We
are solving series of problem based on the concept of transmission of heat. In
the case of conduction of heat, no particle of the solid medium has the
permanent displacement and each particle vibrates about its mean position and
transmits heat energy to the next particle and the conduction keeps happening
that way. In the case of convection, we need a liquid or gas medium and the
particles do get permanent displacement and hence the flow of the heat is quick
when compared with the solid. In the case of radiation, there is no need of any
medium for the propagation and heat flows like electromagnetic wave. This is the
quickest way of transmission of heat and there is no effect on the medium
during this transmission of heat.
Problem
Two
identical rods of same material are joined in series and certain heat is
passing through them for four minutes. If the same two rods are connected in
parallel, we need to find the time required for the flow of same heat and the
problem is as shown in the diagram below.
Solution
When
the rods are connected in series their lengths get added up but area of cross
section remains same. In series rate of flow will be the same. When the rods
are connected in parallel, the lengths of the system remain same but the area
of cross section increases. Here rate of heat flow is shared and the problem is
as shown in the diagram below.
Problem
A
block body at temperature at 400 kelvin is placed in the surrounds of
temperature of 300k and the rate of flow is given to as r. If the temperature
of the body is raised to 800 kelvin, we need to find the rate of flow of heat
in this case and the problem is as shown in the diagram below.
Solution
We
need to use Stefen’s law that the rate of flow of heat is directly proportional
to the forth power of absolute temperature. We shall take that forth power
difference in the case of absolute temperature of the body. Taking this into
consideration, we can solve the problem as shown in the diagram below.
Problem
Two
objects are having same shape and radiating the same power. If their emissivity’s
are different as shown in the diagram below, we need to find the temperature of
the two bodies and the problem is as shown in the diagram below.
Solution
We
know that only perfect elastic body can emit all the heat energy that it has
and other bodies can emit heat energy up to some extend basing on the nature of
the material. How much heat energy a body can emit is measured with a term
called emissivity. For a perfect block body its value is one and for any other
bodies it is more than zero but less than one. The rate of emission of heat is
directly proportional to the forth power of absolute temperature and
emissivity. Taking that into consideration, we can solve the problem as shown
in the diagram below.
Problem
Intensity
of radiation is 100 units when the source is at a distance d and we need to
know the intensity if the distance is doubled and the problem is as shown in
the diagram below.
Solution
We
know that the intensity is defined as the rate of heat energy per unit area of
cross section and it is inversely proportional to the square of the distance of
separation from the source to the observer. Taking that into consideration, we
can solve the problem as shown in the diagram below.
Problem
A
body has taken a time of eight minutes to reduce its temperature from 90 to 80
degree centigrade when it is in a room of surrounding 25 degree centigrade. We
need to know the time required to cool the body from 80 to 70 degree centigrade
in the same surroundings. Problem is as shown in the diagram below.
Solution
We
need to use Newton’s law of cooling to solve this problem and as per it the
rate of cooling of a body is directly proportional to the temperature
difference between body and surrounding. This rule is valid only when the
temperature difference between body and surrounds is small. Taking that into
consideration, problem is solved as shown in the diagram below.
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