Course description

Transmission of heat:

Heat: It is a form of energy which transfers among particles in a substance (or system) by means of kinetic energy of those particles. In other words, a form of energy associated with the motion of atoms or molecules and capable of being transmitted through solid and fluid media by conduction, through fluid media by convection, and through empty space by radiation (Fig. 1). However, heat is a condition of being hot and transferred by particles bouncing into each other. The transfer of energy from one body to another as a result of a difference in temperature or a change in phase. It is often released along with other kinds of energy such as light, radio waves, or sound waves.

                                          (a)                                                                    (b)                                                                  (c)                          

Fig 1

Thermodynamics: It is a branch of physics concerned with heat and temperature and their relation to energy and work. Thermodynamics defines macroscopic variables, such as internal energy, entropy, and pressure, that partly describe a body of matter or radiation. It also describes the bulk behavior of the body, not the microscopic behaviors of the very large numbers of its microscopic constituents, such as molecules.

There are four laws in thermodynamics and the laws are explained by statistical mechanics, in terms of the microscopic constituents. Historically, thermodynamics developed out of a desire to increase the efficiency and power output of early steam engines (Fig. 2). 

                                (a)                                                                    (b)

                                                             Fig 2

(i) Conduction: When heat is applied to one end of a metal rod, the molecules of the rod there vibrate more vigorously about their mean positions of rest and transfer the heat energy to the adjacent molecules by collision (Fig. 3). In this fashion the other end also becomes hot sooner or later. Therefore, to make the mode of conduction a material medium is necessary but there is no bodily motion of the material particles in the process.

(a)                                      Fig. 3                                       (b)

(ii) Convection: Convection is a mode of heat transfer by mass motion of a fluid such as air or water (Fig. 4). When the fluid is heated and caused to move away from the source of heat, carrying energy with it. Convection above a hot surface occurs because hot air expands, becomes less dense, and rises. Hot water is likewise less dense than cold water and rises, causing convection currents which transport energy until the whole mass of the substance becomes uniformly heated. 

                        (a)                                                (b)                                              (c)

                                                                           Fig 4

(iii) Radiation: Heat transfer through radiation takes place in form of electromagnetic waves mainly in the infrared region that does not require a medium (Fig. 5). This thermal radiation (infrared radiation) is generated by the thermal motion of charged particles in matter. All matter with a temperature greater than absolute zero emits thermal radiation. 

                           (a)                                                                                (b)                                                          (c)

Fig 5

Thermal Conductivity: Let us consider a thin slice of a metal bar with parallel faces such that the direction of the flow of heat is normal to the faces (Fig. 6). There will be a gradual fall in temperature between the two faces. Let the upper face of the slice be at a higher temperature θ1, the lower face being at the lesser temperature θ2. Here, we assume that there is no loss of heat from the side of the slab. Let A and x be the area of cross-section and the thickness of the slab respectively. Then the amount of heat Q that flows from one face to the other face in time t will depend,

        (i)              directly on the face area, A

(ii)            directly on the temperature difference, (θ1-θ2)

(iii)          directly on time, t

(iv)           inversely on the thickness (x) of the slab, and

(v)             on the nature of the material (different substances have different conductivity).

Hence,  Q∝(A(θ_1-θ_2)t)/x=KA(θ_1-θ_2)t)/x     ---------------(i)

where K is a constant depending on the nature of the material and is known as the coefficient of thermal conductivity or coefficient of heat conduction or simply as thermal conductivity.

If A= 1 cm2, θ1-θ2 = 10C, x= 1cm and t= 1 second, then from eqn (i) we will get Q = K.

Therefore, thermal conductivity of a material may be defined as the quantity of heat that flows in one second through a cm-cube of the material from the hot face to cold face when there is a steady temperature difference of 10C between the faces. For example: thermal conductivity of iron = 0.175 C.G.S. units implies that 0.175 calories of heat energy flow in one second through a cm-cube of the material from the hot face to cold face when there is a steady temperature difference of 10C between the faces.

Now indicating the fact that the temperature decreases as x increases by a negative sign, then the temperature gradient becomes  -dθ/dx  .

Eqn. (i) may then be written as

  Q=-K A  dθ/dx t .

  Fig 7

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