Question

Convert the following numbers of calories or kilocalories into joules and kilojoules (Remember: kilo means 1000 .) a. 75.2 kcal b. 75.2 cal c. \(1.41 \times 10^{3}\) cal d. 1.41 kcal

Short answer

a. 314668.8 J, 314.6688 kJ b. 314.5168 J, 0.3145168 kJ c. 5899.44 J, 5.89944 kJ d. 5905.44 J, 5.90544 kJ

Step-by-step solution

a. Convert 75.2 kcal to joules and kilojoules

First, convert 75.2 kcal to joules by using the conversion factor 1 kcal = 4184 J. \(75.2 \ \text{kcal} \times \frac{4184 \ \text{J}}{1 \ \text{kcal}} = 314668.8 \ \text{J}\) Now, convert 314668.8 J to kilojoules by using the conversion factor 1 kJ = 1000 J. \(\frac{314668.8 \ \text{J}}{1000}= 314.6688 \ \text{kJ}\)

b. Convert 75.2 cal to joules and kilojoules

First, convert 75.2 cal to joules using the conversion factor 1 cal = 4.184 J. \(75.2 \ \text{cal} \times \frac{4.184 \ \text{J}}{1 \ \text{cal}} = 314.5168 \ \text{J}\) Now, convert 314.5168 J to kilojoules by using the conversion factor 1 kJ = 1000 J. \(\frac{314.5168 \ \text{J}}{1000}= 0.3145168 \ \text{kJ}\)

c. Convert \(1.41 \times 10^{3}\) cal to joules and kilojoules

First, convert \(1.41 \times 10^3\) cal to joules using the conversion factor 1 cal = 4.184 J. \((1.41 \times 10^3) \ \text{cal} \times \frac{4.184 \ \text{J}}{1 \ \text{cal}} = 5899.44 \ \text{J}\) Now, convert 5899.44 J to kilojoules by using the conversion factor 1 kJ = 1000 J. \(\frac{5899.44 \ \text{J}}{1000}= 5.89944 \ \text{kJ}\)

d. Convert 1.41 kcal to joules and kilojoules

First, convert 1.41 kcal to joules by using the conversion factor 1 kcal = 4184 J. \(1.41 \ \text{kcal} \times \frac{4184 \ \text{J}}{1 \ \text{kcal}} = 5905.44 \ \text{J}\) Now, convert 5905.44 J to kilojoules by using the conversion factor 1 kJ = 1000 J. \(\frac{5905.44 \ \text{J}}{1000}= 5.90544 \ \text{kJ}\)

Key concepts

Understanding Calories to Joules Conversion

Calories, often seen in food labels, measure energy. However, while calories are used in dietetics, the scientific community primarily uses joules. This creates a need for converting calories to joules when working with scientific data. The fundamental conversion values are:

• 1 calorie (cal) = 4.184 joules (J)
• 1 kilocalorie (kcal) = 4184 joules (J)

Understanding these conversions is straightforward. Multiply the calorie quantity by 4.184 to get joules. For kilocalories, which are essentially 1000 calories, multiply by 4184.
For example, converting 75.2 kcal involves multiplying 75.2 by 4184, resulting in 314668.8 J. Thus, knowing the basic conversion helps translate everyday energy use to scientific understanding.

The Basics of Energy Conversion

Energy conversion is a crucial aspect of understanding how energy is measured and utilized across different systems. Converting energy from one unit to another allows us to compare different types of energy effectively.
When discussing energy, it's important to recognize that different contexts use different units. In physics, energy is commonly measured in joules. In nutritional contexts, kilocalories or calories are used.
The process of converting between these units involves specific fixed ratios. For example:

• 1 kcal = 4184 J
• 1 cal = 4.184 J

Ensuring unit consistency when converting helps maintain accuracy in calculations, essential for scientific work, engineering, and more.

Converting Kilocalories to Kilojoules

Kilocalories to kilojoules conversion is common in scientific fields, where understanding the precise energy content is important. Since both are larger units of their respective calorie and joule conversions, the process offers simplicity.
To convert kilocalories (kcal) to kilojoules (kJ), use the conversion factor below:

• 1 kcal = 4.184 kJ

The calculation involves multiplying the kilocalorie value by 4.184 to determine the kilojoules. For instance, for 75.2 kcal, the calculation would be 75.2 × 4.184, resulting in 314.6688 kJ.
This conversion is helpful in scientific reporting and global nutrition labeling, ensuring consistent energy value representation across materials and disciplines.