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3. Solve this differential equation, using T(0) = To as initial condition. %3D

3. Solve this differential equation, using T(0) = To as initial condition. %3D

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section: Chapter Questions
Problem 9T
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Imagine pouring a cup of hot coffee and letting it cool at room temperature. How does the tem- perature of the coffee decrease in time? How long must you wait until the coffee is cool enough to drink? When should you add some cold milk to the coffee to accelerate the cooling as much as possible? A fairly accurate model to describe the temperature changes in a conducting object is Newton's Law of Cooling (which applies equally well to heating). Suppose that at timet > 0 an object has a temperature of T(t). The Law of Cooling says that the rate at which the temperature of the object changes over time is given by IP = -k(T – A), dt (1) where A is the ambient (surrounding) temperature and k is a constant called the conductivity (which is a property of the cooling object). Newton's Law of Cooling assumes that the cooling body has a uniform temperature throughout its interior. This is not strictly accurate, as a cooling body loses heat through its surface.
Transcribed Image Text:Imagine pouring a cup of hot coffee and letting it cool at room temperature. How does the tem- perature of the coffee decrease in time? How long must you wait until the coffee is cool enough to drink? When should you add some cold milk to the coffee to accelerate the cooling as much as possible? A fairly accurate model to describe the temperature changes in a conducting object is Newton's Law of Cooling (which applies equally well to heating). Suppose that at timet > 0 an object has a temperature of T(t). The Law of Cooling says that the rate at which the temperature of the object changes over time is given by IP = -k(T – A), dt (1) where A is the ambient (surrounding) temperature and k is a constant called the conductivity (which is a property of the cooling object). Newton's Law of Cooling assumes that the cooling body has a uniform temperature throughout its interior. This is not strictly accurate, as a cooling body loses heat through its surface.
3. Solve this differential equation, using T(0) = To as initial condition.
Transcribed Image Text:3. Solve this differential equation, using T(0) = To as initial condition.
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