To Plot Temperature–Time Graph for a Hot Object as it Cools

# Objective

To plot temperature–time graph for a hot object as it cools.

# Theory

If hot coffee and cool juice are left open on the table, what changes will occur after some time?

We can observe that the coffee loses its hotness, and cold juice loses its coldness over time.

If we measure the temperature of the coffee and juice after some time, we can observe that the temperatures of the coffee and juice are equal. How does this process occur?

Definition of temperature

The degree of hotness or coldness of a body is known as temperature.

Definition of heat

• Heat is the form of energy transferred between two (or more) systems or a system and its surroundings by virtue of temperature difference.
• Heat transfer occurs until two objects reach the same temperature. A hot body loses heat, while a cold body gains heat.

Heat transfer methods

Heat transfer occurs in three methods: Conduction, convection, and radiation.

Conduction – It is the transfer of heat through the vibration of particles. This method involves only the energy flow, and it does not involve any material flow.

Convection – It is the heat transfer through the flow of fluid. The fluid flows from higher-temperature to lower-temperature regions.

Radiation – It is the transfer of heat through electromagnetic waves.

How does the temperature difference between a hot body and its surroundings affect the rate of heat transfer?

Note the temperature of a hot body over several minutes. When we plot a graph with time on the X-axis and the temperature of the hot object on the Y-axis, the resulting figure is as shown.

Figure 1: Curve showing cooling of hot water with time

The slope of the graph represents the rate of heat loss or the rate of cooling of the hot body.

• Initially, there is a significant temperature difference between the hot body and its surroundings, resulting in a steep slope that indicates a high rate of heat transfer or a high rate of cooling.
• As time progresses, this temperature difference decreases, causing the slope to decrease and signifying a slower rate of heat transfer or slower rate of cooling.
• Eventually, the curve becomes parallel to the x-axis, suggesting a substantial reduction in the cooling rate.
• Cooling ceases entirely when the temperature of the hot body becomes equal to that of its surroundings.
• The rate of heat loss or cooling rate depends on the temperature difference between the object and its surroundings. As the temperature difference between the object and its surroundings decreases, the rate of heat loss or cooling also decreases.
• When heating food, the rate of heat transfer from the pot to the food depends on the temperature difference between the pot and the food. Cooking at higher temperatures results in a higher rate of heat transfer, leading to quicker cooking times.

# Learning Outcomes

Students understand:

• How the temperature of a hot body decreases.
• The relationship between the rate of heat loss and the temperature difference between the object and its surroundings.
• The concept of thermal equilibrium.