A chocolate chip cookie contains about \(200 \mathrm{kcal}\). How many kilowatt- hours of energy does it contain? How long could you light a 100-W light bulb with the energy from the cookie?

Short Answer

Expert verified
The energy of the cookie is 0.232444 kWh. A 100-W light bulb could be lit for approximately 139.47 minutes with the energy from the cookie.

Step by step solution

01

Conversion to Kilowatt-hours

First, convert the energy from kilocalories to kilowatt-hours. The conversion factor is 1 kcal = 0.00116222 kWh. So, multiply the energy content of the cookie by this conversion factor: \( 200 \mathrm{kcal} \times 0.00116222 \mathrm{kWh/kcal} = 0.232444 \mathrm{kWh} \).
02

Calculating Light Bulb Lighting Time

Next, to find out how long a 100-W light bulb could be lit with the energy from the cookie, divide the energy of the cookie in kilowatt-hours by the power of the light bulb in kilowatts: \( 0.232444 \mathrm{kWh} \/ 0.1 \mathrm{kW} = 2.32444 \mathrm{hours} \), which can then be converted to minutes by multiplying by 60.
03

Convert Hours to Minutes

Since it is more common to talk about light bulb usage in minutes, convert the hours to minutes. Multiply the time in hours by 60: \( 2.32444 \mathrm{hours} \times 60 \mathrm{minutes/hour} = 139.4664 \mathrm{minutes} \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Kilocalories to Kilowatt-hours
Understanding energy conversion is pivotal in various scientific fields, including chemistry. In our daily lives, we often see energy content expressed in kilocalories (kcal), especially when discussing the nutritional value of food. Electrical energy, on the other hand, is typically measured in kilowatt-hours (kWh). Conveying this understanding to students is crucial, as it bridges the gap between abstract concepts and real-life applications.

When converting from kilocalories to kilowatt-hours, one must use the conversion factor, with 1 kcal equating to 0.00116222 kWh. Therefore, we multiply the energy in kilocalories by this factor to get the equivalent in kilowatt-hours. This concept could be made clearer by illustrating it with more day-to-day examples highlighting the amount of energy in common food items and their equivalent in energy to power electrical appliances.
Energy Content Analysis
The analysis of the energy content of different substances is a crucial aspect of not only chemistry but also fields like nutrition and environmental science. Knowing the energy content in kilocalories can allow us to understand the potential energy available for conversion to other forms. For instance, with the case of the chocolate chip cookie, which contains about 200 kcal, we infer that not only does it provide dietary energy, but if converted, it could also power devices that rely on electrical energy.

Such analysis guides choices in both diet and resource management. When teaching this concept, it's beneficial to explore the energy content of various foods and discuss the implications of this energy in terms of sustainability or health. Exposing students to the multitude of applications can facilitate a deeper appreciation for the significance of energy conversions.
Calculating Lighting Time
Calculating how long we can use electrical appliances with a given amount of energy is both a practical and enlightening exercise. It allows us to visualize the value of energy stored in foods and fuels by comparing it to everyday uses, such as lighting our homes. To calculate lighting time, we divide the energy in kilowatt-hours by the power rating of the appliance (in this case, a light bulb) in kilowatts. This results in the duration in hours, which can then be converted to minutes if required.

For students, incorporating real-life examples, such as lighting a room with the energy from a cookie, can help in understanding energy efficiency and conservation. This knowledge empowers them to make informed decisions about energy usage in their own lives. Equipping them with the ability to perform such calculations independently can be immensely beneficial for their critical thinking skills.

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