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Home / Physics / Study the Relationship between the Temperature of a Hot Body and Time by Plotting a Cooling Curve - Testbook

Study the Relationship between the Temperature of a Hot Body and Time by Plotting a Cooling Curve - Testbook

Last Updated on Jan 26, 2025
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Newton’s law of cooling states that a body's cooling rate is directly proportional to the temperature difference between the body and its surroundings, as long as the difference doesn't exceed 30°C. In this experiment, we will test this law by examining the relationship between the temperature of a hot body and time, creating a cooling curve in the process.

Objective

The goal is to explore the connection between a hot body's temperature and time by generating a cooling curve.

Equipment and Materials Needed
  • Apparatus for demonstrating Newton’s law of cooling (a copper calorimeter with a wooden lid that has two holes for a thermometer and stirrer, and a double-walled open vessel)
  • Two thermometers
  • Stopwatch
  • Heater
  • Burner
  • Water
  • Stand with clamp
  • Two rubber stoppers with holes
  • Strong cotton threads
  • Beaker

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Theoretical Background

According to Newton’s law of cooling, the cooling rate of a body is directly proportional to the temperature difference between the body and its surroundings, assuming the temperature difference is small.

This can be expressed mathematically as follows:

For a body with a mass m and specific heat c , which is kept at a temperature T in an environment with a temperature T 0 , the heat energy can be calculated as follows:

The cooling rate is,

Therefore,

Since ms is constant,

From the above equations, it is clear that as time increases, the temperature T decreases, and consequently, the temperature difference ( T – T 0 ) decreases, which in turn causes the temperature drop ( dT / dt ) to decrease.

Experimental Procedure
  1. Fill the gap between the double walls of the enclosure with water and place it on a table.
  2. Fill two-thirds of the calorimeter with water heated to approximately 80 °C.
  3. Hang the calorimeter inside the enclosure with a thermometer inside it. Cover it with a wooden lid that has a hole in the center.
  4. From the clamp and stand, suspend one thermometer in the enclosure water and the other in the calorimeter water.
  5. Note the thermometers' least count.
  6. Reset the stopwatch to zero and note its least count.
  7. Note the temperature T 0 of the water in the enclosure.
  8. Start stirring the water in the calorimeter to ensure uniform cooling.
  9. Once the calorimeter reaches an appropriate temperature reading, note it down and start and stop the stopwatch.
  10. Continue stirring and record the temperature every few minutes. The temperature will fall rapidly in the first few minutes.
  11. Record the temperature of the enclosure water every five minutes.
  12. When the temperature drop slows down, record the temperature every two minutes for ten minutes, and then every five minutes.
  13. Stop when the temperature drop becomes very slow.
  14. Record your observations as shown in the table below.

Observations

The Least count of enclosure water thermometer = _____ °C

The Least count of calorimeter water thermometer = _____ °C

The Least count of stopwatch = _____ s

S.No of observations

Cooling Time

t

Calorimeter Water Temperature

( T °C)

Enclosure Water Temperature

( T 0 °C)

Temperature Difference

T – T 0 °C

         

Calculations

  1. If the enclosure water temperature is not constant, take its average.
  2. Calculate the temperature difference ( T – T 0 )
  3. Plot a graph of temperature T against time t . This graph is known as the liquid's cooling curve.

Conclusion

Initially, the temperature falls rapidly, then the temperature difference decreases slowly. This observation aligns with Newton’s law of cooling.

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Frequently Asked Questions

Newton’s law of cooling states that the rate of change of temperature of a body is directly proportional to the difference between its own temperature and the temperature of its Surrounding.

Water has high specific heat capacity because of which it absorbs more quantity of heat than others.

Mass and the rate of fall of temperature are inversely proportional to each other. As the mass of a baby is lesser than an adult man, the baby loses a larger amount of heat than a grownup adult. Hence, a baby needs more wrapping.

The heat required to raise the temperature of unit mass by 1o C is known as the specific heat capacity.
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