Thermal Conduction

Heat transfers from a body at a higher temperature to a body at a lower temperature. The transfer of heat from one body to another body may take place by any one of the following modes: Conduction, Convection, and Radiation. These three modes of transfer of heat from one place to another place can be understood with the help of the following simple and interesting activity. 

Let us suppose ten boys are sitting in a row. A teacher asks the first boy in a row to hand over an apple to the last boy in the row. Now, the first boy can hand over the apple to the last boy in the row in three different ways. He hands over the apple to the second boy without leaving his position. The second boy hands it over to the third boy in the same manner. 

• The process of handing over the apple to the next boy continues till the last boy gets the apple. This process of transferring the apple from one boy to the next boy is equivalent to conduction in heat transfer.
• The first boy after getting the apple from his teacher stands up and goes to the last boy to hand over the apple and then comes back to his position. This process of transferring the apple from the first boy to the last boy is equivalent to convection in heat transfer. 
• The first boy simply throws the apple towards the last boy who receives the apple. This process of transferring the apple is equivalent to radiation in heat transfer. Radiation is the fastest mode of transferring heat.

Conduction

The process by which heat is transferred from the hot part to the cold part of a body through the transfer of energy particles to another particle of the body without the actual movement of the particles from their equilibrium positions in from one called conduction. 

e.g., The transfer of heat from one part to another part of a solid takes place through conduction. 

Good Conductors-: Some substances allow the beat to pass through them more easily than others. The substances or solids which allow the heat to pass through them more easily are called good conductors of heat. Silver (the best conductor), copper aluminum, mercury, etc. are examples of good conductors of heat. 

Bad Conductors-: On the other hand, the substances or solids which do not allow the heat to pass through them more easily are called bad conductors of heat. Glass felt, wood, mica, etc. are examples of had conductors of heat.

Mechanism of Thermal Conduction 

According to the kinetic theory of matter, the average kinetic energy of a molecule of a system is directly proportional to the temperature. Thus, the collection of molecules having large average kinetic energy are at a higher temperatures than the molecules having lower average kinetic energy. 

Consider a metallic rod of length L, whose left end is in contact with a hot body at temperature T, and the right end is in contact with the cold body at temperature Insulator Metallic rod T: (Figure 1). The molecules of the rod are closely packed and cannot move from one position to another position of the rod. However, they can vibrate about their equilibrium or mean positions. The molecules at the left end absorb heat energy from the hot body. 

Due to the absorption of heat energy, their average kinetic energy increases. Thus, the average kinetic energy of the molecules at the left end Hot body becomes very high as compared to the average kinetic energy of the molecules at the right end. The molecules at the left end vibrate about their equilibrium positions with large amplitude and collide with the neighboring molecules.

As a result of this, heat is transferred from one The molecule gaining heat vibrates with large amplitude and transfers the heat to the one molecule to the next molecule. Molecule by colliding with it. This process continues till the heat is transferred from the hot end to the cold end of the body. Thus, heat is transferred from one part to another part of the solid without the actual movement of the particles of the solid. The heat is transferred temperature at different points along the rod increases and ultimately a steady state is reached when there is no further transfer of heat from the hot end to the cold end. In a steady-state, the temperature of different points or sections of the rod is constant but different.

As we move away from the hot end of the rod, the temperature at different sections goes on decreasing. The decrease in tune with distance from the hot end of the rod is known as temperature gradient. 

It is denoted by -dθ/dx

SI unit of the temperature gradient is K/m or Km^-1. 

Thermal Conductivity 

Consider a small piece of material in the form of a cube, let the twice 1 of the cube be maintained at a temperature θ+△θ and the face II at a temperature θ . The area of face I is A and the distance between the two faces is △x (say). It is and that the heat (Q)  flows from the face I to II is 

(i) directly proportional to the area (A) of the face I 

(ii) directly proportional to temperature difference (△θ) between the two 

(iii) directly proportional to the time (t) elapsed 

(iv) inversely proportional to the distance (At) between the faces. 

Q∝ A△θt/△x      or       Q=-KA(△θ/△x)t

where K is the constant of proportionality and is called the thermal conductivity of the material. It depends on the nature of the material. 

K=-(Q/t)/A(△θ/△x)

Definition: Thermal conductivity of a material is defined as the quantity of heat energy that flows across the opposite faces meter cube in one second, when the opposite faces of the cube are maintained at a temperature difference of 1° C or 1K.

Unit of Thermal Conductivity

In C.G.S. system, unit of K is  cal s^-1 cm^-1 °C^-1

In SI unit of K is J s^-1 m^-1 K^-1

Dimensional formula of K = [MLT^-3K^-1]

Applications of Thermal Conduction 

1) Wire gauze is placed over the flame of Bunsen burner while heating the flask or a beaker.

