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As shown in the figure below, a small metal bar is placed inside container A, and container A then is placed within a much larger container B. dTA dt dT dt = As the metal bar cools, the ambient temperature T (t) of the medium within container A changes according to Newton's law of cooling. As container A cools, the temperature of the medium inside container B does not change significantly and can be considered to be a constant Tg. Construct a mathematical model for the temperatures T(t) and TA(t), where T(t) is the temperature of the metal bar inside container A. This model can be solved by using prior knowledge. (Use T for T(t) and TA for TA(t). Assume that the temperature of the metal does not affect the temperature of container A and both kA and k are constants.) KA<0 ΚΑΙ T(t) = container B k container A TB metal bar TA (1) = constant k<0 Find a solution of the system subject to the initial conditions T(0) = To, TA(0) = T₁.

As shown in the figure below, a small metal bar is placed inside container A, and container A then is placed within a much larger container B. dTA dt dT dt = As the metal bar cools, the ambient temperature T (t) of the medium within container A changes according to Newton's law of cooling. As container A cools, the temperature of the medium inside container B does not change significantly and can be considered to be a constant Tg. Construct a mathematical model for the temperatures T(t) and TA(t), where T(t) is the temperature of the metal bar inside container A. This model can be solved by using prior knowledge. (Use T for T(t) and TA for TA(t). Assume that the temperature of the metal does not affect the temperature of container A and both kA and k are constants.) KA<0 ΚΑΙ T(t) = container B k container A TB metal bar TA (1) = constant k<0 Find a solution of the system subject to the initial conditions T(0) = To, TA(0) = T₁.

Introduction to Chemical Engineering Thermodynamics
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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As shown in the figure below, a small metal bar is placed inside container A, and container A then is placed within a much larger container B. dTA dt dT dt = KA = k container B As the metal bar cools, the ambient temperature TA(t) of the medium within container A changes according to Newton's law of cooling. As container A cools, the temperature of the medium inside container B does not change significantly and can be considered to be a constant Tg. Construct a mathematical model for the temperatures T(t) and TA(t), where T(t) is the temperature of the metal bar inside container A. This model can be solved by using prior knowledge. (Use T for T(t) and TA for TA(t). Assume that the temperature of the metal does not affect the temperature of container A and both k and k are constants.) KA <0 container A T(t) = TB metal bar ΤΑ (1) = constant k<0 Find a solution of the system subject to the initial conditions T(0) = To, TA(0) = T₁.
Transcribed Image Text:As shown in the figure below, a small metal bar is placed inside container A, and container A then is placed within a much larger container B. dTA dt dT dt = KA = k container B As the metal bar cools, the ambient temperature TA(t) of the medium within container A changes according to Newton's law of cooling. As container A cools, the temperature of the medium inside container B does not change significantly and can be considered to be a constant Tg. Construct a mathematical model for the temperatures T(t) and TA(t), where T(t) is the temperature of the metal bar inside container A. This model can be solved by using prior knowledge. (Use T for T(t) and TA for TA(t). Assume that the temperature of the metal does not affect the temperature of container A and both k and k are constants.) KA <0 container A T(t) = TB metal bar ΤΑ (1) = constant k<0 Find a solution of the system subject to the initial conditions T(0) = To, TA(0) = T₁.
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