Each 1 deg C change in temperature will increase the total volume by
dV = V*1.82·10^-4°C^-1 *1 °C = 0.00016 cm^3
That volume increase will increase the length in the cylindrical column by
dL = dV/(pi*R^2)= 3.9 cm for each 1 degree C change in temperature.
That number seems too high to me
Your physics teacher assigned a thermometer-building project. He gave you a glass tube with an inside diameter of 1.15 mm and a receptacle at one end. He also gave you 8.97 cm^3 of mercury to pour into the tube, which filled the receptacle and some of the tube. You are to add marks indicating degrees Celsius on the glass tube. At what increments should the marks be put on? You know the volume expansion coefficient of mercury is 1.82·10^-4°C^-1
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3.9 cm it's not true :(
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