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.
Is there a way to determine when an object s temperature is falling most rapidly according to Newton s Law of Cooling?
- 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)10
- 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.10
- When the temperature difference is the greatest.30
- 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).20
- 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 time00
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- Yes, but as the temperature differential falls, so does the rate of change.
- The RATE of cooling (or heating) is the temperature difference times the Thermal Resistance of the interface between them.00
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