If you want to design a thermometer with the same spacing between temperature markings as a mercury thermometer, how must the diameter of the inner hollow cylinder of the stem of the alcohol thermometer compare to that of the mercury thermometer? Assume that the bulb has a much larger volume than the stem.

d_alcohol = √5.6 d _ (Hg)

Explanation:

we know that:

ΔV_alcohol = 5.6*ΔV for Hg (ΔV is change in volume)

Area * (Δh) for alcohol = 5.6*Area * (Δh) for Hg

But we want the change in height, Δh, to be the SAME for both Hg and alcohol, as the question states. Thus, the Δh factors cancel out on the left and right sides of the above equation.

(π/4) d^2 (alcohol) = (5.6) (π/4) d^2 (Hg)

Cancel the factors of π/4 on each side, and then take a square root of each side to get:

d_alcohol = √5.6 d _ (Hg)