Question

Write the conversion factors that would be necessary to perform each of the following conversions: a. an energy given in calories to its equivalent in joules b. an energy given in joules to its equivalent in calories c. an energy given in calories to its equivalent in kilocalories d. an energy given in kilojoules to its equivalent in joules

Short answer

a. The conversion factor from calories to joules is \(1 \: \text{calorie} = 4.184 \: \text{joules}\). b. The conversion factor from joules to calories is \(1 \: \text{joule} = 0.239006 \: \text{calories}\). c. The conversion factor from calories to kilocalories is \(1 \: \text{kilocalorie} = 1000 \: \text{calories}\). d. The conversion factor from kilojoules to joules is \(1 \: \text{kilojoule} = 1000 \: \text{joules}\).

Step-by-step solution

Find the relation between calories and joules

The conversion factor between calories and joules is 1 calorie = 4.184 joules (approximately). So, when converting from calories to joules, multiply the energy in calories by 4.184. #b. Conversion factor: Joules to Calories#

Find the relation between joules and calories

The conversion factor between joules and calories is 1 joule = 0.239006 calories (approximately). So, when converting from joules to calories, multiply the energy in joules by 0.239006. #c. Conversion factor: Calories to Kilocalories#

Find the relation between calories and kilocalories

The conversion factor between calories and kilocalories is 1 kilocalorie = 1000 calories. So, when converting from calories to kilocalories, divide the energy in calories by 1000. #d. Conversion factor: Kilojoules to Joules#

Find the relation between kilojoules and joules

The conversion factor between kilojoules and joules is 1 kilojoule = 1000 joules. So, when converting from kilojoules to joules, multiply the energy in kilojoules by 1000.

Key concepts

Calories to Joules Conversion

Understanding the conversion from calories to joules is crucial for areas such as nutrition, physics, and engineering. This conversion is all about changing one unit of energy, the calorie (used often in food energy), to another, the joule (the SI unit for energy).

The key formula to remember is that 1 calorie is approximately equal to 4.184 joules. To put this into practice, if you have a value in calories and you need to convert it to joules, you simply multiply it by 4.184. For instance, if a snack has 250 calories, it contains about \( 250 \times 4.184 = 1046 \) joules of energy.

Remember, precision is important in scientific calculations, so make sure to use the exact conversion factor and consider the significant figures in your measurements.

Joules to Calories Conversion

When moving from the metric unit of joules back into the more dietarily familiar calories, we apply a different conversion factor. As mentioned previously, 1 joule is equal to approximately 0.239006 calories.

To convert energy from joules to calories, you'll want to multiply the number of joules by 0.239006. For example, if you have a gadget that used 500 joules of energy, it would have used around \( 500 \times 0.239006 = 119.503 \) calories of energy.

This type of conversion is often used in food labeling and exercise tracking, helping you understand how much energy your body is consuming and expending in terms that might be more relatable.

Calories to Kilocalories Conversion

Calories and kilocalories can be a point of confusion as some food labels refer to calories when they actually mean kilocalories. True to its prefix 'kilo-', a kilocalorie is equivalent to 1,000 calories. This is the conversion factor used when you're trying to express food energy typically in a larger, more manageable unit.

So, to convert from calories to kilocalories (often simply called 'Calories' with a capital C), you divide the number of calories by 1,000. For instance, an apple with 95 calories can also be said to have \( 95 \div 1000 = 0.095 \) kilocalories. This abstract number conversion plays an important role in dietary planning and nutritional science.

Kilojoules to Joules Conversion

Working between kilojoules and joules is a straightforward process since it hinges on the standard metric system prefix 'kilo-', which denotes a factor of 1,000. 1 kilojoule (kJ) is simply 1,000 joules (J). This means that you can convert kilojoules to joules by multiplying the kilojoule value by 1,000.

For example, if an electrical appliance rating is 3 kJ, this translates to \( 3 \times 1000 = 3000 \) joules. Such conversions are often necessary in physics, chemistry, and various engineering fields where energy computations are frequent. Understanding this relationship helps in accurate scaling of energy values for practical applications.