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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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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:

`T is the rate of change of temperature`

`T`

_{s}is the surroundings temperature

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,

- \(\ T_{o}\) 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 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

- Ambient temperature = 20 Degrees Celsius
- Initial temperature = 3 Degrees Celsius
- Surface area = 0.003\(\ m^{2}\)
- Heat capacity = 4 J/K
- Heat transfer coefficient = 1 W/(m²·K)

**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.

- The difference between the temperature of the body and its surroundings must be small
- Loss of heat should happen via radiation
- The surrounding temperature should remain constant during the cooling of the body or object

Newtons law of cooling is very crucial across physics, and engineering for several reasons, which are:

- Predicting the temperature change of an object over time
- Heat Transfer Analysis
- Engineering Applications

Factors that affect Newton’s Law of Cooling are:

- Surface area
- The difference between the temperature of your object and the surrounding
- Heat transfer coefficient(K)

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,

- \(\ T_1 - T_2\ is\ the\ temperature\ difference\)
- \(\ t\ is\ the\ time\ difference\ \ t=(t_1 - t_2 )\)

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

- K is the cooling coefficient
- H is the Heat transfer coefficient
- A represents the area of heat exchange
- C is the heat capacity

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