A glass tube of length 119cm and of uniform cross section at 0°C is to be filled with mercury so that the volume of unoccupied tube remains same at all the temperatures. The cubical expansion of mercury is seven time that of glass. Find the length of mercury column in the tube.

Solution

If the change in the volume of mercury and glass is same at all the temperatures, the volume unoccupied tube remains constant.
i.e.,

increment straight V subscript straight g space equals space increment straight V subscript Hg

Let, L and l be the length of tube and length of mercury column in the tube at

straight theta

°C and 'a' be the area of cross section of tube.
Since,

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