Question

Express the quantity 55.69 cal in joules.

Short answer

55.69 cal is equivalent to 232.9 J.

Step-by-step solution

Identify the Conversion Factor

To convert calories to joules, we use a known conversion factor: 1 cal = 4.184 J. This factor will allow us to convert the quantity from calories to joules.

Set Up the Conversion

Write down the quantity to be converted, 55.69 cal. Then, multiply it by the conversion factor (4.184 J/cal) to convert the unit from calories to joules:

Perform the Multiplication

Multiply 55.69 cal by the conversion factor 4.184 J/cal:\[55.69 \, \text{cal} \times 4.184 \, \frac{\text{J}}{\text{cal}} = 232.93936 \, \text{J}\]

Round the Result

Round the result to an appropriate number of significant figures. Since the original quantity, 55.69, has four significant figures, we should keep four significant figures in the result:\[55.69 \, \text{cal} = 232.9 \, \text{J}\]

Key concepts

Calories to Joules

When dealing with energy conversions, especially in physics and chemistry, it's essential to understand how to convert between different units. In our task, we're focusing on converting calories to joules. Calories are often used when discussing food energy, while joules are the standard unit of energy in the International System of Units (SI).

To convert calories to joules, we rely on a specific conversion factor: as noted in the exercise, 1 calorie is equivalent to 4.184 joules. This means that any quantity measured in calories can be transformed into an equivalent amount in joules by multiplying it by this factor. For instance, to convert 55.69 calories to joules, as outlined in the solution, you multiply 55.69 by 4.184. This gives you the energy in joules, which is a larger number compared to the calories since joule is a smaller unit of energy compared to a calorie.

Conversion Factor

A conversion factor is a handy tool in unit conversion processes. It acts as a bridge that allows us to translate quantities between different units. When we know how one unit relates to another, we can express any amount initially measured in the first unit in terms of the second.
Here's how the conversion factor works in practice:

• Identify the relationship: Here, 1 calorie equals 4.184 joules.
• Set up the conversion: Use the relationship as a fraction or ratio, like 4.184 J/cal. This ratio reads as '4.184 joules per calorie'.

When you want to convert, for example, 55.69 calories to joules, you multiply by the conversion factor:\[55.69 \times 4.184 = 232.93936\]Since the units "calories" on the top cancel out the same units on the bottom, you're left with the result in joules. Conversion factors are powerful tools because they allow for converting any amount as long as the factor is correctly set up and used accurately.

Significant Figures

Significant figures are crucial for accurately reporting scientific data. They represent the precision of a measurement or calculation. Each significant figure in a number provides information about the level of precision. Here's what you should keep in mind:

• Every non-zero digit is significant.
• Zeros between significant digits are also significant.
• Leading zeros (zeros before the first non-zero digit) are not significant.
• Trailing zeros in a number with a decimal point are significant.

In our scenario, the original number 55.69 has four significant figures. When you perform the calculation to convert to joules, your resulting value must reflect the same number of significant figures. Hence, we keep four significant figures in our final answer, rounding 232.93936 to 232.9 J to match the precision of the original value. Maintaining correct significant figures ensures that the data conveys the accuracy of the measurement process.