A metal piece weighing $$15$$ g is heated to $$1000C$$ and the immersed in a mixture of ice and water in thermal equilibrium. The volume of the mixture is found to be reduced by $$0.15$$ $$cm3$$ with the temperature of the mixture remaining constant. Find the specific heat of the metal. Given specific gravity of ice $$=$$ $$0.92$$, specific gravity of water at $$00C$$ $$=$$ $$1.0$$, latent heat of fusion of ice $$=$$ $$80$$ cal $$g-1$$

Question

A metal piece weighing $$15$$ g is heated to $$1000C$$ and the immersed in a mixture of ice and water in thermal equilibrium. The volume of the mixture is found to be reduced by $$0.15$$ $$cm3$$ with the temperature of the mixture remaining constant. Find the specific heat of the metal. Given specific gravity of ice $$=$$ $$0.92$$, specific gravity of water at $$00C$$ $$=$$ $$1.0$$, latent heat of fusion of ice $$=$$ $$80$$ cal $$g-1$$

Infinity Learn · Accepted Answer

mρ$$ice-m$$ρ$$H2O=0.15$$⇒$$m=0.15$$×$$0.920.08Hlost=Hgained$$⇒$$15$$×S×$$100=0.15$$×$$0.920.08$$×$$80$$ ⇒$$S=0.092$$ $$cal/g0C$$

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