Foundations of Materials Science and Engineering
Foundations of Materials Science and Engineering
6th Edition
ISBN: 9781259696558
Author: SMITH
Publisher: MCG
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Chapter 10.14, Problem 85AAP
To determine

The activation energy for elastomer relaxation process using an Arrhenius-type rate equation.

Expert Solution & Answer
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Answer to Problem 85AAP

The activation energy for elastomer relaxation process using an Arrhenius-type rate equation is 37.65kJ/mol_.

Explanation of Solution

Express the first relaxation time.

    τ1=tln(σ/σ0)                         (I)

Express the second relaxation time.

    τ2=tln(σ/σ0)                         (II)

Express the Arrhenius-type rate equation.

For first,

    1τ1=CeQ/RT                            (III)

For second,

    1τ2=CeQ/RT                           (IV)

Dividing the Equation (IV) and (III).

    τ2τ1=exp[QR(1T11T2)]                (V)

Conclusion:

Unit conversion of temperature from Celsius to Kelvin.

  T1=27°C=27°C+273=300K

  T2=50°C=50°C+273=323K

The average molecular mass of the butadiene mer is 54g/mol.

The average molecular mass of the Sulphur is 32g/mol.

Substitute 25 days for t, 750 psi for σ, and 1000 psi for σ0 in Equation (I).

    τ1=(25days)ln(750psi/1000psi)=(25days)ln(0.75)=(25days)0.28768=86.90days

Substitute 30 days for t, 400 psi for σ, and 1100 psi for σ0 in Equation (II).

    τ1=(30days)ln(400psi/1100psi)=(30days)ln(0.3636)=(25days)1.0116=29.66days

Substitute 29.66days for τ2, 86.90days for τ1, 8.314J/molK for R, 300 K for T1 and 323 K for T2 in Equation (V).

    29.66days86.90days=exp[Q(8.314J/molK)(1300K1323K)]Q=((8.314J/molK)2.3736×104/K)ln(29.66days86.90days)Q=37,653J/molQ=37,653J/mol×(1kJ/mol1000J/mol)

    Q=37.65kJ/mol

Thus, the activation energy for elastomer relaxation process using an Arrhenius-type rate equation is 37.65kJ/mol_.

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Foundations of Materials Science and Engineering

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