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Consider a 41°F object placed in 66°F room. (a) Write a differential equation for H, the temperature of the object at time t, using k > 0 for the constant of proportionality, and write your equation in terms of H, k, and t. H' = (b) Give the general solution for your differential equation. Simplify your solution in terms of an unspecified constant C, which appears as the coefficient of an exponential term, and the growth factor k. H = (Your answer may involve the constant of proportionality k.) (c) The temperature of the object is 41°F initially, and 50°F one hour later. Find the temperature of the object after 4 hours. H(4) = degrees F Note: You can eam partial credit on this problem.

Consider a 41°F object placed in 66°F room. (a) Write a differential equation for H, the temperature of the object at time t, using k > 0 for the constant of proportionality, and write your equation in terms of H, k, and t. H' = (b) Give the general solution for your differential equation. Simplify your solution in terms of an unspecified constant C, which appears as the coefficient of an exponential term, and the growth factor k. H = (Your answer may involve the constant of proportionality k.) (c) The temperature of the object is 41°F initially, and 50°F one hour later. Find the temperature of the object after 4 hours. H(4) = degrees F Note: You can eam partial credit on this problem.

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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Can you help me solve this question? (Topic: Differential Equations)

Consider a 41°F object placed in 66°F room. (a) Write a differential equation for H, the temperature of the object at time t, using k > 0 for the constant of proportionality, and write your equation in terms of H, k, and t. H' = (b) Give the general solution for your differential equation. Simplify your solution in terms of an unspecified constant C, which appears as the coefficient of an exponential term, and the growth factor k. H = (Your answer may involve the constant of proportionality k.) (c) The temperature of the object is 41°F initially, and 50°F one hour later. Find the temperature of the object after 4 hours. H(4) = degrees F Note: You can earn partial credit on this problem.
Transcribed Image Text:Consider a 41°F object placed in 66°F room. (a) Write a differential equation for H, the temperature of the object at time t, using k > 0 for the constant of proportionality, and write your equation in terms of H, k, and t. H' = (b) Give the general solution for your differential equation. Simplify your solution in terms of an unspecified constant C, which appears as the coefficient of an exponential term, and the growth factor k. H = (Your answer may involve the constant of proportionality k.) (c) The temperature of the object is 41°F initially, and 50°F one hour later. Find the temperature of the object after 4 hours. H(4) = degrees F Note: You can earn partial credit on this problem.
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