one week left for my board exams.... so

PLEASE ANSWER

When we consider tranfer of heat through a body of length x area of c.s. A and having temperature diff. T₂-T₁ (which is fixed) and termally insulated side walls, then it is considered that initially the energy from the molecules present at one cross sec^n is used by the molecules in the immediate next c.sec^n in 2 ways :-

1) in increasing its temperature

2) in conducting it to the next layer...

But after sometime when steady state is reached it is said that the layers donot increase their temperature further and each layer maintains a constant temperature which decreases as we move towards the colder end. It then only conducts. But why does the process of increasing tempearature cease after sometime? what is the reason behind this?

When we talk about heat transfer in a material, especially in the context of your board exams, it's essential to grasp the concept of steady state and how temperature changes occur over time. Let's break this down step by step to clarify why the temperature increase stops after a certain period.

The Basics of Heat Transfer

Heat transfer occurs through conduction, where thermal energy moves from a region of higher temperature to a region of lower temperature. In your scenario, we have a body with a fixed temperature difference (T2 - T1) across its length (x) and a constant cross-sectional area (A). Initially, when heat is applied, the molecules at one end of the body gain energy and start vibrating more vigorously, which leads to an increase in temperature.

Initial Phase of Heating

During the initial phase, the energy absorbed by the molecules at one cross-section is indeed used in two ways:

• Increasing Temperature: The energy raises the kinetic energy of the molecules, which increases the temperature of that layer.
• Conducting Heat: Some of that energy is transferred to adjacent layers, causing them to heat up as well.

Reaching Steady State

As time progresses, the system approaches what we call a "steady state." This is a condition where the temperature at each layer becomes constant over time. The reason for this cessation of temperature increase can be understood through the following points:

Energy Balance

In steady state, the amount of heat entering a layer equals the amount of heat leaving that layer. This balance means that while energy is still being conducted through the material, the temperature of each layer remains constant. The energy gained by a layer from the layer below it is exactly offset by the energy lost to the layer above it.

Temperature Gradient

In steady state, there exists a temperature gradient along the length of the body. The temperature decreases from the hot end (T1) to the cold end (T2). Each layer maintains a constant temperature that corresponds to its position in this gradient. The heat conduction continues, but since the temperatures are stable, there is no further increase in temperature.

Thermal Equilibrium

Once thermal equilibrium is achieved, the system has reached a state where the temperature distribution is stable. The molecules in each layer are still vibrating and conducting heat, but they do so at a constant temperature. This is why, after some time, the process of increasing temperature ceases.

Conclusion

In summary, the reason the temperature increase stops after a while is due to the establishment of a steady state where the heat entering and leaving each layer is balanced. The temperature gradient remains, but each layer's temperature stabilizes, allowing for continuous conduction without further temperature rise. Understanding this concept is crucial for your exams, as it illustrates the principles of thermal conduction and energy transfer in materials.