Chapter 5: Problem 21
Heating a typical house might require something like \(200 \mathrm{~W}\) of power for every degree Celsius difference between inside and outside temperatures. If the inside temperature is kept at \(20^{\circ} \mathrm{C}\) and the outside temperature holds steady all day and night at \(0^{\circ} \mathrm{C}_{t}\) how much power is required to maintain the temperature?
Short Answer
Expert verified
Answer: The power required to maintain the temperature in this house is 4000 W.
Step by step solution
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Thermal Energy Transfer
Understanding thermal energy transfer is crucial when considering the energy required to heat a home. Thermal energy, often referred to as heat, is transferred in three primary ways: conduction, convection, and radiation. In homes, this transfer occurs both within the internal spaces and between the inside and outside environments.
Conduction happens when heat moves through materials, like the walls and floors. If there's a temperature difference between the inside and outside, heat will conduct through the walls, prompting the need for extra energy to maintain the desired indoor temperature. In the given exercise, we account for this by calculating the power needed to offset the energy lost through the house's exterior.
To quantify this, we need to consider not just the temperature difference but also the house's insulation properties, which can inhibit conduction and therefore reduce the amount of power necessary to keep the house warm.
Conduction happens when heat moves through materials, like the walls and floors. If there's a temperature difference between the inside and outside, heat will conduct through the walls, prompting the need for extra energy to maintain the desired indoor temperature. In the given exercise, we account for this by calculating the power needed to offset the energy lost through the house's exterior.
To quantify this, we need to consider not just the temperature difference but also the house's insulation properties, which can inhibit conduction and therefore reduce the amount of power necessary to keep the house warm.
Power Calculation
The concept of power in the context of home heating is tied to the rate at which energy is used to maintain a steady temperature inside, despite the colder external environment. Power is expressed in watts (W), where one watt is equal to one joule per second. In our exercise scenario, given a specific wattage required per degree Celsius difference, the power calculation is straightforward.
Calculating Power Requirement
To find the total power requirement, we use the formula: \[\text{Power} = \text{Temperature difference} \times \text{Power per degree Celsius difference}\]This computation effectively gives us the rate at which the heating system must operate to maintain a steady internal temperature. The solution reveals that with a temperature difference of 20 degrees Celsius and a rate of 200 watts per degree, our home in question needs 4000 watts of power. This figure translates into the steady energy input required to counteract the continuous thermal energy transfer from the inside out.Heat Maintenance Energy
Heat maintenance energy refers to the energy needed to keep a building at a consistent temperature over a given period. It's a measure of the home's ongoing energy consumption. In the context of our example, we're exploring how much energy is required to keep a house comfortable when there's a stark temperature contrast with the outside.
Maintaining this equilibrium is a battle against heat loss. The quality of insulation, the construction materials, and the efficiency of the heating system all play vital roles in the amount of heat maintenance energy required. The calculated power tells us the rate at which energy must be provided, but the actual energy consumption over time would be found by multiplying this power by the duration the heating is on — something that might be continuous during colder days.
Maintaining this equilibrium is a battle against heat loss. The quality of insulation, the construction materials, and the efficiency of the heating system all play vital roles in the amount of heat maintenance energy required. The calculated power tells us the rate at which energy must be provided, but the actual energy consumption over time would be found by multiplying this power by the duration the heating is on — something that might be continuous during colder days.
