Writing equation for integration regarding rate of change

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SUMMARY

The discussion centers on applying Newton's Law of Cooling to determine the temperature of an object placed in water. The object starts at 26 degrees Celsius and rises to 70 degrees Celsius in five minutes when placed in water at a constant temperature of 90 degrees Celsius. The key equation discussed is d(temp)/d(t) = -k(temp(object) - temp(surrounding medium), which describes the heat transfer dynamics. The participants clarify that the law can be adapted to account for heat transfer from the water back to the object by introducing a negative sign in the derivative.

PREREQUISITES
  • Understanding of Newton's Law of Cooling
  • Basic calculus concepts, particularly derivatives
  • Knowledge of temperature measurement in Celsius
  • Familiarity with heat transfer principles
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  • Study the derivation and applications of Newton's Law of Cooling
  • Explore differential equations related to heat transfer
  • Learn about the concept of thermal equilibrium
  • Investigate real-world applications of heat transfer in engineering
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Students in physics or engineering, educators teaching thermodynamics, and anyone interested in understanding heat transfer dynamics in practical scenarios.

Poppynz
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Hi

An object with temperature 26 degrees Celsius is placed in water with constant temperature of 90 degrees Celsius. If the temperature of the object rises to 70 degrees Celsius in five minutes, what will be the temperature after 10 minutes?

I thought of using Newtons law of cooling d(temp)/d(t) = -k(constant of proportionality) (temp(object)-temp(surrounding medium)) but have read on the internet that it only describes transfer of heat from object to water not the other way around.

Any ideas would be appreciated
 
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Well, if the object transfers some amount of heat to water, then you can say that the water transfers the same amount with opposite sign to the object,
And all you need to do is to add a minus sign in from of the derivative.
(I think so)
 

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