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Newton's law of cooling

by 2013
Tags: cool, cooling, newton, newton law
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2013
#1
Jun28-13, 07:12 AM
P: 92
1. The problem statement, all variables and given/known data

In autumn 2011 a whale was stranded.
Although the whale was already dead for some time
and the ambient temperature is approximately constant at
the freezing point was, the body temperature was inside lying on the beach of Wales on 21 November is still about 20 C.
Three days later, this had dropped to about 15 C.
The cooling of a body on an unheated air can be modeled by a temperature profile. However, for different initial and ambient temperatures, and different bodies to scale the axes are different.
Treasures with the help of the information given on when the whale is dead on the beach when its body temperature amounted to 37 C. the time of death.


2. The attempt at a solution

Newton's law of cooling
20=To * e^-0k
15=To * e^-3k

k=0,09589
To=20

37=0+(20-0)e^-kt

-kt = ln(1,85)
t = ln(1,85)/(-0,09589)
t = -6,42

What is the initial value?
How can I scale the axes?


thank you in advance
1. The problem statement, all variables and given/known data



2. Relevant equations



3. The attempt at a solution
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SteamKing
#2
Jun28-13, 08:31 AM
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t = 6.42 what? Years, days, minutes, months, femtoseconds, fortnights?
2013
#3
Jun28-13, 08:36 AM
P: 92
days

Is it a right solution?
How can I scale the axes?

2013
#4
Jun28-13, 03:25 PM
P: 92
Newton's law of cooling

hi,
can somebody please help me?
How should I scale the time and temperature axes?
What is the start temperature?
gneill
#5
Jun28-13, 04:17 PM
Mentor
P: 11,805
Quote Quote by 2013 View Post
hi,
can somebody please help me?
How should I scale the time and temperature axes?
What is the start temperature?
What temperature did the body start with (at the time of death)? So your max temp on the temperature scale should be what? What's the eventual temperature that the body is heading towards?

You've calculated the time of death to be over six days ago (from when?). What units would be convenient? Then you have to decide what times to indicate on the axis. Will you place t=0 as the time of death, or perhaps t=0 occurs at the instant you took one of the temperature readings, or perhaps you want to use the date? Your choice, really; it depends on how the chart will be used.
2013
#6
Jun29-13, 02:21 AM
P: 92
Six days before the body temperature is 20 C is the time of death.

The bottom line in the diagram is the freezing point (ambient temperature).

I should label/scale the axes of the diagram, but I do not know what the starting value is.
I only have the information that is given in the task, and I have calculated above.
How would the axis scale? Do I understand the task wrong?
gneill
#7
Jun29-13, 06:47 AM
Mentor
P: 11,805
Quote Quote by 2013 View Post
Six days before the body temperature is 20 C is the time of death.

The bottom line in the diagram is the freezing point (ambient temperature).

I should label/scale the axes of the diagram, but I do not know what the starting value is.
I only have the information that is given in the task, and I have calculated above.
How would the axis scale? Do I understand the task wrong?
This graph you're labeling is presumably to be used as an aid to finding the time of death of a body from a temperature reading taken upon discovery of the body.

Is the body ever at 10,000 C? No? Why not? Is it ever at -200 C? No? Why not? Is it ever at 37 C? YES! When it's alive. And 37 C is the temperature it has throughout the time that it's alive. As soon as the whale dies it begins to cool FROM 37 C. The time of death is pinpointed as the instant when the body temperature starts falling from 37 C. So what maximum and minimum values will you put on your temperature axis? What units will you use?

For the time axis, what sort of time frame do you think will be useful? One hour? Ten years? Look at the curve and judge a practical total period. What units of time might be convenient?
2013
#8
Jun29-13, 10:13 AM
P: 92
you mean the start point is at 37C

The one axis days and the other degrees.

Do you think it is right?
gneill
#9
Jun29-13, 10:25 AM
Mentor
P: 11,805
Quote Quote by 2013 View Post
you mean the start point is at 37C

The one axis days and the other degrees.

Do you think it is right?
Well, you do want the chart to represent temperature versus time, right? After all, the question is about Newton's Law of Cooling...
2013
#10
Jun29-13, 10:34 AM
P: 92
yes of course

this was my task:
The cooling of a body on an unheated air by means of a temperature curve, as shown in Figure 1 to be modeled. However, for different initial and ambient temperatures, and different bodies to scale the axes are different.
Treasures with the help of the information given on when the whale is dead on the beach when its body temperature amounted to 37 C. the time of death.

So I have to scale the axis and I am not shire if I have solved it right.
gneill
#11
Jun29-13, 11:52 AM
Mentor
P: 11,805
If you can label the axes so that the temperature axis includes at least the maximum and minimum temperatures, and the time axis includes the time since death of the measurements taken (plus some more time for other cases where the time since death happens to be longer) then you should be okay.


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