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13. Heat transfer from a body to its surroundings by radiation, Stefan-Boltzmann law, is described by the differential based on the equation du dt (35) where u(t) is the absolute temperature of the body at time t, T is the absolute temperature of the surroundings, and a is a constant depending on the physical parameters of the body. However, if u is much larger than T, then solutions of equation (35) are well approximated by solutions of the simpler equation du dt = -a(u² - T4), (36) Suppose that a body with initial temperature 2000 K is surrounded by a medium with temperature 300 K and that a 2.0 x 10-12 K-3/s. a. Determine the temperature of the body at any time by solving equation (36). G b. Plot the graph of u versus t. Nc. Find the time 7 at which u(T) = 600-that is, twice the ambient temperature. Up to this time the error in using equation (36) to approximate the solutions of equation (35) is no more than 1%. = -auª. -

13. Heat transfer from a body to its surroundings by radiation, Stefan-Boltzmann law, is described by the differential based on the equation du dt (35) where u(t) is the absolute temperature of the body at time t, T is the absolute temperature of the surroundings, and a is a constant depending on the physical parameters of the body. However, if u is much larger than T, then solutions of equation (35) are well approximated by solutions of the simpler equation du dt = -a(u² - T4), (36) Suppose that a body with initial temperature 2000 K is surrounded by a medium with temperature 300 K and that a 2.0 x 10-12 K-3/s. a. Determine the temperature of the body at any time by solving equation (36). G b. Plot the graph of u versus t. Nc. Find the time 7 at which u(T) = 600-that is, twice the ambient temperature. Up to this time the error in using equation (36) to approximate the solutions of equation (35) is no more than 1%. = -auª. -

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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13. Heat transfer from a body to its surroundings by radiation, based on the law, is described by the differential 5 Stefan-Boltzmann equation du dt -a(uª – T4), (35) where u(t) is the absolute temperature of the body at time t, T is the absolute temperature of the surroundings, and a is a constant depending on the physical parameters of the body. However, if u is much larger than 7, then solutions of equation (35) are well approximated by solutions of the simpler equation du =-au4. dt (36) Suppose that a body with initial temperature 2000 K is surrounded by a medium with temperature 300 K and that a = 2.0 x 10-12 K-3/s. a. Determine the temperature of the body at any time by solving equation (36). G b. Plot the graph of u versus t. Nc. Find the time at which u(T) = 600-that is, twice the ambient temperature. Up to this time the error in using equation (36) to approximate the solutions of equation (35) is no more than 1%. 14. Consider an insulated box (a building, perhaps) with internal temperature u(t). According to Newton's law of cooling, satisfies the differential equation
Transcribed Image Text:13. Heat transfer from a body to its surroundings by radiation, based on the law, is described by the differential 5 Stefan-Boltzmann equation du dt -a(uª – T4), (35) where u(t) is the absolute temperature of the body at time t, T is the absolute temperature of the surroundings, and a is a constant depending on the physical parameters of the body. However, if u is much larger than 7, then solutions of equation (35) are well approximated by solutions of the simpler equation du =-au4. dt (36) Suppose that a body with initial temperature 2000 K is surrounded by a medium with temperature 300 K and that a = 2.0 x 10-12 K-3/s. a. Determine the temperature of the body at any time by solving equation (36). G b. Plot the graph of u versus t. Nc. Find the time at which u(T) = 600-that is, twice the ambient temperature. Up to this time the error in using equation (36) to approximate the solutions of equation (35) is no more than 1%. 14. Consider an insulated box (a building, perhaps) with internal temperature u(t). According to Newton's law of cooling, satisfies the differential equation
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