The relationship between the nutritional unit for energy and the metric unit is 1 Calorie = 1 kcal.
a. One donut contains 350 Calories. Convert this to calories and joules.

Verified step by step guidance

1. Step 1: Understand the relationship between Calories and calories. Note that 1 Calorie (nutritional calorie) is equivalent to 1 kilocalorie (kcal), and 1 kcal is equal to 1000 calories (small 'c').
2. Step 2: Convert the given 350 Calories into calories using the relationship: \( 1 \text{ Calorie} = 1000 \text{ calories} \). Multiply 350 by 1000 to find the value in calories.
3. Step 3: Recall the relationship between calories and joules. The conversion factor is \( 1 \text{ calorie} = 4.184 \text{ joules} \). Use this to convert the value obtained in calories to joules by multiplying the number of calories by 4.184.
4. Step 4: Write the final expressions for both conversions: \( 350 \text{ Calories} \times 1000 = \text{ calories} \) and \( \text{calories} \times 4.184 = \text{ joules} \).
5. Step 5: Ensure the units are consistent and verify the calculations conceptually to confirm the conversions are correct.

Key Concepts

Calorie vs. Kilocalorie

A calorie (cal) is a unit of energy defined as the amount of heat needed to raise the temperature of 1 gram of water by 1 degree Celsius. A kilocalorie (kcal), often referred to simply as a 'Calorie' in dietary contexts, is equal to 1,000 calories. Understanding this distinction is crucial for converting between these units when discussing food energy.

Energy Conversion

Energy can be expressed in various units, including calories and joules. The conversion factor between these units is important: 1 calorie is approximately equal to 4.184 joules. This means that to convert calories to joules, one must multiply the calorie value by 4.184, which is essential for accurately expressing energy content in different contexts.

Nutritional Energy Content

The energy content of food is typically measured in kilocalories (Calories) and indicates how much energy the body can obtain from consuming that food. For example, a donut containing 350 Calories provides a specific amount of energy that can be converted into other units for scientific or dietary analysis. Understanding this concept helps in evaluating dietary choices and energy balance.