Conduction using Kinetic Model
We can see in our daily life, the metal conducts more heat as compared to the nonmetal.
When we put the one end of the spoon in the cup of tea. After some time, another end of the spoon also gets hot.
This happens due to the conduction of heat in the spoon.
Hence, to ignore the heating of the handle of the spoon, we use the spoon with the wooden handle as it does not conduct the heat.
Let's Know, how a material conducts heat.
The kinetic model states that " the molecules carry the net energy from a region of high energy to the region of low energy.
Hence, the molecules actually move from a region of high temperature to the region of low temperature.
Now, we will consider a gas, which is kept under the verticle temperature gradient.
Now, let's consider the net rate of heat transfer from high temperature to low temperature is H.
$H$
depends on five parameters. Here,
$n$
= number of particles per unit volume,
$C$
= Specific heat per particle
$v$
= mean velocity of particles,
$A$
= area of cross section and
$ΔT$
= temperature difference across the surface
Now,
$ΔT$
is the temperature difference of the gas between two collisions.
Where, l = mean free path and
$dZdT $
= temperature gradient
Now, to remove the proportionality sign, we have to use the constant. That will be
$−31 $
. It is an experimental value.
Also, the rate of heat transfer can be given by Fourier's law of conduction.
And after comparing the equations obtained for heat transfer, we will get the expression for the conductivity of the material
$(K)$
Now, for the gas mean free path is inversely proportional to the particle density (n) and collision cross-section (
$σ$
).
Now, we have got the expression for thermal conductivity.
Hence, the thermal conductivity is directly proportional to the specific heat and mean velocity.
And the thermal conductivity is inversely proportional to the collision cross-section
In the case of gas, the specific heat and collision cross-section are do not depend on temperature.
But, the velocity factor depends on the temperature. So,
$K∝v$
.
Now, the gas which we have taken is monoatomic. For monoatomic gas, velocity will be as given.
Hence, K depends on temperature and molecular weight.
Now, we can see the variation of thermal conductivity with temperature and molecular weight.
If we increase the temperature of gas then the thermal conductivity of the gas would increase.
If we take the gases of very low molecular weight then the thermal conductivity would be extremely high.
Hence, the thermal conductivity of hydrogen and helium is very high. Because, its molecular weight is low.
Now, in the case of metals, the thermal conductivity depends upon the number of free electrons in the metal.
Hence, the number of free electrons available in pure metal is high. So, its conductivity is high.
Hence, the thermal conductivity of silver and copper is more as compared to other metals.
In the alloys, the impurity density is high and the presence of free electron is very low.
Hence, the stainless steel is considered as the thermal insulator.
Revision
When we put the one end of the spoon in the cup of tea. After some time, another end of the spoon also gets heat up.
The thermal conductivity of gases increases with increase in temperature.
While, the thermal conductivity of metals decreases with increase in temperature.
The End