Experimental Setup of Verification of Newton's Law of Cooling

Shubham studied the concept of Newton's law of cooling.

He is going to perform an experiment on it in his school lab under the guidance of his teacher.

In the laboratory, his teacher provides a setup for the experiment in a group of 5 members.

Let's see the experimental verification of Newton's law of cooling

The following apparatus required- two calorimeters, two thermometers, insulating lid, heating element, wire, stirrer and a stopwatch.

First, we fill the inner calorimeter with some liquid.

Now let's put the smaller calorimeter into the bigger calorimeter.

We cover both the calorimeters with the insulating lids and put two thermometers $T_{1}$ and $T_{2}$ into the inner and outer calorimeter respectively.

After that we put the stirrer into the liquid which mixes the heat throughout the liquid uniformly.

For heating the liquid, we must introduce a heating element.

The setup may look like this-

The gap between inner calorimeter and outer calorimeter is filled with air, whose temperature is taken as $T_{0}$.

Newton' law of cooling states that the rate of cooling is directly proportional to the temperature difference $(ΔT)$.

It is only applicable when the temperature of the system is approximately equal to the temperature of the surrounding.

If we turn on the current, the heating element will start heating the water inside the inner calorimeter.

Stirring should be performed continuously for uniform distribution of heat throughout the liquid.

When the temperature of water reaches $2−3°C$ above the temperature of outer calorimeter$(T_{0})$, the heating element is removed.

It is important to note that small increment is done in temperature of water because Newton's law of cooling is only applicable at small temperature difference.

Now, we let the liquid to cool and measure the drop in temperature at regular interval of time with the help of a stopwatch.

Let's make a table between time$(t)$ and temperature drop into the water $T_{0}$.

When the temperature of inner and outer calorimeter becomes equal, the experiment must be stopped i.e. at $T_{0}=T_{0}$.

From Newton's law of cooling equation, we can write,

Where $T$ is the temperature of the liquid at any time, $T_{0}$ is the temperature of the surrounding and $T_{_{′}}$ is the initial temperature of liquid.

The Newtons' law off cooling can be shown on a graph as,

As we move from point $A$ to $C$, the difference in temperature($ΔT$) gets reduced.

As per the Newton's law of cooling, we can show the slope of curve as,

The negative sign in the slope denotes that the temperature is reducing with time. As $ΔT$ decreases, the slope will also decrease.

After modifying the Newton's law of cooling equation, we get,

The graph of the above equation is plotted as-

On further modification of the equation, we get,

where $k$ is a constant. So, the equation becomes linear and the graph of the above equation is a straight line.

Revision

Newton' law of cooling states that the rate of cooling is directly proportional to the temperature difference $(ΔT)$.

The whole experimental setup is shown here.

We can also show the Newton's law of cooling on a graph as,