Newton's law of cooling question, no inital temperature given

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Homework Help Overview

The problem involves determining the initial temperature of an object cooling in a room, applying Newton's law of cooling. The object’s temperature is recorded at two points in time: 31°C and 30°C, with the ambient room temperature noted as 20°C.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to apply Newton's law of cooling but expresses uncertainty about how to proceed without the initial temperature. They typically use the initial temperature in their calculations, which complicates the current situation.
  • Some participants question the completeness of the problem statement, noting a missing part regarding the room's temperature.
  • One participant suggests an assumption that the initial temperature could be taken as the first recorded temperature, 31°C, at time t=0.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the initial conditions and the implications of the missing information. Some guidance has been offered regarding assumptions, but no consensus has been reached on the best approach to take.

Contextual Notes

The problem lacks clarity due to the incomplete statement about the room's temperature, which may affect the application of Newton's law of cooling. Participants are navigating this ambiguity while trying to formulate a solution.

miniradman
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Homework Statement


The temperature of an object has been lying at rest and cooling for sometime had been found to be 31oC. An hour later, the same object was found to be 30oC. The room was also What was the initial temperature of the object, assume Newton's law of cooling applies.


Homework Equations


Newton's law of cooling

\frac{dT}{dt} = k (T - Ts) where:

Ts = ambient temperature
T = the temperature at anytime
k = constant of proportionality


The Attempt at a Solution


Ok, normally when I do a Newtons law of cooling question, I start off with the inital temperature followed by a temperature at an "X" time. And then I would convert the formula into it's exponential form i.e. y = Aekt+c. then I would use the initial temperature (or the temperature when t=) to cancel out one of the variables. However, I'm trying to find the inital temperature, so this method won't work for me anylonger and I'm not sure how to proceede :confused:

Thanks guys/gals, any help will be greatly appreciated :biggrin:
 
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miniradman said:

Homework Statement


The temperature of an object has been lying at rest and cooling for sometime had been found to be 31oC. An hour later, the same object was found to be 30oC. The room was also What was the initial temperature of the object, assume Newton's law of cooling applies.
"The room was also" - what? Where's the rest of this sentence?
miniradman said:

Homework Equations


Newton's law of cooling

\frac{dT}{dt} = k (T - Ts) where:

Ts = ambient temperature
T = the temperature at anytime
k = constant of proportionality

The Attempt at a Solution


Ok, normally when I do a Newtons law of cooling question, I start off with the inital temperature followed by a temperature at an "X" time. And then I would convert the formula into it's exponential form i.e. y = Aekt+c. then I would use the initial temperature (or the temperature when t=) to cancel out one of the variables. However, I'm trying to find the inital temperature, so this method won't work for me anylonger and I'm not sure how to proceede :confused:

Thanks guys/gals, any help will be greatly appreciated :biggrin:
 
Sorry, the room was also found to be 20 degrees celsius
 
Take the initial temperature to be 31°C at t=0. The time spent lying at rest in the room doesn't matter before the temp was measured.
 

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