Ch 14: Fluids and Elasticity

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook

Knight Calc 5th Edition

Ch 14: Fluids and Elasticity

Problem 7a

Chapter 14, Problem 7a

What volume of water has the same mass as 8.0 m³ of ethyl alcohol?

Verified step by step guidance

Step 1: Identify the given data. The problem provides the volume of ethyl alcohol (8.0 m³) and asks for the volume of water that has the same mass. To solve this, we need the densities of ethyl alcohol and water. The density of ethyl alcohol is approximately 790 kg/m³, and the density of water is approximately 1000 kg/m³.

Step 2: Calculate the mass of ethyl alcohol using the formula for mass:

m = ρ V

, where

ρ

is the density and

V

is the volume. Substitute the values for ethyl alcohol:

m = 790 8.0

Step 3: Use the calculated mass of ethyl alcohol to determine the volume of water. Rearrange the formula for mass to solve for volume:

V = \frac{m}{ρ}

. Substitute the mass of ethyl alcohol and the density of water:

V = \frac{790 8.0}{1000}

Step 4: Simplify the expression to find the volume of water. Perform the division to calculate the equivalent volume of water.

Step 5: Verify the units and ensure the final volume is expressed in cubic meters (m³), as this is consistent with the given data in the problem.

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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 and is a crucial property of materials. It is typically expressed in kilograms per cubic meter (kg/m³). Understanding density allows us to compare the mass of different substances given their volumes, which is essential for solving the problem of finding the equivalent volume of water for a specific mass of ethyl alcohol.

Specific Gravity

Specific gravity is the ratio of the density of a substance to the density of a reference substance, usually water. It is a dimensionless quantity that helps in comparing the densities of different materials. For example, if ethyl alcohol has a specific gravity less than 1, it will float on water, and knowing this helps in determining how much water corresponds to the same mass as a given volume of ethyl alcohol.

Volume-Mass Relationship

The volume-mass relationship is a fundamental concept in physics that describes how the mass of a substance can be calculated from its volume and density. This relationship is expressed mathematically as mass = density × volume. In this problem, we need to use the density of ethyl alcohol to find its mass and then use the density of water to find the corresponding volume that has the same mass.

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