Question

If a gas furnace releases 450 kcal of heat energy, what is the energy in kilojoules? ( 1 cal \(=4.184\) J)

Short answer

450 kcal of heat energy is equivalent to 1882.8 kJ.

Step-by-step solution

Identify the Conversion Factor

To convert kcal to kilojoules, we use the conversion factor between calories and joules. We know that 1 cal = 4.184 J. We need to convert kcal (kilocalories) to kilojoules (kJ). Since 1 kcal = 1000 cal, we find 1 kcal = 1000 cal * 4.184 J/cal = 4184 J = 4.184 kJ.

Convert Kilocalories to Kilojoules

Given that the furnace releases 450 kcal, we convert this to kilojoules using the factor determined in Step 1. The conversion is calculated as follows: 450 kcal * 4.184 kJ/kcal = 1882.8 kJ.

Key concepts

Converting Kilocalories to Kilojoules

When working with energy conversion, one very common scenario is converting kilocalories (kcal) to kilojoules (kJ). This is important in many fields such as dietetics, physics, and engineering, where energy consumption and release need to be measured accurately. Kilocalories are often used in diet and food contexts, whereas kilojoules are typically used in scientific calculations.
To perform this conversion, understanding the relationship between calories, joules, and their larger counterparts, kilocalories and kilojoules is crucial.

• 1 calorie (cal) is equivalent to 4.184 joules (J).
• 1 kilocalorie (kcal) is equivalent to 1000 calories (cal).
• Consequently, 1 kilocalorie (kcal) is equal to 4184 joules (J), which is the same as 4.184 kilojoules (kJ).

By knowing these conversions, you can switch between units depending on the context of your calculation. So, for example, to convert 450 kcal to kilojoules, multiply by the conversion factor 4.184, resulting in 1882.8 kJ.

Understanding the Conversion Factor

To make the conversion between different energy units, a conversion factor—a specific ratio—is used. This factor expresses how one measurement unit relates to another. For converting kilocalories (kcal) to kilojoules (kJ), the conversion factor is derived from the relationship between calories and joules.
Given that 1 cal = 4.184 J, when calculating for kilocalories to kilojoules, we scale up the units:

• Since 1 kilocalorie equals 1000 calories, then 1 kcal equates to 1000 cal = 1000 * 4.184 J = 4184 J.
• To further convert joules to kilojoules (as 1 kJ = 1000 J), you divide the result in joules by 1000.

This gives us the simple conversion factor that is 1 kcal = 4.184 kJ.
Using conversion factors simplifies calculations, enabling easy transitions between different units of measurement.

From Joules to Kilojoules

Understanding how to convert joules to kilojoules is essential for interpreting results within the International System of Units (SI). Joules are the base unit of energy in the SI system, and many scientific calculations start with joules.
Sometimes, due to the large magnitude of energy values involved, it might be convenient to express energy in kilojoules.

• The conversion process turns smaller units into more manageable larger units: 1000 joules = 1 kilojoule (kJ).
• When the energy is given in joules, divide by 1000 to convert to kilojoules.

For example, if you have 4184 joules, dividing by 1000 yields 4.184 kJ. This conversion is helpful for simplifying expression of energy in contexts that involve large quantities, making numbers more manageable and easier to communicate.