A and B are two thermometers made of glass and both contains the same liquid. Both thermometers have spherical bulbs. The internal diameter of the bulb of A is 7.5 mm and radius of the capillary tube is 1.25 mm. The corresponding values for B are 6.2 mm and 0.9 mm. Find the ratio of the lengths between two consecutive graduations in thermometers A and B.

Explanation

Let the separations between two consecutive graduations for `1^(@)` in thermometers A and B be x cm and y cm respectively.
Hence, for the thermometer A, volume expansion of liquid in the bulb due to an increase of `1^(@)C` in temperature = volume of x cm length in the tube.
`" "4/3pi(0.75/2)^(3) times gamma^(.) times 1=x times pi(0.125)^(2) " ...(1)"`
where `gamma^(.)` is the coefficient of apparent expansion of the liquid.
Similarly for the thermometer B,
`" "4/3pi(0.62/2)^(3) times gamma^(.) times 1=gamma times pi times (0.09)^(2) " ...(2)"`
Dividing equation (1) by (2) we get,
`" "(x times pi times (0.125)^(2))/(gamma times pi times (0.09)^(2))=(4/3pi(0.75/2)^(2) times gamma^(.) times 1)/(4/3pi(0.62/2)^(3) times gamma^(.) times 1)`
or, `" " x/y=((0.75)^(3) times (0.09)^(2))/((0.62)^(3) times (0.125)^(2))=0.92` (approx).