury column in terms of relevant variables. Ignore tube volume compared to bulb volume.

α_PYREX = 3 × 10^-6 (Degrees Celsius)^-1
β_PYREX = 9 × 10^-6 (Degrees Celsius)^-1
β_MERCURY = 180 × 10^-6 (Degrees Celsius)^-1

Homework Equations

(I) ∆V = β(V₀)∆T
(II) ∆L = α(L₀)∆T

The Attempt at a Solution

I calculated the change in the volume of the bulb via equation I, but I am unsure where to head from here. Without knowing the height of the mercury within the thermometer (save for the temperature intervals), I am unsure of how to find the change in volume of the tube or the change in volume of the mercury itself. Any hints?

 

[member 553083]

For (b), I was thinking of an equation in the form of:∆L = mα(L0)∆T + nβ(V0)∆TWhere m and n are coefficients to be determined. Is this a valid approach?