A mercury thermometer is constructed as shown if Fig. 1.9. The capillary tube has a diameter of 0.004 00 cm, and the bulb has a diameter of 0.250 cm. neglecting the expansion of the glass, find the change in height of the mercury column with a temperature change of 30.`0^@C`.

Explanation

For an easy to read thermometer, the column should rise by a few centimetres.
We use the definition of the coefficient of expansion. Neglecting the expansion of the glass, the volume of liquid in the capillary will be `DeltaV=A Delta h`, where A is the cross-sectional area of the capillary. Let `V_i` represent the volume of the bulb.
`DeltaV=V_igammaDeltaT`
`Deltah=((V_i)/(A))gammaDeltaT=[((4)/(3)piR_("bu lb")^3)/(piR_("cap")^2)]gammaDeltaT`
`Deltah=(4)/(3)((0.125cm)^2)/((0.002 00 cm)^2)(1.82xx10^-4//^@C)(30.0^@C)=3.55cm`
This is a practical thermometer. Glass expands so little as compared to mercury that only the third digit of the answer would be affected by including the expandion of the glass in our analysis.