Newton's Law of Cooling Calculator

Have a look at the detailed steps on calculating the temperature of an object using the Newton's Law of Cooling. Follow these rules and guidelines to obtain the result easily.

• Get the ambient temperature, cooling constant, initial temperature and time from the question.
• Multiply cooling coefficient with the time of cooling and find exponential of negative product.
• Subtract ambient temperature from the initial temperature.
• Multiply it by the result in step 2.
• Add ambient temperature to the result to get the temperature of the object at the time.

There are three main mechanisms of heat exchange. The are thermal conduction, convection and radiation. Newton's law of cooling is applicable for thermal conduction, convection. The cooling time of an object depends on two factors. One of the factor is difference between the temperature of an object and surroundings. The greater difference means faster cooling. Second factor is cooling coefficient that depends on the mechanism and amount of heat exchanged.

Cooling coefficient formula is

k = hA/C

Where,

k is the cooling coefficient

h is the heat transfer coefficient

A is the area of the heat exchange

C is the heat capacity.

Newton's law of cooling states that the rate of change of temperature of an object is directly proportional to the difference between body temperature and its surroundings.

The Newton's law of cooling formula is along the lines:

T = T_ambient + (T_initial - T_ambient) * e-kt

Where,

T is the temperature of the object at the time t

T_ambient is the surrounding temperature

T_initial is the object temperature

k is the cooling coefficient

t is the time of cooling

Example

Question: Water is heated to 70°C for 15 min. How much would be the temperature if k = 0.56 per min and the surrounding temperature is 30°C?

Solution:

Given that

Surrounding temperature T_ambient = 30°C

Water temperature T_initial = 70°C

Time t = 15 min

Cooling coefficient k = 0.56

Newton's law of cooling formula is T = T_ambient + (T_initial - T_ambient) * e-kt

T = 30 + (70 - 30) * e-0.56

= 30 + 40 x 0.57

= 30 + 22.8 = 52.8°C

Temperature cools down from 70°C to 52.8°C after 15 minutes.

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1. What is Newton's Law of Cooling?

According to the Newton's Law of cooling, the rate of loss of heat from a body is directly proportional to the difference in the temperature of the body and its surroundings.

2. What are the limitions of Newton's law of cooling?

The limitations of Newton's law of cooling are along the lines:

• The loss of heat from a body should be by radiation only.
• The difference in temperature between the body and its surroundings should be less.
• The temperature of the body surroundings must be constant during the process of cooling.

3. What is Newtons law of cooling used for?

Newton's Law of Cooling can be used to find the victim's time of death. It describes the cooling of a warmer object to the cooler temperature of the environment.

4. What is the cooling rate?

In terms of mathematics, cooling rate is equal to the temperature difference between two objects multiplied by the constant material.