Question

A person obtains approximately \(2.5 \times 10^{3}\) Calories a day from his or her food. How much energy is that in a. calories? b. joules? c. kilowatt-hours?

Short answer

a. \(2.5 \times 10^{6}\) caloriesb. \(1.046 \times 10^{7}\) joulesc. \(2.906 \times 10^{-3}\) kilowatt-hours

Step-by-step solution

Understanding Calorie to calorie conversion

Recognize that the term 'Calorie' used in the context of food is actually a kilocalorie. Therefore, to convert food Calories to calories, multiply by 1,000 since 1 food Calorie is equal to 1,000 calories.

Converting food Calories to calories

To convert from food Calories to calories, multiply the number of food Calories by 1,000. Calculation: \(2.5 \times 10^{3}\) food Calories \(\times 1,000 = 2.5 \times 10^{6}\) calories.

Understanding calorie to joule conversion

1 calorie is defined as 4.184 joules. To convert calories to joules, multiply the number of calories by 4.184.

Converting calories to joules

To find the energy in joules, multiply the number of calories by 4.184 joules/calorie. Calculation: \(2.5 \times 10^{6}\) calories \(\times 4.184\) joules/calorie \(= 1.046 \times 10^{7}\) joules.

Understanding joule to kilowatt-hour conversion

1 kilowatt-hour is equivalent to 3.6 \(\times\) 10^6 joules. To convert joules to kilowatt-hours, divide the number of joules by 3.6 \(\times\) 10^6.

Converting joules to kilowatt-hours

To convert the energy in joules to kilowatt-hours, divide the energy in joules by 3.6 \(\times\) 10^6 joules/kilowatt-hour. Calculation: \(1.046 \times 10^{7}\) joules \(/ 3.6 \times 10^{6}\) joules/kilowatt-hour \(\approx 2.906 \times 10^{-3}\) kilowatt-hours.

Key concepts

Calorie to calorie conversion

In discussing food energy, it is vital to distinguish between the small calorie, often used in chemistry, and the large calorie, commonly referred to as the food Calorie, denoted with a capital 'C'. The food Calorie is equivalent to a kilocalorie, meaning it is 1,000 times larger than the small calorie. Consequently, when converting food Calories to calories, one needs to multiply by 1,000. For instance, if a person consumes approximately 2,500 food Calories a day, the energy intake in small calories is actually 2,500,000. This difference between the calorie scales is crucial for accurate nutritional and scientific calculations.

Understanding this concept simplifies the complexity of food energy content displayed on nutrition labels, thereby allowing one to better manage their dietary intake. It is also an essential standard in scientific studies where precise measurement of energy is required.

calorie to joule conversion

When converting energy from calories to joules, the standard conversion factor that is utilized is 1 calorie equals 4.184 joules. This factor is rooted in the definition of the calorie as the amount of heat needed to raise the temperature of one gram of water by one degree Celsius. Therefore, to find out how much energy is in joules, we multiply the calories by 4.184. For example, if we start with 2,500,000 calories (as calculated from the previous conversion of food Calories), and we want to express this energy in joules, we multiply it by 4.184 to get approximately 10,460,000 joules.

• This conversion is fundamental in fields such as nutrition, physics, and any other that demands the precise measurement of energy transfer or consumption.
• Moreover, understanding this can help in grasping the basic principles of thermodynamics and energy efficiency in biological systems.

joule to kilowatt-hour conversion

The conversion from joules to kilowatt-hours is particularly useful when considering energy usage in electrical appliances or even at a larger scale in power generation and consumption. A kilowatt-hour (kWh) is a unit commonly used in the electrical industry and represents the energy consumption of one thousand watts running for one hour. The conversion factor here is that one kilowatt-hour equals 3.6 million joules (or 3.6 x 10^6 joules).

To perform this conversion, we divide the energy in joules by the factor of 3.6 million. Taking our previous example of 10,460,000 joules, and converting this to kilowatt-hours gives us approximately 0.002906 kWh.

• This understanding enables students to better appreciate the scale of energy consumption and production, and the efficiency of various energy sources and appliances.
• It promotes energy literacy which is an invaluable skill in today's world driven by sustainability and energy conservation efforts.