**Thermal resistance**

The rate of flow of heat energy through a given solid
material is directly proportional to temperature difference between the two
ends of the rod.

The rate of flow of the heat is inversely proportional to the
combination of length area and coefficient of thermal conductivity as shown.

Thermal resistance can be defined as the ratio of length of
the material to the coefficient of thermal conductivity and the area of
cross-section.

Thermal resistance is a measure of opposition to the flow of
heat.

More the thermal resistance it becomes difficult for the heat
energy to flow from one place to another place.

Thermal resistance is similar to electric resistance.

**Resultant coefficient of thermal conductivity when rods are connected in series**

When different materials are connected with different
coefficients of thermal conductivity, we can calculate the effective
coefficient of thermal conductivity.

When the rods are connected in series the same rate of flow
happens through both the parts. But the temperature difference in the different
junctions is going to be different because of the receiving of different heat
energy.

The temperature difference between the first and the last end
is equal to the sum of temperature difference between the junctions as shown.

The effective thermal resistance when the 2 rods are
connected in series is equal to the sum of the individual thermal resistances.

When the two materials are connected in series are having the
same physical dimensions, we can derive a simple equation for the effective coefficient
of thermal conductivity as shown below.

**Effective thermal conductivity when the rods are connected in parallel**

When different materials are connected in parallel the total
available heat energy per second will be shared across both of them.

Anyway the temperature at the end is going to be the same.

The effect to thermal resistance when the rods are connected
is similar to the electric resistance when the rods are connected in parallel.

When the two different rods are having same length and same
area of cross-section we can derive a simple equation for the effect to
coefficient of thermal conductivity as shown below.

**Problem and solution**

The solid material having the coefficient of thermal conductivity
of 50 SI units is having a length of 1 m and area of cross-section of 5 cm
Squire. One end of the rod is placed in the ice and other end is in the steam.
How much ice melts in five minutes?

We know that rate of flow of heat can be expressed in terms
of coefficient of thermal conductivity as per the definition.

Latent heat is defined as the amount of the heat energy
required to convert unit mass of substance from one state to another state at
constant temperature. We can equate the rate of flow of heat energy to read of
energy required to convert the total mass of substance from one state to
another.

By equating both the energies we can get the answer as shown
below.

**Problem and solution**

When two different metals of coefficient of thermal
conductivity three and four SI units are connected in series and parallel what
is the ratio of their effect to coefficient of thermal conductivity? Assume
that both are having similar physical dimensions.

We know that effect to coefficient of thermal conductivity
value both the series combination as well as the parallel combination. They
were derived in the previous post.

We can use those formulas to solve this problem.

There is another problem on the same page.

Two materials of same thermal conductivity and same
dimensions are connected in series pass heat of two joule’s per second. When
they are connected in parallel how much heat we can pass per second?

We can solve this problem using the concept of resistance. We
know that when the rods are connected in series effective resistance increases
and when they are connected in parallel effective resistance decreases.

Using their corresponding formula which is derived in the
previous lessons we can substitute and get the required answer.

**Related Posts**

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