Question

Consider heat loss through 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

The house will lose more heat through the wall with the tightly fit glass window. This is because the glass has a higher thermal conductivity than most wall materials, allowing more heat to pass through and escape the house.

Step-by-step solution

Identify the Factors Impacting Heat Loss

To determine which wall will lose more heat, we need to analyze and compare the heat transfer properties of the wall materials and the glass window. Thermal conductivity, a material property that measures the rate of heat transfer through a material, is the most important factor in this comparison. Higher thermal conductivity values indicate better heat transfer, whereas lower values show that the material impedes heat transfer.

Compare the Thermal Conductivity of Wall and Glass Window

We are given that the two walls are identical, meaning they have the same material and thermal conductivity. The only difference between the walls is the presence of a tightly fit glass window in one of them. Therefore, our focus should be the difference in thermal conductivity of the wall and the glass window. Typically, the thermal conductivity of glass is higher than that of most building wall materials like brick, wood, or insulation.

Analyze Heat Transfer Through the Walls

Heat transfer can occur through three processes: conduction, convection, and radiation. In this scenario, we are mostly concerned with conduction as the primary mode of heat transfer. The wall without a glass window experiences heat transfer through its solid material, while the wall with a glass window has heat transferred through both the solid material and the glass. Given that glass has a higher thermal conductivity than most wall materials, the wall with the glass window will have a higher overall heat transfer rate.

Determine which Wall Loses More Heat

Based on the analysis of thermal conductivities and heat transfer processes, we can conclude that the house will lose more heat through the wall with the tightly fit glass window. This is due to the higher thermal conductivity of the glass window compared to the other wall material, thus allowing more heat to pass through the window and escape the house.