CBSE Class 12 Physics Conduction Theory and Examples

CBSE Class 12 Physics Conduction Theory and Examples Please refer to the examination notes which you can use for preparing and revising for exams. These notes will help you to revise the concepts quickly and get good marks.

Heat can be transmitted from one place to the other by three modes these are :
(1) Conduction
(2) Convection
(3) Radiation.
We will discuss only conduction in this chapter.

1. CONDUCTION
Conduction is the phenomenon of transfer of heat through one part of the body to another, from particle to particle in the direction of fall of temperature without any actual movement of the particles.
For example : When we heat one end of a solid, its other end becomes hot. Heat goes from one end of the rod to the other end by conduction. In the process of conduction when an object is heated, the particle of the body at higher temperature give heat to the particle at lower temperature. Hence the molecular collisions takes place by which the transfer of energy occurs and the heat is transferred from one end to the other.

2. THERMAL CONDUCTIVITY
Thermal conductivity of a solid is a measure of the ability of the solid to conduct heat through it. Substances differ considerably from one another in this respect. For example, copper, silver etc. are very good conductors of heat whereas glass, wood etc. are bad conductors.

3. TERMS RELATED TO THE THERMAL CONDUCTIVITY
(i) VARIABLE STATE : As temperature of every cross section of the rod goes on increasing, the rod is said to be in variable state.

(ii) STEADY STATE : This state of the rod, in which temperature of each part becomes constant and there is no further absorption of heat any where in the rod is called steady state. Note that in steady state temperature of each part of the rod is constant but not same.
Note :– Theory of conduction is valid only at steady state.

(iii) ISOTHERMAL SURFACE :– If we consider a metallic rod in which heat flows from one end to the other so that after some time, a steady state is reached. In this state temperature of every transverse section of rod is same on the whole area of section. This transverse section of the rod behaves as an isothermal surface.

(1) At isothermal surface, the temperature of all the molecules is same.
(2) These surfaces never intersect each other
(3) The shape of isothermal surface depends on the shape of conductor and nature of flow of heat. It can be (1D, 2D or 3D) heat flow.
(4) The direction of heat flow is always normal to the isothermal surface.

(3) TEMPERATURE GRADIENT : – The rate of change of temperature with distance along the direction of flow of heat is called temperature gradient. If we consider a metallic rod having θ and θ – Δθ as the temperature of two isothermal surfaces which are being at a distance of Δx from each other, than Temperature gradient =Δθ/Δx= –dθ/dx

(i) The negative sign indicates that temperaturedecreases with distance in the direction of heatflow.
(ii) The unit of temperature gradient is ºC per meter.

4. LAW OF HEAT TRANSFER THROUGH CONDUCTION
In steady state, the rate of flow of heat (dQ/dt), through the cross–section of the conductor is,
(i) Directly proportional to the area A of surface(dQ/dt)∝ A
(ii) Directly proportional to the temperature gradient
(–dθ/dx) i.e. (dQ/dt) ∝ (-dθ/dt) 
On combining the above two forms, we get, 

 (dQ/dt) ∝ (-dθ/dt) 

 (dQ/dt) =-KA (dθ/dt) 
Where k is constant called as coefficient of thermal conductivity of the material. The unit of coefficient of thermal conductivity is J/m–sec–k. Now if dH is the amount of heat transfer in time interval dt then, dQ/dt=dH/dt=

dH/dt= KAΔθ/Δx = rate of heat flow

If heat enters from one end such that temperature decreases with distance in the direction of heat flow than,
dH/dt = – KAdθ/dx

Special Point : If heat enters from one end and the temperature is measured from the other end opposite to the direction of flow than,dH/dt = – KAdθ/dx

5. THERMAL RESISTANCE
Eqn. (1) can be rewritten as dQ/dt=dθ/dx/KA
This is analogous to ohm’s law equation
Ι =V/R

the quantity dx/KA  is called Thermal Resistance, in analogy to electrical resistance greater the thermal resistance, better will be the thermal insulation and poorer will be the thermal conduction.

6. COMPARISON OF HEAT CONDUCTION WITHELECTRICAL CONDUCTION
Electrical Conduction
1. Electrical charge flows from higher potential to lower potiontial
2. The rate of flow of charge is called electric current. I = dq/dt
3. By Ohm’s law, I = v₁ − v₂/R
4. The electrical resistance is given by R=ρ l/A=l/σA Where ρ is resistivity and σ is conductivity

Thermal Conduction
1. Heat flows from higher temperature to lower temperature
2. The rate of flow of heat is called as heat current I = dQ/dt
3. The heat current is given as I = T₁ − T₂/R _Th
4. The thermal resistance is given by R_Th=l/KA
Where k is thermal conductivity of the conductor Heat conduction

Ex.1 Transmission of heat by molecular collisions is –
(A) Conduction (B) Convection (C) Radiation (D) Scattering
Sol.(A) In the conduction mode, the molecule remain at their place and transmission of energy occurs by
molecular collisions.

Ex.2 Coefficient of thermal conductivity depends on –
(A) Nature of material
(B) Heat produced
(C) Difference in temperature
(D) Atmospheric pressure

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