Science & Mathematics » Physics » Is there a way to determine when an object s temperature is falling most rapidly according to Newton s Law of Cooling?

# Is there a way to determine when an object s temperature is falling most rapidly according to Newton s Law of Cooling?

• Yes.
The math behind this is the definition of Newton's law of cooling itself, where it says dT/dt = T - T_s
Where T_s is the temp. of surroundings, assumed to stay constant.

Initially as T is largest, dT/dt is largest and then it starts to shrink as the difference T - T_s approaches 0.

If you solve the equation for temperature, you get an exponential function of time whose slope (rate of change) is most negative at t=0.

Have in mind this also works if the object is colder than its surroundings. In a way the law of "cooling" is only half of the story as it applies to heating as well.
Here we just flip the sign so that dT/dt = T_s - T, and the object's temperature increases most rapidly at the start.
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• Cooling rate is proportional to temperature difference:

dT/dt = - k ( T - Tsurrounding)

This differential equation has solution

T(t) = Tsurr + (T(0) - Tsurr) exp(-k t)
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• If the surrounding temperature remains constant the fastest change is always at the start when the difference at its biggest. If the surrounding temperature is a function of time then you have to solve the whole expression as a differential equation.
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• When the temperature difference is the greatest.
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• Yes, you're right that cooling is rapid when the temperature difference is high, and also when the medium is a good conductor. (Does not work in hell, I believe).
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• Basically during motion of a mass toward an increasing gravity field the mass experiences a decrease in mass.
A decrease in mass causes a decrease in temperature.
When the power content of a mass changes we have a temperature energy changes with time
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• Use thermister. Ask your teacher the method to connect to measure the voltage. Immerse the thermistor in the hot water and measure the voltage. This voltage is proportional to the temperature. You can complete the project.
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• An object's temperature is falling most rapidly when the heat differential between the object and it's environment is greatest. This, of course, assumes a constant heat conduction rate in the environment.
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• Yes, but as the temperature differential falls, so does the rate of change.
https://www.petropedia.com/definition/94...
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• The RATE of cooling (or heating) is the temperature difference times the Thermal Resistance of the interface between them.
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