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PROBLEM 9. A bottle of milk was taken from a refrigerator and put in a bowl of hot water to warm. According to Newton's empirical law of cooling, change of temperature of the milk in the bottle M(t) and change of temperature of water in the bowl W (t) can be described by the differential equations dM dt = -k, (M – W) dW dt :-k2(W – Ta) – k3( – M), where t is time (in minutes), Tą is the ambient temperature, k, = 0.1, k2 = 0.03, and kg = 0.18 are constants of proportionality. The temperature in the refrigerator is 5°C, the room temperature is 20°C and the initial temperature of the water in the bowl is 80°C. a) Find the solution of the nonhomogeneous system X(t)=X.(t) + Xp(t) if the particular solution Xp(t) is given by: 20 20 b) Find the temperature of milk and water as function of time. c) Find the values of W (t) and M(t) when t → o.

PROBLEM 9. A bottle of milk was taken from a refrigerator and put in a bowl of hot water to warm. According to Newton's empirical law of cooling, change of temperature of the milk in the bottle M(t) and change of temperature of water in the bowl W (t) can be described by the differential equations dM dt = -k, (M – W) dW dt :-k2(W – Ta) – k3( – M), where t is time (in minutes), Tą is the ambient temperature, k, = 0.1, k2 = 0.03, and kg = 0.18 are constants of proportionality. The temperature in the refrigerator is 5°C, the room temperature is 20°C and the initial temperature of the water in the bowl is 80°C. a) Find the solution of the nonhomogeneous system X(t)=X.(t) + Xp(t) if the particular solution Xp(t) is given by: 20 20 b) Find the temperature of milk and water as function of time. c) Find the values of W (t) and M(t) when t → o.

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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PROBLEM 9. A bottle of milk was taken from a refrigerator and put in a bowl of hot water to warm. According to Newton's empirical law of cooling, change of temperature of the milk in the bottle M(t) and change of temperature of water in the bowl W (t) can be described by the differential equations dM dt = -k, (M – W) dW dt :-k2(W – Ta) – k3( – M), where t is time (in minutes), Tą is the ambient temperature, k, = 0.1, k2 = 0.03, and kg = 0.18 are constants of proportionality. The temperature in the refrigerator is 5°C, the room temperature is 20°C and the initial temperature of the water in the bowl is 80°C. a) Find the solution of the nonhomogeneous system X(t)=X.(t) + Xp(t) if the particular solution Xp(t) is given by: 20 20 b) Find the temperature of milk and water as function of time. c) Find the values of W (t) and M(t) when t → o.
Transcribed Image Text:PROBLEM 9. A bottle of milk was taken from a refrigerator and put in a bowl of hot water to warm. According to Newton's empirical law of cooling, change of temperature of the milk in the bottle M(t) and change of temperature of water in the bowl W (t) can be described by the differential equations dM dt = -k, (M – W) dW dt :-k2(W – Ta) – k3( – M), where t is time (in minutes), Tą is the ambient temperature, k, = 0.1, k2 = 0.03, and kg = 0.18 are constants of proportionality. The temperature in the refrigerator is 5°C, the room temperature is 20°C and the initial temperature of the water in the bowl is 80°C. a) Find the solution of the nonhomogeneous system X(t)=X.(t) + Xp(t) if the particular solution Xp(t) is given by: 20 20 b) Find the temperature of milk and water as function of time. c) Find the values of W (t) and M(t) when t → o.
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