Question

Consider heat loss through the two walls of a house on a winter night. The walls are identical, except that one of them has a tightly fit glass window. Through which wall will the house lose more heat? Explain.

Short answer

Answer: The house will lose more heat through the wall with the tightly fit glass window due to the higher emissivity value of the glass, which causes more heat to be radiated away from the wall.

Step-by-step solution

Identify the modes of heat transfer

In this problem, there are three modes of heat transfer to consider: conduction, convection, and radiation. Conduction occurs through solid materials, convection occurs through air or fluids, and radiation occurs through electromagnetic waves. We need to examine each of these modes of heat transfer in the context of the walls with and without the glass window.

Compare conduction heat transfer for the two walls

Conduction is the primary mode of heat transfer through the solid materials of the walls. The walls are said to be identical, meaning they have the same material and thickness. Since the glass window is tightly fit, it can be assumed to conduct heat similarly to the rest of the wall material. Therefore, the conduction heat transfer through the two walls is nearly the same.

Compare convection heat transfer for the two walls

Convection is the mode of heat transfer that occurs through air or fluids. In this case, convection occurs at the inner and outer surfaces of both walls. However, the presence of the glass window can impact the convective heat transfer on that wall, as the glass surface might have different convective properties compared to the rest of the wall material. Nevertheless, the difference between the two walls in terms of convection would be relatively small and may not be a significant factor to consider.

Compare radiation heat transfer for the two walls

Radiation is the mode of heat transfer that occurs through electromagnetic waves. All objects emit heat radiation, but the amount of heat emitted depends on the object's emissivity, which is a property that measures how efficiently an object emits and absorbs heat radiation. Glass has a different emissivity value compared to the wall material, making it more efficient in emitting and absorbing heat radiation. As a result, there will be a difference in the radiative heat transfer between the two walls.

Determine which wall will lose more heat

Since conduction and convection heat transfers are similar for both walls, the difference in heat loss between the two walls is mainly determined by the radiation heat transfer. Since the glass window has a higher emissivity value compared to the rest of the wall material, the wall with the glass window will have more heat radiated away from it. Therefore, the house will lose more heat through the wall with the tightly fit glass window.

Key concepts

Conduction

When we talk about heat transfer through a wall, conduction is often the first concept that comes to mind. It involves the transfer of heat through solid materials. This happens when particles within the material collide, passing energy and heat from one particle to the next.
In the context of our exercise, both walls are made of the same material and thickness, ensuring that conduction occurs similarly in each. Despite one wall having a tightly fit glass window, the glass acts similar to the material of the wall regarding heat conduction.
Thus, conduction alone doesn't significantly differentiate the heat loss of the two walls.

Convection

Convection is another mode of heat transfer that occurs through fluids, such as air or liquids. It involves the movement of heat particles through the fluid, resulting in the transfer of heat.
In our scenario, convection plays a role at the surfaces of the wall, both inside and outside the house. Because both walls share almost identical exterior and interior surfaces, the impact of convection will be relatively similar.

• It involves air movement, which could vary based on window presence.
• But generally, its effect on our comparison is minimal.

Overall, convection doesn't cause a large difference in heat transfer for the walls under consideration.

Radiation

Radiation is a fascinating mode of heat transfer because it involves the emission of electromagnetic waves. Every object emits radiation, and the intensity depends on its material property known as emissivity.
In our exercise, the glass window has a higher emissivity compared to the typical wall material, meaning it emits and absorbs thermal radiation more efficiently.
This concept tells us that the wall with the glass window will allow more heat to radiate away, leading to greater heat loss.
Radiation ultimately is the key differentiator here, making the house lose more heat through the wall with the glass window.