Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Newton's law of cooling states that- = -k (x- A), where x(t) is the temperature of an object at dt time t, A is the temperature of the object's surroundings and k is a constant. a) If the ambient temperature A is constant, only one choice of sign for k makes physical sense - either k is positive or k is negative. Explain which choice is correct. b) Suppose the object sits outside, in Potsdam, over the course of a year. The ambient temperature will vary with time - suppose A = Ao cos(wt), where Ao and wo are constants. i. What might be reasonable values for A, and wo? 0) the object is at room temperature (so x(0) = T, ii. Let's say that initially (at time t = where To represents room temperature). %3D What impact, in the long-run, does the value T, have on the temperature x(t) of the obiect?

Newton's law of cooling states that- = -k (x- A), where x(t) is the temperature of an object at dt time t, A is the temperature of the object's surroundings and k is a constant. a) If the ambient temperature A is constant, only one choice of sign for k makes physical sense - either k is positive or k is negative. Explain which choice is correct. b) Suppose the object sits outside, in Potsdam, over the course of a year. The ambient temperature will vary with time - suppose A = Ao cos(wt), where Ao and wo are constants. i. What might be reasonable values for A, and wo? 0) the object is at room temperature (so x(0) = T, ii. Let's say that initially (at time t = where To represents room temperature). %3D What impact, in the long-run, does the value T, have on the temperature x(t) of the obiect?

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
See similar textbooks
icon
Related questions
Question
Linear example: Problem 3 (modified from exercise 1.4.10): dx Newton's law of cooling states that dt = -k (x - A), where x(t) is the temperature of an object at time t, A is the temperature of the object's surroundings and k is a constant. a) If the ambient temperature A is constant, only one choice of sign for k makes physical sense - either k is positive or k is negative. Explain which choice is correct. b) Suppose the object sits outside, in Potsdam, over the course of a year. The ambient temperature will vary with time suppose A Ao cos(wt), where Ao and wo are constants. %3D i. What might be reasonable values for A, and w,? ii. Let's say that initially (at time t = 0) the object is at room temperature (so x(0) = To, where T, represents room temperature). What impact, in the long-run, does the value T, have on the temperature x(t) of the object?
Transcribed Image Text:Linear example: Problem 3 (modified from exercise 1.4.10): dx Newton's law of cooling states that dt = -k (x - A), where x(t) is the temperature of an object at time t, A is the temperature of the object's surroundings and k is a constant. a) If the ambient temperature A is constant, only one choice of sign for k makes physical sense - either k is positive or k is negative. Explain which choice is correct. b) Suppose the object sits outside, in Potsdam, over the course of a year. The ambient temperature will vary with time suppose A Ao cos(wt), where Ao and wo are constants. %3D i. What might be reasonable values for A, and w,? ii. Let's say that initially (at time t = 0) the object is at room temperature (so x(0) = To, where T, represents room temperature). What impact, in the long-run, does the value T, have on the temperature x(t) of the object?
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS