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Using Newton’s Law of Cooling calculator, you can easily figure out how long it takes for an object to cool down from one temperature to another.
“The rate of heat loss of a body or object is proportional to the difference between its temperature and the surrounding temperature (ambient temperature)”
In simple words, It is a scientific principle that defines the changes in the temperature of an object when it gets exposed to a surrounding medium having a different temperature.
The mechanisms of heat exchange include thermal conduction, convection, and radiation. When heat loss happens because of thermal conduction and convection then Newton’s Law of Cooling is applicable.
The Newton’s Law of Cooling Formula is as follows:
\( \dfrac{dT}{dt} = -k \cdot (T – T_s) \)
\( \ T(t) = -k \cdot (T – T_s) \)
Where
To figure out how temperature changes over time, we can further simplify it as:
\(\ T(t) =\ T_{s} + (T_{o} – T_{s})*e^{(-k*t)})\)
Where
This equation enables us to determine the temperature of the body or object at any given time.
For more information, visit the source wikipedia.org.
Go through the following steps:
Determine The Ambient Temperature: It is the temperature of the air present in the object’s surroundings
Calculate The Initial Temperature: Measure the initial temperature of the object in degrees Celsius
Determine The Value of The Cooling Coefficient(k): Calculate the cooling coefficient by considering the material properties and the surface area
Measure The Final Temperature: Put the values in Newton’s law of cooling formula and get the final temperature
Find the final temperature of a body after 3 seconds using the law of cooling with the provided parameters:
Solution:
\(\ K = \dfrac{hA}{C}\)
\(\ K = \dfrac{1\times 0.003}{4}\)
\(\ K = \ 0.00075\)
Now put values in Newton’s law of cooling formula
\(\ T(t) =\ T_{s} + (T_{o} – T_{s})*e^{(-k*t)})\)
\(\ T(t) =\ 20 + (3 – 20)*e^{(-k*t)})\)
\(\ T(t) =\ 20 + (-17)*e^{(-1*3)})\)
\(\ T(t) =\ 20 -16.96)\)
\(\ T(t) =\ 3.038\ Degrees\ Celsius\)
Rather than dragging yourself into this long calculation, make things easier by using Newton’s law of cooling calculator and get precise results in seconds.
Newtons law of cooling is very crucial across physics, and engineering for several reasons, which are:
Factors that affect Newton’s Law of Cooling are:
The constant “k” can be calculated by dividing the temperature by the time that it takes to reach the temperature difference.
\(\ k =\ \dfrac{(T_1 – T_2)}{t}\)
Where
If you have the values of the heat transfer coefficient and the area of heat exchange, then use the following equation:
\(\ K = \dfrac{hA}{C}\)
Where