Question

Consider heat conduction through a plane wall. Does the energy content of the wall change during steady heat conduction? How about during transient conduction? Explain.

Short answer

Answer: The energy content of a plane wall does not change during steady heat conduction, as there is no net heat transfer taking place. However, during transient heat conduction, the energy content of the wall can change due to the changing temperature distribution and heat transfer within the wall, resulting in net heat transfer and either an accumulation or loss of heat within the wall.

Step-by-step solution

Understand Steady Heat Conduction

Steady heat conduction occurs when the rate of heat flow and temperature distribution within the wall remains constant with time. In other words, the temperature at any point within the wall does not change over time. In this case, the heat entering the wall is equal to the heat leaving it, so there is no net heat transfer taking place.

Understand Transient Heat Conduction

Transient heat conduction, also known as unsteady or time-dependent heat conduction, occurs when the temperature within the wall changes with time. In this case, the heat transfer across the wall isn't constant, and there may be an accumulation or loss of heat within the wall.

Analyze Energy Content of the Wall during Steady Heat Conduction

During steady heat conduction, the temperature within the wall doesn't change with time, so the energy content of the wall remains constant. There is no net accumulation or loss of heat within the wall, as the heat entering the wall is equal to the heat leaving it. Therefore, the energy content of the wall does not change during steady heat conduction.

Analyze Energy Content of the Wall during Transient Heat Conduction

During transient heat conduction, the temperature within the wall changes with time, indicating an imbalance between the heat entering and leaving the wall. This imbalance results in a net heat transfer, which may cause an accumulation or loss of heat within the wall. Therefore, the energy content of the wall does change during transient heat conduction.

Provide an Explanation and Conclusion

In conclusion, the energy content of a plane wall doesn't change during steady heat conduction, as there is no net heat transfer within the material. However, during transient heat conduction, the energy content of the wall can change, as the temperature distribution and heat transfer within the wall are not constant and result in net heat transfer leading to an accumulation or loss of heat in the wall.

Key concepts

Steady Heat Conduction

Imagine placing your hand on a mug of hot coffee and feeling the warmth without getting hotter over time. That's similar to what happens during steady heat conduction. It's a scenario where the temperature within an object, like the walls of the mug, does not change over time, even though heat is constantly being transferred. This is because the heat entering one side is exactly balanced by the heat exiting the opposite side. As a result, if you were to measure the temperature at any point within the wall, you'd find that it remains unchanged, regardless of how long the coffee has been sitting there. This balance implies that the energy content within the wall is static—there's no increase or decrease, just a constant flow of energy through the material.

Transient Heat Conduction

Now, consider that same coffee mug, but immediately after you pour in boiling water. At first, the mug warms up until it reaches the same temperature as the coffee. This process exemplifies transient heat conduction. It's when the temperature distribution within an object changes over time due to a non-constant rate of heat flow. Unlike the stable scenario of steady heat conduction, the heat absorbed by the coffee mug's walls initially differs from the heat it emits to the surroundings, leading to a change in the mug's energy content. Over time, the mug's temperature increases until it finally stabilizes, signaling the end of the transient period and the beginning of steady conduction once again.

Energy Content in Materials

The energy content in materials relates directly to their temperature, which is, in layman's terms, a measure of the internal energy or vibration of molecules. This energy can be thought of as the material's ability to do work or transfer heat. During steady heat conduction, since temperature remains constant throughout the material, the energy content also stays the same. No extra work or heat transfer occurs. On the other hand, during transient heat conduction, temperature changes indicate that the energy content is shifting. An increase in temperature corresponds to an increase in internal energy, while a decrease means energy is being lost. It's crucial to understand this relationship to predict how materials will behave when they are subjected to heat transfer in practical applications, like insulating a house or designing engine parts.

Temperature Distribution

Temperature distribution is the map or profile of temperature across a substance at any given time. It's essential in understanding how heat conduction affects a material. A uniform temperature distribution, typically seen in steady state conditions, implies a stable energy flow with no gradients to drive heat from one area to another. Conversely, a non-uniform temperature distribution, which occurs during transient heat conduction, means there's an imbalance causing heat to flow within the material itself until uniformity—and thus equilibrium—is achieved. In practical terms, engineers consider temperature distribution when creating thermal insulation or designing heating and cooling systems to ensure efficiency and safety.