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Chapter 1: Problem 69

In each of the following pairs, which has the greater volume? a. \(1.0 \mathrm{~kg}\) of feathers or \(1.0 \mathrm{~kg}\) of lead b. \(100 \mathrm{~g}\) of gold or \(100 \mathrm{~g}\) of water c. \(1.0 \mathrm{~L}\) of copper or \(1.0 \mathrm{~L}\) of mercury

Short Answer

Expert verified
a. Feathers have a greater volume. b. Water has a greater volume. c. Copper and Mercury have the same volume.

Step by step solution

01

Gather density values

To determine the volume, we need the density values for each substance. Here are their densities: - Feathers: \(1.2 \mathrm{~kg/m^3}\) - Lead: \(11,340 \mathrm{~kg/m^3}\) - Gold: \(19,320 \mathrm{~kg/m^3}\) - Water: \(1,000 \mathrm{~kg/m^3}\) - Copper: \(8,960 \mathrm{~kg/m^3}\) - Mercury: \(13,534 \mathrm{~kg/m^3}\)
02

Calculate the volumes

Now, we can use the densities to find the volumes: a. Feathers, \(V_f = \frac{1.0\mathrm{~kg}}{1.2 \mathrm{~kg/m^3}} = 0.833\mathrm{~m^3}\), and Lead, \(V_l = \frac{1.0\mathrm{~kg}}{11,340 \mathrm{~kg/m^3}} = 8.81 \times 10^{-5}\mathrm{~m^3}\). b. Gold, \(V_g = \frac{0.1\mathrm{~kg}}{19,320 \mathrm{~kg/m^3}} = 5.17 \times 10^{-6}\mathrm{~m^3}\), and Water, \(V_w = \frac{0.1\mathrm{~kg}}{1,000 \mathrm{~kg/m^3}} = 0.0001\mathrm{~m^3}\).Note that we converted 100g of gold and water to 0.1kg each. c. Copper, \(V_c = 1.0\mathrm{~L} = 0.001\mathrm{~m^3}\) (since 1 L = 0.001 m³), and Mercury, \(V_m = 1.0\mathrm{~L} = 0.001\mathrm{~m^3}\).
03

Compare the volumes

Lastly, we'll compare the volumes: a. Feathers have a volume of \(0.833\mathrm{~m^3}\), while Lead has a volume of \(8.81 \times 10^{-5}\mathrm{~m^3}\). Feathers have a greater volume than lead. b. Gold has a volume of \(5.17 \times 10^{-6}\mathrm{~m^3}\), while Water has a volume of \(0.0001\mathrm{~m^3}\). Water has a greater volume than gold. c. Both Copper and Mercury have a volume of \(0.001\mathrm{~m^3}\), so their volumes are equal. Final answers: a. Feathers have a greater volume. b. Water has a greater volume. c. Copper and Mercury have the same volume.

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