A piece of metal weighs $$46$$ g in air. When it is immersed in a liquid of specific gravity $$1.24$$ at $$270C$$ it weighs $$30$$ g. When the temperature of liquid is raised to $$420C$$ the metal piece weighs $$30.5$$ g. Specific gravity of liquid at $$420C$$ is $$1.20$$. Calculate the coefficient of linear expansion of the metal.

Question

A piece of metal weighs $$46$$ g in air. When it is immersed in a liquid of specific gravity $$1.24$$ at $$270C$$ it weighs $$30$$ g. When the temperature of liquid is raised to $$420C$$ the metal piece weighs $$30.5$$ g. Specific gravity of liquid at $$420C$$ is $$1.20$$. Calculate the coefficient of linear expansion of the metal.

Infinity Learn · Accepted Answer

$$W0$$ $$=$$ mg $$=$$ $$46$$ gmat   θ$$1$$ $$=$$ $$270C$$        $$W1$$ $$=$$ $$30$$ gm $$=$$ $$w0-B1$$         $$B1=$$ $$46-30$$         $$B1$$ $$=$$ $$16$$ $$=$$ $$V1$$ρ$$1gat$$   θ$$2$$ $$=$$ $$420C$$   ⇒ $$W2$$ $$=$$ $$30.5$$ gm $$=$$ $$W0-B2$$        $$B2$$ $$=$$ $$15.5$$ $$=$$ $$V2$$ρ$$2g$$    ∴ $$B2B1$$ $$=$$ $$V2p2V1p1$$         $$15.516$$ $$=$$ (1+3$$α×$$15)×$$1.21.24$$        αs $$=$$ [$$(15.516$$×$$1.241.2)-1$$]×$$145$$          αs $$=$$ $$2.31$$×$$10-5/0C$$ $$=$$ $$143200/0C$$

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