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Heat conduction is a process where thermal energy transfers from a region of higher temperature to a region of lower temperature within a material or between materials in thermal contact. This process occurs because of the random motion and collisions of microscopic particles such as atoms or molecules. In the context of our problem, heat conduction happens through a glass window from the warm inside to the cold outside.
The ability of a material to conduct heat is quantified by its thermal conductivity. In our problem, we deal with a glass window, having a given thermal conductivity. Let's delve deeper into thermal conductivity next.

Thermal conductivity, denoted by the symbol k, is a material-specific property that measures a material's ability to conduct heat. A higher thermal conductivity means a material can transfer heat more efficiently. For example, metals like copper have high thermal conductivity, while materials like glass or air have lower thermal conductivity.
In the given problem, the thermal conductivity of glass is provided as 0.84 W/(m·K). This means that for every meter of glass thickness and every degree Celsius of temperature difference, 0.84 watts of heat energy is transferred per second.
Understanding the thermal conductivity helps in calculating the rate of heat transfer using Fourier's Law of Heat Conduction: \[ Q = \frac{k \times A \times \triangle T}{d} \]
where:

• Q is the rate of thermal energy transfer (W).
• A is the area through which heat is flowing (m²).
• \( \triangle T \) is the temperature difference across the material (K).
• d is the thickness of the material (m).

Let's proceed to discuss the importance of the temperature difference in heat conduction.

Temperature difference, symbolized as \( \triangle T \), plays a crucial role in the process of heat conduction. It represents the driving force behind the flow of thermal energy. A larger temperature difference results in a higher rate of heat transfer. In the problem, the temperature difference between the inside (22°C) and outside (-29°C) is calculated to be 51°C.
This significant temperature difference means there is a strong thermal gradient driving heat from the warmer interior to the colder exterior. In practical terms, this is why insulation or additional barriers like storm windows are used—they reduce the effective temperature difference and thus the overall heat transfer. In our problem, adding the storm window with an air gap significantly reduces the rate of thermal energy transfer as air is a poor conductor of heat, providing extra resistance.
Using both the glass and air gap, represented by their respective thermal resistances, we can calculate the total resistance and subsequently the reduced heat transfer rate, highlighting the effectiveness of adding insulation. This illustrates how structures can be optimized for thermal efficiency.