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A solid whose volume does not change with temperature, floats in a liquid. Fractions 𝑓1and 𝑓2 of its volume remain submerged for two different temperatures 𝑡1 and 𝑡2 of liquid. The volume coefficient of expansion of liquid is

Question

A solid whose volume does not change with temperature, floats in a liquid. Fractions 𝑓1and 𝑓2 of its volume remain submerged for two different temperatures 𝑡1 and 𝑡2 of liquid. The volume coefficient of expansion of liquid is

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Solution

The volume coefficient of expansion of the liquid can be calculated using the formula:

β = (f2 - f1) / [(t2 - t1) * f1 * f2]

Where:

  • β is the volume coefficient of expansion of the liquid
  • f1 and f2 are the fractions of the solid's volume that remain submerged at temperatures t1 and t2 respectively
  • t1 and t2 are the two different temperatures of the liquid

This formula is derived from the principle of floatation, which states that the weight of the liquid displaced by a floating object is equal to the weight of the object. Since the volume of the solid does not change with temperature, the volume of liquid displaced changes with temperature, which changes the fraction of the solid's volume that remains submerged. This change in volume of the liquid with temperature is characterized by the volume coefficient of expansion.

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