EBK COLLEGE PHYSICS, VOLUME 2
EBK COLLEGE PHYSICS, VOLUME 2
11th Edition
ISBN: 8220103599924
Author: Vuille
Publisher: CENGAGE L
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Question
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Chapter 11, Problem 34P

(a)

To determine

Five thermal energy transfers that occur.

(a)

Expert Solution
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Explanation of Solution

Aluminum container at 20°C contains ethyl alcohol at 30°C and ice at 0°C . Heat transfer from hot to cold body occurs. The mixture and the container attains an equilibrium temperature.

Ice at 10°C increases in temperature and becomes Ice at 0°C , then phase change occurs from ice to cold water at 0°C , then the temperature of the cold water at 0°C raises to a value T. Temperature of the Aluminum container at 20°C raises to a value T and ethyl alcohol at 30°C temperature rises to a value. The mixture and the container attain an equilibrium temperature T.

Conclusion: All the five thermal energy transfer that occurs is identified.

(b)

To determine

Construct a table similar to table 11.5

(b)

Expert Solution
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Explanation of Solution

A comprehensive table is constructed for all the five thermal energy transfers.

Q m(kg) c(J/kg°C) L(J/kg) Tf(°C) Ti(°C) Expressions
Qice 1.00 2090 - 0 10.0 micecice[TfTi]=micecice[0(10.0°C)]
Qmelt 1.00 - 3.33×105 0 0 miceLf
Qwater 1.00 4186 - T 0 micecwater[TfTi]=micecwater[Tf0]
QAl 0.500 900 - T 20.0 mAlcAl[TfTi]=mAlcAl[Tf20.0°C]
QEAlc 6.00 2430 - T 30.0 mEAlccEAlc[TfTi]=mEAlccEAlc[Tf30.0°C]

Conclusion:

The comprehensive table similar to table 11.5 is constructed.

(c)

To determine

Conservation of energy equation.

(c)

Expert Solution
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Explanation of Solution

According to the conservation of energy, heat lost by one in a mixture is equal to heat gained by the other.

Summing up all the energy expressions and equating it to zero.

{micecice[0(10.0°C)]+miceLf+micecwater[Tf0]+mAlcAl[Tf20.0°C]+mEAlccEAlc[Tf30.0°C]=0}

Conclusion:

The equation denoting the conservation of energy after summing up all the expression and setting it to zero is constructed.

(d)

To determine

The final equilibrium temperature.

(d)

Expert Solution
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Answer to Problem 34P

The final equilibrium temperature is T=4.81°C

Explanation of Solution

Given Info: Mass of aluminum container is 0.500 kg, initial temperature of the aluminum container is 20.0°C , mass of ethyl alcohol is 6.00 kg, initial temperature of ethyl alcohol is 30.0°C , mass of ice is 100 kg, initial temperature of ice is 10.0°C .

Formula to calculate the heat gained by cold water is,

{micecice[0(10.0°C)]+miceLf+micecwater[Tf0]+mAlcAl[Tf20.0°C]+mEAlccEAlc[Tf30.0°C]=0}

Rearrange in terms of Tf .

{micecice(10.0°C)+miceLf+micecwaterTf+mAlcAlTfmAlcAl(20.0°C)+mEAlccEAlcTfmEAlccEAlc(30.0°C)}=0micecwaterTf+mAlcAlTf+mEAlccEAlcTf={micecice(10.0°C)miceLf+mAlcAl(20.0°C)+mEAlccEAlc(30.0°C)}Tf={mice[cice(10.0°C)+Lf]+mAlcAl(20.0°C)+mEAlccEAlc(30.0°C)}micecwater+mAlcAl+mEAlccEAlc

Substitute all quantities in the second through sixth columns into the last column and sum to find T.

Tf={(1.00kg)[(2090J/kg°C)(10.0°C)+(3.33×105J/kg)]+[(0.500kg)(900J/kg°C)(20.0°C)]+[(6.00kg)(2430J/kg°C)(30.0°C)]}((1.00kg)(4186J/kg°C)+(0.500kg)(900J/kg°C)+[(6.0kg)(2430J/kg°C)])=9250019216=4.81°C

Conclusion:

Therefore, the final equilibrium temperature is 4.81°C .

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Chapter 11 Solutions

EBK COLLEGE PHYSICS, VOLUME 2

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