Regression (I think) of Newton's Law of Cooling

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Homework Help Overview

The discussion revolves around modeling temperature data collected from two cooling cups using Newton's Law of Cooling. The original poster (OP) is tasked with applying two methods: one involving regression analysis in Excel and the other requiring the determination of constants in a linear function derived from the logarithmic form of the cooling equation.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The OP describes their attempts to use Excel for regression analysis and expresses difficulty with the second method, which involves finding constants A0 and k. Participants discuss the relationship between the linear equation and the parameters in the context of the logarithmic transformation of the cooling model.

Discussion Status

Participants are actively engaging with the OP's questions, providing guidance on the interpretation of the linear relationship. There is a recognition of the need to clarify the definitions of the constants involved in the equations being discussed. Some participants correct earlier assumptions and emphasize the importance of the specific forms of the equations.

Contextual Notes

There appears to be some confusion regarding the interpretation of the constants A0 and k in relation to the linear equation derived from the logarithmic form of Newton's Law of Cooling. The OP is working under the constraints of a homework assignment that requires the application of both methods without providing complete solutions.

HalcyonStorm
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Homework Statement


Using a data logger, I have collected data for two cooling cups: the temperature (c) at 1 second intervals. My task was to model this data using two methods.

"METHOD 1: Use EXCEL or the regression analysis capability of your graphic calculator"
"METHOD 2: Find the constants in the model (A0 and k) by constructing a linear function relating lny and t."

I chose to use Excel for method 1. I have attached the spreadsheet.

Homework Equations


Newton's Law of Cooling: y=A0*e^kt


The Attempt at a Solution


I have attached the graphs that I have been able to produce (method 1) in a word document. I am unable to do method 2, as I'm really stuck for ideas.

Thank-you! Any help is much appreciated :)
 

Attachments

Last edited:
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HalcyonStorm said:

Homework Statement


Using a data logger, I have collected data for two cooling cups: the temperature (c) at 1 second intervals. My task was to model this data using two methods.

"METHOD 1: Use EXCEL or the regression analysis capability of your graphic calculator"
"METHOD 2: Find the constants in the model (A0 and k) by constructing a linear function relating lny and t."

I chose to use Excel for method 1. I have attached the spreadsheet.

Homework Equations


Newton's Law of Cooling: y=A0*e^kt


The Attempt at a Solution


I have attached the graphs that I have been able to produce (method 1) in a word document. I am unable to do method 2, as I'm really stuck for ideas.

Thank-you! Any help is much appreciated :)

For method 2, the idea is to find constants A0 and k for which lny = kt + A0. If you plot lny versus t, this equation represents a straight line.
 
Thanks for your response!

Would it be safe for me to assume that (from y= mx + c), k is equal to m and A0 is equal to c?
 
HalcyonStorm said:
Thanks for your response!

Would it be safe for me to assume that (from y= mx + c), k is equal to m and A0 is equal to c?
Yes.
 
Be careful! - Its really "c = ln(A0)"
 
TheoMcCloskey said:
Be careful! - Its really "c = ln(A0)"
No, not if the OP is working with the equation lny = kt + A0.
 
No, not if the OP is working with the equation lny = kt + A0.

Yes, that is is correct, and I stand corrected. I was assumming the OP's original equation was, as he stated in "Relevant equations", of the form y = A_0 \cdot e^{kt}.
 

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