Newton's Law of Cooling Calculator

Use the given tool to determine the rate at which an object cools in a surrounding environment according to Newton’s Law of Cooling.

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Ambient Temperature:

°C ▾

Initial Temperature:

°C ▾

Area:

mm² ▾

Heat Capacity:

J/K ▾

Heat Transfer Coefficient:

W/(m²·K) ▾

Heat Capacity:

sec ▾

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Newton's regulation of Cooling?

“The fee of heat lack of a body or object is proportional to the difference between its temperature and the surrounding temperature (ambient temperature)”

what's the formula of Newton’s law of Cooling?

The Newton’s regulation of Cooling formulation is as follows:

\(\dfrac{dT}{dt} = -k \cdot (T - T_s) \)

\(\ T(t) = -k \cdot (T - T_s) \)

Where:

T is the fee of alternate of temperature
Ts is the surroundings temperature

To parent out how temperature modifications over time, we are able to further simplify it as::

\(\ T(t) =\ T_{s} + (T_{o} - T_{s})*e^{(-k*t)})\)

Where,

\(\ T_{o}\) is initial temperature of the object
\(\ T_{s}\) is the surroundings temperature\)
\(\ T\) is the time
\(\ K\) is the heat transfer coefficient in W/(m²·K)

This equation enables us to determine the temperature of the frame or object at any given time. For extra information, visit the supply wikipedia.org.

Example:

Find the final temperature of a cup of coffee after 5 minutes using the law of cooling with the provided parameters:

Ambient temperature = 25 Degrees Celsius
Initial temperature = 90 Degrees Celsius
Surface area = 0.005\(\ m^{2}\)
Heat capacity = 3.5 J/K
Heat transfer coefficient = 2 W/(m²·K)

Solution:

\(\ K = \dfrac{hA}{C}\)

\(\ K = \dfrac{2 \times 0.005}{3.5}\)

\(\ K = \ 0.00286\)

Now put values in Newton's law of cooling formula:

\(\ T(t) =\ T_{s} + (T_{o} - T_{s})*e^{(-k*t)}\)

\(\ T(t) =\ 25 + (90 - 25)*e^{(-0.00286*300)}\)

\(\ T(t) =\ 25 + (65)*e^{(-0.858)}\)

\(\ T(t) =\ 25 + (65)*(0.424)\)

\(\ T(t) =\ 25 + 27.56\)

\(\ T(t) =\ 52.56\ Degrees\ Celsius\)

as opposed to appearing this prolonged calculation manually, you can use Newton's regulation of cooling calculator for quick and accurate results in seconds.