Relationship Between Temperature of Hot Body and Time by Plotting Cooling Curve

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Cooling Curve Practical

The primary aim of this experiment is to understand the cooling curve graph that is plotted by studying the relationship between the temperature of a hot body and time. The experiment is based upon Newton’s Law of Cooling. It states that there is a direct relationship between the rate of cooling of an object and the temperature difference of the objects and its surroundings. Therefore, the rate of cooling is always proportional provided that the difference in the temperatures of the object and it is surroundings does not exceed 30oC. If a body has mass “m” and the specific hear is “s” then the initial temperature of the body is “θ” higher than the surrounding temperature and “θo” is the rate of loss of heat. 

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Cooling Curve Graph

Two important assumptions that are undertaken with Newton’s Cooling law is that the temperature difference between the object and the surrounding should be small, less than 30o.  The second assumption is that the nature of the radiating surface should remain the same. 

Newton’s Law of Cooling can also be represented with a physical experiment that is commonly conducted in schools and colleges. To obtain a cooling curve graph, some apparatus and materials are required to conduct the experiment. Below is the list of materials required to conduct this practical.

  1. Beaker

  2. Strong cotton threads

  3. Two rubber stoppers with holes

  4. Clamp Stand

  5. Water

  6. Burner

  7. Heater

  8. Stop Clock

  9. Two thermometers

  10. Copper calorimeter with a wooden lid that has two holes for inserting a thermometer and a stirrer and lastly an open double-walled vessel. This apparatus is also known as Newton’s law of cooling apparatus. 

The next step after arranging all the products is to follow the procedure for running the cooling curve practical. This list below draws steps that should be followed during a cooling curve practicals.

  1. The very first step involves filling the space with water between the double wall of the enclosure. After the water is filled, you can place the vessel on top of a table.

  2. The next step requires a calorimeter. The calorimeter is two-third filled with water which was heated to about 80oC. 

  3. After heating the water in the calorimeter, it is suspended inside the enclosure with a thermometer in it. This setup is covered with a wooden lid that has a hole in the middle.

  4. One thermometer is suspended from the clamp and stands into the enclosure water while the other thermometer is in calorimeter water.

  5. At this stage, note the least count of thermometers

  6. Take a stopwatch and set it to zero. Now note down its least count. 

  7. At this stage, note the temperature T0  of the water in the enclosure.

  8. In order to make sure that water is uniformly cool, start stirring the water in the calorimeter

  9. Note down the temperature reading of the calorimeter, start and stop the stopwatch again

  10. Note the temperature again after some time. Continue stirring. It can be observed that the temperature falls quickly in the first few minutes.

  11. At this stage, note down the temperature in the enclosure water every five minutes.

  12. The temperature fall will gradually slow down and when this happens note down the temperature readings at every two minutes for the next ten minutes and then at an interval of five minutes

  13. When the temperature becomes very slow, stop the recording

  14. Record your observation in a tabular form. 

When following the procedure, be cautious about two things. Firstly, the double-walled enclosure should be used to maintain the surrounding of a constant temperature. And secondly, in order to make sure that the cooling is uniform, stirring should remain continuous. 

Temperature Time Graph 

The completion of the experiment is followed by the mathematical calculation using the recordings from the practical. The excess temperature (θ - θ0) can be calculated as well as the   log10 (θ - θ0) can be calculated for each reading. These values should be recorded in the columns of the table. The cooling curve graph or the temperature vs time graph can then be plotted using these values where x-axis corresponds to the time “t” taken and the y-axis corresponding to the log10 (θ - θ0). 

Mathematically, the heat energy for a body of mass “m” at a specific heat “c”, the temperature denoted as θ” and θ0” can be calculated from the equation below:

 dQ/dt =  ms.dθ0/dθ

It can be, therefore, derived from this equation that when time increases,  (θ - θ0) decreases. 

FAQ (Frequently Asked Questions)

1.What are Some of the Limitations of Newton’s Law of Cooling?

Every phenomenon has some strengths and some limitations. In the case of Newton’s Law of Cooling also there are certain limitations. One of the limitations is that this law is only applicable at lower temperatures. It can only be applied when the difference between the initial and final temperatures is less than 50-80 degrees Celsius. Furthermore, another limitation states that the temperature of the surroundings need to stay constant throughout the cooling of the body, only then can Newton's Law of Cooling be applied. These are three popular limitations of Newton’s Law of Cooling. 

2.What are the Real-life Applications of Newton’s Law of Cooling?

One of the popular applications of this law is wrapping more woolen clothes to a baby than an adult. As it has been stated that the made and the rate of fall of temperature are inversely proportional to each other, a baby that weighs less in mass loses a larger amount of heat than an adult weighs more. Therefore, more wrapping of clothes is required for a baby in order to prevent the loss of heat. Similarly, it is easy to heat food on a large plate as compared to a bowl. The rate of cooling is directly proportional to the volume, therefore the large plate cools and heats faster than a bowl.