3.9.1 Show that the rate of absorption is maximized at T = 1 with the absorption function A ( T ) = αT (Equation 3.9.2) for the following values of α, r , and γ . With α = 0.5, r = 1, and γ = 5.0.
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3.9.2 Show that the rate of absorption is maximized at T = 1 with the absorption function A ( T ) = αT (Equation 3.9.2) for the following values of α, r , and γ . With α = 0.5, r = 0.5, and γ = 5.0. Why is the optimal absorption lower than in Exercise 1?
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3.9.3 Show that the rate of absorption is maximized at T = 1 with the absorption function A ( T ) = αT (Equation 3.9.2) for the following values of α, r , and γ . With r = 1.0 and γ = 5.0, but without picking a value for α. How does the optimal absorption depend on α?
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3.9.4 Show that the rate of absorption is maximized at T = 1 with the absorption function A ( T ) = αT (Equation 3.9.2) for the following values of α, r , and γ . In general, without picking values for any of the parameters.
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3.9.5 Check the following formulas. The equilibrium given in Equation 3.9.8. Equation 3.9.8. ...
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3.9.6 Check the following formulas. The equilibrium given in Equation 3.9.10. Equation 3.9.10. ...
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3.9.7 Find the value of T that
maximizes the rate of absorption with the absorption function ...
(Equation 3.9.9) for the following parameter values. α = 0.5, r = 0.5, γ = 5.0, and k = 0.1. You should find that the best T is ...
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3.9.8 Find the value of T that
maximizes the rate of absorption with the absorption function ...
(Equation 3.9.9) for the following parameter values. Check that
... in general.
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3.9.9 Find the value of T that
maximizes the rate of absorption with the absorption function ...
(Equation 3.9.9) for the following parameter values. How does the
optimal T change if r becomes larger?
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3.9.10 Find the value of T that
maximizes the rate of absorption with the absorption function ...
(Equation 3.9.9) for the following parameter values.How does the
optimal T change if α becomes larger? Does this make sense?
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3.9.11 Solve for the following without substituting in a particular functional form for A(T ). The equilibrium concentration.
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3.9.12 Solve for the following without substituting in a particular functional form for A(T ). The equilibrium rate of absorption.
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3.9.13 Substitute the following forms for A(T ) into the expressions found in Exercise 12 and compare with the results in the text. With A(T )=αT .
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3.9.14 Substitute the following forms for A(T ) into the expressions found in Exercise 12 and compare with the results in the text. ...
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3.9.15 Substitute the following forms for A(T ) into the expressions found in Exercise 12 and compare with the results in the text. ...
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3.9.16 Substitute the following forms for A(T ) into the expressions found in Exercise 12 and compare with the results in the text. With ... (a case not considered in the text).
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3.9.17 Find ... for the following forms of A(T ). Do the results make sense? A ( T )=αT .
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3.9.18 Find ... for the following forms of A(T ). Do the results make sense? ...
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3.9.19 Find ... for the following forms of A(T ). Do the results make sense? ...
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3.9.20 Find ... for the following forms of A(T ). Do the results make sense? In general, assuming A(0) = 0.
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3.9.21 Find ... for the following forms of A(T ). Do the results make sense? Do a complete analysis of the case ...
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3.9.22 Use a computer to reproduce all of the figures in this section.
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3.9.23 Use the computer to experiment with the effects of the parameter α on the absorption function in Equation 3.9.6. Set r = 0.5, γ = 5.0, and k = 5. Test values of α ranging from 0.1 to 1.0. Can you explain your results?
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