Suppose that you need to design a large thermometer made of a glass bulb connect

Question

Suppose that you need to design a large thermometer made of a glass bulb connected to a thin cylindrical tube filled with 2 cm3 of ethanol ( with a little bit of red dye added so that you can see the liquid inside the tube). The volume expansion coefficient of ethanol is 11.1x10-4 K-1. The intended range of temperatures to be measured is from -40 degrees C to +40 degrees C. How large must the internal diameter of the tube be so that the liquid level rises by 0.5 m inside the tube over that range of temperature variation? Neglect the change in volume of the glass in this problem. Make a diagram and explain your reasoning clearly and completely!

Explanation / Answer

volume coefficient is gamma = (v2-v1)/(v1*dT)

11.1*10^-4 = (v2-v1)/(v1*80)

v1 = 2 cm^3

v2-v1 = 0.1776 cm^3

pi*r^2*h = 0.1776

3.142*r^2*0.5 = 0.1776

r = 0.3362 cm

diameter d = 2*r = 0.6724 cm

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