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The general form of Newton's Law of cooling is: T(t) = T₂+ (T(0)-Tale-kt where I is the temperature at any time, t. Ta is the surrounding ambient temperature and k is the cooling constant. Consider a cup of coffee at an initial temperature, T(0) of 80°C placed into the open air at 15°C. After 5 minutes the coffee cools to 65°C. Using these initial conditions: i) Calculate the cooling constant, k ii) How long will it take for the coffee to reach 20°C?

The general form of Newton's Law of cooling is: T(t) = T₂+ (T(0)-Tale-kt where I is the temperature at any time, t. Ta is the surrounding ambient temperature and k is the cooling constant. Consider a cup of coffee at an initial temperature, T(0) of 80°C placed into the open air at 15°C. After 5 minutes the coffee cools to 65°C. Using these initial conditions: i) Calculate the cooling constant, k ii) How long will it take for the coffee to reach 20°C?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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b) The general form of Newton's Law of cooling is: T(t) = Ta + (T(0) - Ta)e-kt where I is the temperature at any time, t. Ta is the surrounding ambient temperature and k is the cooling constant. Consider a cup of coffee at an initial temperature, T(0) of 80°C placed into the open air at 15°C. After 5 minutes the coffee cools to 65°C. Using these initial conditions: i) Calculate the cooling constant, k ii) How long will it take for the coffee to reach 20°C?
Transcribed Image Text:b) The general form of Newton's Law of cooling is: T(t) = Ta + (T(0) - Ta)e-kt where I is the temperature at any time, t. Ta is the surrounding ambient temperature and k is the cooling constant. Consider a cup of coffee at an initial temperature, T(0) of 80°C placed into the open air at 15°C. After 5 minutes the coffee cools to 65°C. Using these initial conditions: i) Calculate the cooling constant, k ii) How long will it take for the coffee to reach 20°C?
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