Question

Perform each conversion. (a) \(45.6 \mathrm{~J}\) to calories (b) \(355 \mathrm{cal}\) to joules (c) \(43.8 \mathrm{~kJ}\) to calories (d) \(215 \mathrm{cal}\) to kilojoules

Short answer

\(45.6 \text{ J} = 10.9031 \text{ cal}\), \(355 \text{ cal} = 1485.32 \text{ J}\), \(43.8 \text{ kJ} = 10,461.7425 \text{ cal}\), \(215 \text{ cal} = 0.89924 \text{ kJ}\)

Step-by-step solution

- Convert Joules to Calories

To convert energy from Joules (J) to calories (cal), use the conversion factor 1 J = 0.239005736 cal. Multiply the given value by this factor: \[45.6 \text{ J} \times 0.239005736 \frac{\text{cal}}{\text{J}} = 10.9030609 \text{ cal}\]

- Convert Calories to Joules

To convert calories to Joules, use the conversion factor 1 cal = 4.184 J. Multiply the given calories by this factor: \[355 \text{ cal} \times 4.184 \frac{\text{J}}{\text{cal}} = 1485.32 \text{ J}\]

- Convert Kilojoules to Calories

First, convert kilojoules to joules by multiplying by 1,000. Then use the conversion factor to change joules to calories: \[43.8 \text{ kJ} \times 1,000 \frac{\text{J}}{\text{kJ}} \times 0.239005736 \frac{\text{cal}}{\text{J}} = 10,461.7425 \text{ cal}\]

- Convert Calories to Kilojoules

To convert calories to kilojoules, first use the calories to joules conversion factor, then convert joules to kilojoules by dividing by 1,000: \[215 \text{ cal} \times 4.184 \frac{\text{J}}{\text{cal}} \div 1,000 = 0.89924 \text{ kJ}\]

Key concepts

Joules to Calories Conversion

Understanding how to convert joules to calories is an essential skill in energy conversion chemistry. It's like learning how to translate between two languages—in this case, the language of physics and the language of nutrition. When you see a value expressed in joules (J), think of it as a raw measure of energy based on the International System of Units (SI). To convert joules to calories, which are more commonly used in food energy, we apply the conversion factor: 1 J = 0.239005736 cal.

For example, to convert 45.6 joules into calories, you would multiply the joules value by this conversion factor:\[\begin{equation}45.6 J \times 0.239005736 \frac{cal}{J} = 10.9030609 cal\end{equation}\]This conversion is practical for understanding the energy contained in foods or for comparing the energy released in chemical reactions to everyday examples of dietary energy.

Calories to Joules Conversion

On the flip side, we sometimes need to convert from calories back to joules. This is especially common in scientific contexts where joules are preferred. A calorie (cal) is a non-SI unit of energy and often used to quantify the energy content in food. One calorie is the amount of energy needed to raise the temperature of one gram of water by one degree Celsius.

To perform this conversion, we use the factor: 1 cal = 4.184 J. So, turning 355 calories into joules involves multiplication:\[\begin{equation}355 cal \times 4.184 \frac{J}{cal} = 1485.32 J\end{equation}\]This process helps bridge the gap between nutritional energy values and the physical energy measurements used in various fields of science and engineering.

Energy Units Conversion

The conversion between different energy units is a fundamental concept in chemistry and physics. It allows scientists and students to understand and compare different forms of energy regardless of the units used. Energy can be expressed in multiple units such as joules, calories, kilojoules, kilocalories, electronvolts, and more. Each unit can be relevant depending on the context, such as food labeling (calories), scientific studies (joules), or even physics research (electronvolts).

Converting one unit to another requires a clear understanding of the conversion factors, for instance:

• 1 cal = 4.184 J
• 1 J = 0.239005736 cal
• 1 kJ = 1,000 J
• 1 J = 0.001 kJ

Knowing these conversions allows for accurate and meaningful comparisons and calculations across different disciplines.

Kilojoules to Calories Conversion

Kilojoules are another common energy unit that you'll encounter, especially on food labels outside of the United States. One kilojoule (kJ) is equal to 1,000 joules (J). The conversion from kilojoules to calories involves two steps. First, you convert kilojoules to joules, and then from joules to calories using the previous conversion factor we've discussed.

Let's illustrate this with an example. To convert 43.8 kJ to calories:\[\begin{equation}43.8 kJ \times 1,000 \frac{J}{kJ} \times 0.239005736 \frac{cal}{J} = 10,461.7425 cal\end{equation}\]It's essential to be proficient in these conversions to understand energy content in both scientific and everyday contexts, such as comparing the energy value of different foods or evaluating the energy produced by a chemical reaction.