Question

Convert an energy of \(2430 \mathrm{~J}\) to units of Calories.

Short answer

The equivalent energy in Calories is approximately \(581.181 \mathrm{~Calories}\)

Step-by-step solution

Identify the conversion factor between Joules and Calories

It's known that \(1 \mathrm{~Calorie} = 4.184 \mathrm{~Joules}\). This will be the conversion factor used to convert Joules into Calories.

Apply the conversion factor

To convert from Joules to Calories, the value in Joules should be divided by the conversion factor. The calculation will be as follows: \[ \frac{2430 \mathrm{~Joules}}{4.184 \mathrm{~J/C}} \]

Calculate the result

Perform the division to find the equivalent energy in Calories.

Key concepts

Joules to Calories

Understanding the conversion from Joules to Calories is crucial when dealing with energy values in different units. In our daily lives, we talk about calories when referring to food energy, while scientists and engineers commonly use joules in various calculations. To bridge this gap, we convert energy values from joules to calories when needed. In the exercise, you're asked to convert an energy of 2430 Joules into Calories.

Let's break down the process. When converting, it's essential to start with the known conversion factor: 1 Calorie is equivalent to 4.184 Joules. With this knowledge, the conversion from joules to calories involves dividing the energy value in joules by 4.184. Thus, for the given problem, the calculation would be structured as follows:
\[\begin{equation}\frac{2430 \mathrm{~J}}{4.184 \mathrm{~J/Cal}}\end{equation}\]
By performing this division, you'll arrive at the equivalent energy value in Calories.

Conversion Factor

A conversion factor is a number used to change one set of units to another, by multiplying or dividing. In the context of energy, using the right conversion factor is vital to accurately convert from one unit of energy to another. In our exercise, the conversion factor is 4.184, which is the exact number of joules that make up one Calorie.

To properly use the conversion factor, it must be applied correctly based on the direction of the conversion. If you are converting from Joules to Calories, as highlighted in our example, you would divide by the conversion factor. On the other hand, if the conversion was from Calories to Joules, you would multiply by the conversion factor. The precise application of the conversion factor ensures that the converted value accurately represents the same amount of energy, just in different units.

Energy Units

There are various units used to measure energy, with Joules and Calories being two of the most commonly encountered ones. A Joule, symbolized as 'J', is the SI unit of energy and is defined as the amount of work done when a force of one newton displaces an object by one meter. On the other hand, a Calorie, with a capital 'C', is a non-SI unit of energy often used in nutrition to express the energy content of food.

It's vital to understand that there are different types of calories, including small calories (cal), also known as gram calories, and large Calories (Cal), which are also known as food calories. This distinction is important because 1 large Calorie (Cal) is equivalent to 1 kilocalorie (kcal) or 1000 small calories (cal). In the context of energy conversion, 1 large Calorie (Cal) is equal to 4.184 Joules. Always ensure you're using the correct unit when performing conversions to avoid confusion and inaccuracies.