A body immersed in a liquid is balanced on scales (Fig.). Will the reading of the scales be altered if the liquid be heated together with the body?

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Sol. At a temperature of 0º the force acting on a body immersed in a liquid equals P–v 0 d 0 , where P is the weight of the body, and v 0 d 0 is the weight of a volume of the liquid equal to the volume occupied by the body (v 0 being the volume of the body, d 0 being the specific gravity of the liquid). As the temperature is raised, the volume of the body increases, while the specific gravity of the liquid decreases. The weight of the same volume of liquid as that of the immersed body at temperature t equals
. Since the thermal coefficient of cubical expansion for solid bodies (α) is usually less than that for liquids (β), it follows that
< v 0 d 0 . Therefore in the majority of cases the upthrust exerted on the body by the liquid decreases with a rise in temperature, i.e. the scales incline to the left.
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