### Transmission of Heat Problems with Solutions one

We are solving series of problems based on the concept transmission of heat. In this lesson we are going to solve problems based on conduction, convection and radiation. These three are the different modes of transmission of heat. Conduction happens via solid medium, convection happens via fluid medium and for the radiation, we don’t need any medium for the propagation. In the case of conduction, molecules of the solid body vibrates about its mean position and pass the heat energy to the next particle and there is no permanent displacement of the particle. Thus it is the slowest method of transmission of heat and it happens via solids because the molecular force of attraction is strongest.

Problem

In a rod heat is passing through in a study state and the temperature at the both ends is different as given in the problem. If the length of the rod is one meter, we need to find the temperature at a point who is at a distance of 60 centimetre from the first end.

Solution

We know that the rate of heat flow in a solid material it is directly proportional to the area of cross section, temperature difference and is inversely proportional to the length of the rod. Taking that into consideration a proportionality constant is defined. In a given rod rate of flow will be the same but as the length of the rod varies, temperature of the body also varies. Taking that into consideration, we can solve the problem as shown in the diagram below.

Problem

An aluminium rod area of cross section and coefficient of conductivity is given to us and a study of rate of flow of heat 360 calorie per minute is given to us in the problem. We need to find the temperature gradient of the rod and the problem is given as shown in the diagram below.

Solution

Temperature gradient is defined as the ratio of temperature per unit length. We can get the value of this temperature gradient from the definition of coefficient of thermal conductivity. Problem is solved as shown in the diagram below.

Problem

One end of a metal bar is in ice and the end is in contact with stream as shown in the diagram below. Coefficient of thermal conductivity is given to us and we need to find the amount of the ice that melts per minute.

Solution

We know that there is certain amount of heat flows in the rod per second and we can find it using the definition of coefficient of thermal conductivity. This heat energy is used in converting ice into water. All transferred heat is used to convert ice into water. We can get the mass of the ice converted using the definition of latent heat. It is defined as the amount of heat required to convert unit mass of substance from one state to the other. Using these definitions, we can solve the problem as shown in the diagram below.

Problem

Three rods of same length and area of cross section are joined in parallel. Their respective coefficient of thermal conductivity is given to us and we need to find the effective thermal conductivity of the system. Problem is as shown in the diagram below.

Solution

We know that when rods are connected in parallel, the temperature at common point will be the same but the rate of flow of the total heat is the sum of individual values. Taking that into consideration, we can solve the problem as shown in the diagram below.

Problem

Water is changing into ice at zero degree centigrade and atmospheric temperature is much less than that as shown in the diagram below. If the time taken for the formation of ice layer of thickness one centimetre is seven hours we need to find the time taken for the formation of ice layer of thickness two centimetre.

Solution

We can prove that the time taken for the formation of ice layer is directly proportional to the square of thickness of the layer. Taking that into consideration, we can solve the problem as shown in the diagram below.

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