Concept explainers
The coefficient of volume expansion of the liquid.
Answer to Problem 19PQ
The coefficient of volume expansion of the liquid is
Explanation of Solution
After the ball sinks, the buoyant force from the displaced liquid must be equal to the gravitational force of the sphere.
Write the expression for the gravitational force of the sphere.
Here,
Write the expression for the buoyant force due to the displaced liquid.
Here,
Write the expression to find the radius of the sphere.
Here,
Equate the right hand sides of equations (I) and (II) and solve for
As the temperature of the liquid increases, the volume of the liquid expands.
Write the expression to find the final volume of the liquid after the expansion of liquid.
Here,
The mass of the liquid always remain constant at all the temperature and is equal to the product of density and the volume of the liquid.
From equation (VI) it can be deduced that,
From equation (V), take the ratio between the volumes of liquid.
Use equation (VIII) in (VII).
Solve equation (IX) for
Conclusion:
Given that the density of the liquid at
Substitute
Substitute
Substitute
Therefore, the coefficient of volume expansion of the liquid is
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Chapter 19 Solutions
Physics For Scientists And Engineers: Foundations And Connections, Advance Edition, Volume 1
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