When a wire gauze is placed over the flame of a Bunsen burner, the flame does not go beyond the gauze and hence there is no direct contact between the flame and the flask. The wire gauze being a good conductor of heat, absorbs the heat of the flame. So, the temperature of the gases above the gauze is not high enough for the burning of the gases. Davy’s safety lamp has been designed on this principle. The temperature outside the gauze placed around the flame of the lamp is not high , so the gases outside the gauze do not catch fire.

2) In winter, the iron chairs appear to be colder than the wooden chairs. 

Iron is a good conductor of heat. When touched, it absorbs the heat from our body and hence the transfer of heat from our body to the iron chair begins. Since our body loses heat, so we feel cold. On the other hand, wood is a bad conductor of heat. So the transfer of heat from our body to the wooden chair is very less. Hence the wooden chairs appear less cold than that of iron chairs.

3) Cooking utensils are made of aluminum and brass whereas their handles are made of wood. 

Aluminum and brass are good conductors of heat. So, they absorb heat from the fire more rapidly and in turn supply it to the food to be cooked. On the other hand, wood being a bad conductor of heat absorbs less heat and hence the handles are less hot. Therefore, we can pick up the hot cooking utensils without burning our hands. 

4) Steel utensils with copper bottom are good for uniform heating of food. 

Copper is better conductor than the steel because thermal conductivity of copper (K 385 W m K) is much more than the thermal conductivity of steel (K 50-2 W m K). Therefore, copper is heated quickly. The copper is in contact with the steel. The heat is transferred to the steel utensil at the junction of the steel and copper. Now, the steel does not transfer the heat to the food so quickly but it transfers the heat to the food slowly. Hence, food is heated uniformly in steel utensils with copper base.

5) Ice is covered in gunny bags to prevent melting of ice. 

The material of gunny bags is a bad conductor of heat Moreover, the air filled in the pores of gunny bags is also a bad conductor of heat. So the flow of heat from outside to the ice is not allowed. Hence ice is prevented from melting.

6) We feel warm in woolen clothes. 

Wool itself is a bad conductor of heat. Also, the pores in the woolen clothes enclose air in them. This air reduces the thermal conductivity of the clothes. So, woolen clothes allow less amount of heat from our body to flow out and hence we feel warmer.

7) Two thin blankets are warmer than a single blanket of double the thickness. 

Two blankets enclose a layer of air between them. Air being a bad conductor of heat reduces the thermal conductivity of the blankets considerably. Thus, the layer of air between two blankets allow comparatively less amount of body heat to flow out than a single blanket. Hence two blankets appear more warmer than a single blanket.

8) We feel warmer in a fur coat. 

The air enclosed in the fur coat being bad conductor of heat does not allow the body heat to flow outside. Hence we feel warmer in a fur coat.

9) Birds often swell their feathers in winter. 

By doing so, they enclose more air between their bodies and the feathers The air, being bad conductor of beat prevents the out flow of their body heat. Thus, birds feel warmer in winter by swelling their feathers.

10)A new quilt is warmer than old one. 

In a new quilt, there are number of pores in the cotton. These pores contain large quantity of air. Air being bad conductor of heat slows down the flow of our body heat to the outside. Thus, a new quilt appears warmer The old quilt, because of continuous use, loses some of the air. Thus, the flow of our body heat to the outside becomes faster. Hence, an old quilt appears cold.

11) Eskimos make double walled ice houses. 

The air enclosed between the walls is a bad conductor of heat. This air reduces the out flow of heat from inside the houses. Thus, the people living in these houses feel warmer.

Sample Questions

Question 1: Write down the name of three mode of transfer of heat.

Solution:

Conduction, Convection and radiation.

Question 2: What is steady state of heat?

Solution:

When there is no transfer of heat between two ends of a substance, steady state is said to be reached.

Question 3: By which mode the heat reaches from sun to earth?

Solution-:

Radiation.

Question 4: Why we feel warmer in fur coat?

Solution:

The air enclosed in the fur coat being bad conductor of heat does not allow the body heat to flow outside. Hence we feel warmer in a fur coat.

Question 5: Why cooking utensils are made of aluminum and brass whereas their handles are made of wood?

Solution:

Aluminum and brass are good conductors of heat. So, they absorb heat from the fire more rapidly and in turn supply it to the food to be cooked. On the other hand, wood being a bad conductor of heat absorbs less heat and hence the handles are less hot. Therefore, we can pick up the hot cooking utensils without burning our hands.

Question 6:  In winter, why the iron chairs appear to be colder than the wooden chairs?

Solution:

Iron is a good conductor of heat. When touched, it absorbs the heat from our body and hence the transfer of heat from our body to the iron chair begins. Since our body loses heat, so we feel cold. On the other hand, wood is a bad conductor of heat. So the transfer of heat from our body to the wooden chair is very less. Hence the wooden chairs appear less cold than that of iron chairs.

Question 7: Write down the dimensional formula of thermal conductivity.

Solution:

Dimensional formula of thermal conductivity is [MLT^-3K^-1]