Newton's law of cooling

Newton's law of cooling

Newton's law of cooling is a scientific law that describes the rate at which a body loses heat to its surroundings. The law is named after Sir Isaac Newton, the famous physicist and mathematician who discovered it in the 17th century.

According to the law, the rate of heat loss from a body is proportional to the difference in temperature between the body and its surroundings. Mathematically, this can be expressed as:

                T(t) = Ts + (To – Ts) e-kt

Where,

• t = time,
• T(t) = temperature of the given body at time t,
• Ts = surrounding temperature,
• To = initial temperature of the body,
• k = constant.

The law of cooling is used in many areas of science and engineering, including physics, chemistry, and thermodynamics. It can be applied to a wide range of phenomena, such as the cooling of hot objects in the air, the dissipation of heat from electronic devices, and the temperature changes in living organisms.

For example, if a hot cup of coffee is left to cool in a room, the temperature of the coffee will decrease over time according to Newton's law of cooling. The rate of cooling will depend on factors such as the temperature of the coffee, the temperature of the room, the thermal conductivity of the cup, and the surface area of the cup. By measuring the temperature of the coffee at different times, it is possible to determine the rate of cooling and calculate the time it will take for the coffee to reach the desired temperature.

Limitations of Newton’s Law of Cooling

1. The difference in temperature between the body and surroundings must be small
2. The loss of heat from the body should be by radiation only
3. The major limitation of Newton’s law of cooling is that the temperature of the surroundings must remain constant during the cooling of the body