## Monday, January 9, 2017

### Transmission of Heat Problems with Solutions Two

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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