A piece of brass (Cu and Z n ) weighs 12.9 g in air. When completely immersed in water, it weig

step 1 Hi friends, loss in weight when alloy is submerged in the liquid, sorry, in the water, will be w

A piece of brass (Cu and Z n ) weighs 12.9 g in air. When...

A piece of brass (Cu and $Z n$ ) weighs $12.9 \mathrm{~g}$ in air. When completely immersed in water, it weighs $11.3 \mathrm{~g}$. The relative densities of $\mathrm{Cu}$ and $\mathrm{Zn}$ are $8.9$ and $7.1$, respectively. Calculate the mass of copper in the alloy (in decigram).

Key Concepts

System of Equations

Solving an alloy composition problem typically involves setting up a system of equations based on the total mass, the total volume (obtained through the buoyant force), and the densities of the constituent metals. The simultaneous equations can then be solved to determine the unknown mass fractions, such as the mass of copper in the alloy.

Composite Materials Analysis

When dealing with an alloy, the overall mass and volume are the sum of the contributions from each component metal. By using the known densities of the pure metals, one can set up equations that relate the individual masses to their corresponding volumes. This approach allows for the determination of the composition (i.e., the mass fractions) of the alloy.

Density

Density is defined as mass per unit volume and is a fundamental property used to relate the mass and volume of materials. In problems involving alloys, the densities (or relative densities) of the component metals help in establishing a relation between how much mass each metal contributes to the overall volume of the object.

Archimedes' Principle

Archimedes’ Principle states that a body immersed in a fluid experiences an upward buoyant force equal to the weight of the displaced fluid. In the context of this problem, the difference in the object's apparent weight in air and water is used to determine the volume of the immersed brass, as the weight loss corresponds to the weight of the water displaced.

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