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Ch.1 - Introduction: Matter, Energy, and Measurement
Chapter 1, Problem 85a

Two spheres of equal volume are placed on the scales as shown. a. Which one is more dense?

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Density

Density is defined as mass per unit volume, typically expressed in grams per cubic centimeter (g/cm³). It is a physical property that indicates how much matter is packed into a given space. In this scenario, comparing the density of the two spheres involves determining which one has a greater mass while maintaining the same volume.
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Mass

Mass is a measure of the amount of matter in an object, usually measured in grams or kilograms. It is an intrinsic property that does not change regardless of the object's location. In the context of the question, the mass of each sphere is crucial for determining their respective densities, as density is calculated by dividing mass by volume.
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Volume

Volume is the amount of space an object occupies, typically measured in cubic centimeters (cm³) or liters. For the two spheres mentioned, since they are stated to have equal volume, this factor remains constant when comparing their densities. Understanding volume is essential for calculating density, as it serves as the denominator in the density formula.
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Related Practice
Textbook Question

The U.S. quarter has a mass of 5.67 g and is approximately 1.55 mm thick. (c) How much money would this stack contain?

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Open Question

An Olympic swimming pool is 164 ft long and 82 ft wide. Assume that it is filled to a depth of 3.0 m, which is the Olympic recommendation.

a. What volume of water in gal is needed to fill the pool?

b. What volume of water in L is needed to fill the pool?

c. The U.S. Geological Survey estimates that in 2015 U.S. domestic use of water was 82 gal/day per person. Using this value for daily usage, for what length of time could the water used to fill an Olympic swimming pool provide the domestic water usage for a community of 25,000 residents?

Textbook Question

A watt is a measure of power (the rate of energy change) equal to 1 J/s. (b) An adult person radiates heat to the surroundings at about the same rate as a 100-watt electric incandescent light bulb. What is the total amount of energy in kcal radiated to the surroundings by an adult over a 24 h period?

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Textbook Question

Water has a density of 0.997 g/cm3 at 25 °C; ice has a density of 0.917 g/cm3 at -10 °C. (a) If a soft-drink bottle whose volume is 1.50 L is completely filled with water and then frozen to -10 °C, what volume does the ice occupy? (b) Can the ice be contained within the bottle?

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Open Question

The mass of an empty oil drum is listed as 2.0×104 g. After a quantity of biodiesel fuel is added to the drum, the total mass is 7.05×105 g.

a. To how many significant figures should the mass of the biodiesel in the drum be reported?

b. The density of the biodiesel fuel is 0.875 g/cm3. What is the volume of biodiesel that has been added to the drum, in L?

Textbook Question

A 32.65-g sample of a solid is placed in a flask. Toluene, in which the solid is insoluble, is added to the flask so that the total volume of solid and liquid together is 50.00 mL. The solid and toluene together weigh 58.58 g. The density of toluene at the temperature of the experiment is 0.864 g/mL. What is the density of the solid?

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