Question

The U.S. Department of Energy estimates that up to 10 percent of the energy use of a house can be saved by caulking and weatherstripping doors and windows to reduce air leaks at a cost of about \(\$ 90\) for materials for an average home with 12 windows and 2 doors. Caulking and weatherstripping every gas- heated home properly would save enough energy to heat about 4 million homes. The savings can be increased by installing storm windows. Determine how long it will take for the caulking and weatherstripping to pay for itself from the energy they save for a house whose annual energy use is \(\$ 1500\).

Short answer

Answer: It will take 0.6 years (about 7.2 months) for the caulking and weatherstripping to pay for itself from the energy saved.

Step-by-step solution

Calculate annual energy saved

To calculate the energy saved per year, we need to find 10% of the annual energy use. We are given the annual energy use as $1500. So, the annual energy saved will be: \(0.10 \times 1500\)

Evaluate annual energy saved

Evaluating the expression gives us the annual energy saved: \(0.10 \times 1500 = 150\) So, the house saves $150 per year after caulking and weatherstripping.

Determine how long it takes to pay for itself

Now we need to determine how long it takes for the energy savings to cover the initial costs of materials. To do this, we divide the total cost of materials by the annual energy savings: \(\text{Years to pay for itself} = \frac{\text{Total cost of materials}}{\text{Annual energy savings}}\) Substituting in the given values: \(\text{Years to pay for itself} = \frac{90}{150}\)

Evaluate the expression

Evaluating the expression gives us: \(\text{Years to pay for itself} = \frac{90}{150} = 0.6\) So, it will take 0.6 years (about 7.2 months) for the caulking and weatherstripping to pay for itself from the energy they save.

Key concepts

Thermodynamics Principles

Understanding the basic principles of thermodynamics is essential when calculating energy efficiency savings. Thermodynamics is the branch of physics that deals with the relationships between heat and other forms of energy. In the context of a household, it's primarily concerned with how thermal energy is transferred and how it can be contained.

One key principle is the First Law of Thermodynamics, which states that energy can neither be created nor destroyed, only transferred or transformed. This principle underlies the importance of insulation in a home—by reducing the transfer of heat, we don't lose the energy we've already used to heat the space.

Another important concept is the Second Law of Thermodynamics, which tells us that systems naturally progress toward a state of disorder, or entropy. In practical terms, this means that without intervention, heat will flow from a warmer area to a cooler one. Insulation slows down this process, allowing us to maintain a comfortable temperature inside a home more efficiently.

Heat Insulation Methods

The exercise example highlights the significance of preventing heat loss through air leaks. Heat insulation methods can be quite effective in saving energy, and there are various ways to apply them:

• Caulking: Using a sealant for gaps and joints less than one-quarter-inch wide.
• Weatherstripping: This involves applying materials to seal components that move, such as doors and operable windows, to prevent drafts.
• Storm Windows: Adding an extra layer of glass or plastic helps to reduce heat loss.

Through these methods, the insulation performance of a building can improve significantly. This reduces the amount of energy required to maintain a desired temperature, leading to cost savings over time. Understanding insulation is vital, as it directly impacts the efficiency of energy use, contributing to the whole building's thermal performance.

Energy Conservation Techniques

Energy conservation techniques, in the context of household energy use, focus on reducing waste and improving efficiency. The example of caulking and weatherstripping as preventive measures against air leaks is a classic technique for conserving energy. These techniques save on heating costs, as less energy is needed to maintain a constant temperature when there are fewer air leaks.

Other techniques include:

• Upgrading to energy-efficient appliances which consume less power for the same functionality.
• Utilizing programmable thermostats for better regulation of heating and cooling.
• Improving home insulation in walls, attics, and floors.
• Employing smart home technology that can adjust energy use automatically.

By combining these techniques, homeowners can maximize energy conservation, leading to significant savings on utility bills and reduced environmental impact. The initial investments, such as the cost for caulking and weatherstripping, often pay for themselves over a short period, as demonstrated by our exercise.