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Chapter 1: Problem 110

A lump of pure copper weighs \(25.305 \mathrm{g}\) in air and 22.486 g when submerged in water \((d=0.9982 \mathrm{g} / \mathrm{mL})\) at \(20.0^{\circ} \mathrm{C} .\) Suppose the copper is then rolled into a \(248 \mathrm{cm}^{2}\) foil of uniform thickness. What will this thickness be, in millimeters?

Short Answer

Expert verified
The thickness of the copper foil is approximately \(0.0114 cm\) or \(0.114 mm\).

Step by step solution

01

Calculate the Volume of Copper using Archimedes' Principle

First, the difference in weight when the copper is in air and then in water will give us the volume of the water displaced which is also the equal to the volume of the copper. This is based on Archimedes' principle which states that the buoyant force (the force with which a fluid pushes an object upward) exerted on an object equals the weight of the fluid that the object displaces. Therefore, we calculate the volume \(V\) by using the formula: \( V = \frac{25.305g - 22.486g}{0.9982g/mL} \)
02

Calculate the Volume of Copper

Using the values in the previous formula, we calculate for the volume of the copper which is approximately equal to \( V = 2.823 mL \). Note that mL and cm³ are equivalent units of volume so we can say \( V = 2.823 cm³ \).
03

Calculate Thickness of the Copper Foil

Now that we have the volume of the copper, we can determine the thickness of the copper foil. A rectangular prism's volume is the product of its length, width, and height. In the context of the foil, these dimensions correspond to the area (\(A\)) and thickness (\(t\)) of the foil. Thus, we solve for \( t \) with the equation: \( t = \frac{V}{A} \)With \( V = 2.823 cm³ \) and \( A = 248 cm² \) in the equation, we can calculate the thickness of the copper foil.

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