|Aim||To study the relationship between the temperature of a hot body and time by plotting a cooling curve.|
|Apparatus Required||A hot body (e.g., a metal block)|
A thermometer to measure the temperature
A stopwatch to measure time
Insulation material (e.g., Styrofoam) to minimize heat loss to the environment
Graph paper or computer software to plot the cooling curve
|Theory||When a hot body is left in a cooler environment, it loses heat to the surroundings through conduction, convection, and radiation. As a result, its temperature decreases over time. This process of losing heat and cooling down is called thermal cooling. The rate at which the body cools down depends on the temperature difference between the body and the surroundings, the surface area of the body, the material of the body, and the insulation of the body.|
Newton’s law of cooling is a physical law that describes the rate of cooling of a hot body in contact with a cooler environment. It states that the rate of change of the temperature of a hot body is proportional to the temperature difference between the body and its surroundings.
The law can be mathematically expressed as:
dT/dt = -k (T – Ts)
Where: dT/dt is the rate of change of temperature with respect to time T is the temperature of the hot body Ts is the temperature of the surrounding environment k is a proportionality constant, called the cooling constant, which depends on the thermal properties of the hot body and the surrounding medium.
According to this law, the temperature of a hot body decreases exponentially with time as it loses heat to the surrounding environment. The larger the temperature difference between the hot body and the surroundings, the faster the body will cool down.
Newton’s law of cooling applies to a wide range of physical systems, including objects cooling in air, liquids, and solids. It has practical applications in many fields, such as engineering, thermodynamics, and meteorology, where it is used to model and predict heat transfer processes.
Overall, Newton’s law of cooling provides a fundamental understanding of the physical processes involved in heat transfer and cooling, and is an important tool for scientists and engineers working in fields related to thermal dynamics.
|Procedure||Fill the space between the double wall of the enclosure with water and place it on a table.|
Fill two-thirds of the calorimeter with water that is heated to approximately 80°C.
Hang the calorimeter inside the enclosure using a thermometer and cover it with a wooden lid that has a hole in the middle.
Suspend one thermometer from a clamp stand into the water inside the enclosure and another thermometer into the water inside the calorimeter. Take note of the least count of both thermometers.
Set the stopwatch to zero and record its least count.
Take note of the initial temperature T0 of the water inside the enclosure.
Stir the water in the calorimeter to ensure uniform cooling.
When the calorimeter water reaches a convenient temperature, record its temperature and start the stopwatch.
Continue stirring the calorimeter water and take temperature readings at regular intervals, noting the temperature every few minutes. The temperature will initially decrease rapidly.
Take note of the temperature of the water inside the enclosure every five minutes.
When the rate of temperature decrease becomes slower, take temperature readings every two minutes for ten minutes, and then at intervals of five minutes.
Stop taking readings when the temperature decrease becomes very slow.
Record your observations in the given table.
|Observation and Result||As the hot body loses heat to the surroundings, its temperature decreases over time. The cooling curve shows a gradual decrease in temperature until it reaches the temperature of the surroundings. The rate of cooling is faster at the beginning of the experiment when the temperature difference between the body and the surroundings is high. As the temperature difference decreases, the rate of cooling also decreases. The slope of the cooling curve is steeper for materials with low thermal conductivity and high surface area-to-volume ratio. The experiment helps us understand the relationship between the temperature of a hot body and time during the process of thermal cooling.|