Practice Problem 14.4 In this example we will compare the volume expansion of a

Question

Practice Problem 14.4

In this example we will compare the volume expansion of a liquid with the volume expansion of the vessel that holds the liquid. A glass flask with a volume of 200 cm3 is filled to the brim with mercury at 20 C. When the temperature of the system is raised to 100 C, does the mercury overflow the flask? If so, by how much? The coefficient of volume expansion of the glass is 1.2×105K1.

SOLUTION

SET UP Both the flask and the mercury expand. The mercury overflows because its coefficient of volume expansion is much greater than that of the glass: 18×105K1 versus 1.2×105K1.

SOLVE The increase in the volume of the flask is Vflask=flaskV0T , and the increase in the volume of mercury is Vmercury=mercuryV0T:

VmercuryVflask====(18×105K1)(200cm3)(100C20C)2.9cm3(1.2×105K1)(200cm3)(100C20C)0.19cm3

The volume of mercury that overflows is the difference between these values:

VmercuryVflask=2.9cm30.19cm3=2.7cm3

Part A - Practice Problem:

Suppose we replace the mercury with glycerin. How much glycerin runs over the flask?

Express your answer in cubic centimenters to three significant figures.

Practice Problem 14.4

In this example we will compare the volume expansion of a liquid with the volume expansion of the vessel that holds the liquid. A glass flask with a volume of 200 cm3 is filled to the brim with mercury at 20 C. When the temperature of the system is raised to 100 C, does the mercury overflow the flask? If so, by how much? The coefficient of volume expansion of the glass is 1.2×105K1.

SOLUTION

SET UP Both the flask and the mercury expand. The mercury overflows because its coefficient of volume expansion is much greater than that of the glass: 18×105K1 versus 1.2×105K1.

SOLVE The increase in the volume of the flask is Vflask=flaskV0T , and the increase in the volume of mercury is Vmercury=mercuryV0T:

VmercuryVflask====(18×105K1)(200cm3)(100C20C)2.9cm3(1.2×105K1)(200cm3)(100C20C)0.19cm3

The volume of mercury that overflows is the difference between these values:

VmercuryVflask=2.9cm30.19cm3=2.7cm3

REFLECT This is basically the way a mercury-in-glass thermometer works, except that instead of letting the mercury overflow and run all over the place, the thermometer has it rise inside a sealed tube as Tincreases.

Part A - Practice Problem:

Coefficients of volume expansion Material (K1 ) Solids Quartz (fused) 0.12×105 Invar 0.27×105 Glass 1.22.7×105 Steel 3.6×105 Copper 5.1×105 Brass 6.0×105 Aluminum 7.2×105 Liquids Mercury 18×105 Glycerin 49×105 Ethanol 75×105 Carbon disulfide 115×105

Suppose we replace the mercury with glycerin. How much glycerin runs over the flask?

Express your answer in cubic centimenters to three significant figures.

Explanation / Answer

Overflowed volume of glycerine, Vover = Vgly - Vf = (gly - f)VoT

=> Vover = (49 - 1.2) * 10-5 * 200 * (100 - 20) = 7.65 cm3

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