A glass windowpane in a home is 0.62 cm thick and has dimensions of 1.0 m ×2.0 m. On a certai

step 1 This problem covers the concept of the thermal conductivity and the rate of energy transfer is g

A glass windowpane in a home is 0.62 cm thick and has...

A glass windowpane in a home is $0.62 \mathrm{~cm}$ thick and has dimensions of $1.0 \mathrm{~m} \times 2.0 \mathrm{~m}$. On a certain day, the indoor Lemperature is $25^{\circ} \mathrm{C}$ and the outdoor temperature is $0^{\circ} \mathrm{C}$. (a) What is the rate at which energy is transferred by heat through the glass? (b) How much energy is lost through the window in one day, assuming the temperatures inside and outside remain constant?

A glass windowpane in a home is $0.62 \mathrm{~cm}$ thick and has dimensions of $1.0 \mathrm{~m} \times 2.0 \mathrm{~m}$. On a certain day, the indoor Lemperature is $25^{\circ} \mathrm{C}$ and the outdoor temperature is $0^{\circ} \mathrm{C}$.
(a) What is the rate at which energy is transferred by heat through the glass? (b) How much energy is lost through the window in one day, assuming the temperatures inside and outside remain constant?

Key Concepts

Energy Loss Over Time

Energy loss over time is determined by multiplying the constant rate of heat transfer by the duration of time over which the transfer occurs. This concept allows for the calculation of total energy lost, such as over the course of a day, by integrating the continuous flow of energy described by the heat transfer rate.

Heat Transfer Rate

The heat transfer rate is the amount of energy transferred per unit time through conduction. By applying the conduction equation, this rate is calculated using the material's thermal conductivity, the surface area, the temperature gradient, and the thickness, providing a quantitative measure of energy transfer through the material.

Temperature Gradient

The temperature gradient refers to the change in temperature per unit distance in a material. In heat conduction, it is determined by the difference in temperature between two sides of a material divided by its thickness, and it drives the heat flow according to Fourier's law.

Thermal Conductivity

Thermal conductivity is a property of a material that measures its ability to conduct heat. It quantifies the ease with which heat energy passes through a material when there is a temperature difference across it, making it a critical factor in calculating the heat transfer rate in conduction problems.

Fourier's Law of Heat Conduction

This law states that the rate of heat transfer through a material is proportional to the negative gradient of temperature and the cross-sectional area through which the heat flows. It provides the fundamental equation used to calculate how much heat is transferred over time by conduction, linking thermal conductivity, area, temperature difference, and thickness of the material.

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