Practice Problems:1. Convert The Following From One Unit To Another:a) 1.69 Joules To Caloriesb) 68 Calories To Kilocaloriesc) 3780 Calories To KJd) 5.26 Kcal To KJ

by ADMIN 165 views

Introduction

Energy is a fundamental concept in chemistry, and understanding different units of energy is crucial for accurate calculations and conversions. In this article, we will practice converting energy from one unit to another, focusing on joules (J), calories (cal), kilocalories (kcal), and kilojoules (kJ).

Conversion Factors

Before we dive into the practice problems, let's review the conversion factors between these units:

  • 1 calorie (cal) = 4.184 joules (J)
  • 1 kilocalorie (kcal) = 1000 calories (cal) = 4184 joules (J)
  • 1 kilojoule (kJ) = 1000 joules (J) = 239.006 calories (cal) = 0.239006 kilocalories (kcal)

Practice Problems

a) Convert 1.69 joules to calories

To convert joules to calories, we can use the conversion factor: 1 calorie (cal) = 4.184 joules (J). We can set up a proportion to solve for the number of calories:

1 cal = 4.184 J 1.69 J = x cal

To solve for x, we can divide both sides by 4.184:

x = 1.69 J / 4.184 J/cal x ≈ 0.404 cal

Therefore, 1.69 joules is approximately equal to 0.404 calories.

b) Convert 68 calories to kilocalories

To convert calories to kilocalories, we can use the conversion factor: 1 kilocalorie (kcal) = 1000 calories (cal). We can set up a proportion to solve for the number of kilocalories:

1 kcal = 1000 cal 68 cal = x kcal

To solve for x, we can divide both sides by 1000:

x = 68 cal / 1000 cal/kcal x ≈ 0.068 kcal

Therefore, 68 calories is approximately equal to 0.068 kilocalories.

c) Convert 3780 calories to kJ

To convert calories to kilojoules, we can use the conversion factor: 1 kilojoule (kJ) = 239.006 calories (cal). We can set up a proportion to solve for the number of kilojoules:

1 kJ = 239.006 cal 3780 cal = x kJ

To solve for x, we can divide both sides by 239.006:

x = 3780 cal / 239.006 cal/kJ x ≈ 15.84 kJ

Therefore, 3780 calories is approximately equal to 15.84 kilojoules.

d) Convert 5.26 kcal to kJ

To convert kilocalories to kilojoules, we can use the conversion factor: 1 kilojoule (kJ) = 0.239006 kilocalories (kcal). We can set up a proportion to solve for the number of kilojoules:

1 kJ = 0.239006 kcal 5.26 kcal = x kJ

To solve for x, we can divide both sides by 0.239006:

x = 5.26 kcal / 0.239006 kcal/kJ x ≈ 22.0 kJ

Therefore, 5.26 kilocalories is approximately equal to 22.0 kilojoules.

Conclusion

In this article, we practiced converting energy from one unit to another, focusing on joules (J), calories (cal), kilocalories (kcal), and kilojoules (kJ). We reviewed the conversion factors and applied them to solve practice problems. By mastering these conversions, you will be able to accurately calculate and convert energy values in various contexts, from chemistry to physics and beyond.

Key Takeaways

  • 1 calorie (cal) = 4.184 joules (J)
  • 1 kilocalorie (kcal) = 1000 calories (cal) = 4184 joules (J)
  • 1 kilojoule (kJ) = 1000 joules (J) = 239.006 calories (cal) = 0.239006 kilocalories (kcal)
  • To convert joules to calories, divide by 4.184
  • To convert calories to kilocalories, divide by 1000
  • To convert calories to kilojoules, divide by 239.006
  • To convert kilocalories to kilojoules, divide by 0.239006

Additional Practice Problems

Try converting the following values:

  • 2500 J to cal
  • 120 kcal to kJ
  • 4500 cal to kJ
  • 3.5 kcal to kJ

Introduction

In our previous article, we practiced converting energy from one unit to another, focusing on joules (J), calories (cal), kilocalories (kcal), and kilojoules (kJ). Now, let's address some common questions and concerns related to energy unit conversions.

Q: What is the difference between joules and calories?

A: Joules (J) and calories (cal) are both units of energy, but they are not interchangeable. Joules are a more fundamental unit of energy, while calories are a unit of energy that is commonly used in the context of food and nutrition. 1 calorie (cal) is equal to 4.184 joules (J).

Q: How do I convert joules to kilocalories?

A: To convert joules to kilocalories, you can use the conversion factor: 1 kilocalorie (kcal) = 4184 joules (J). You can set up a proportion to solve for the number of kilocalories:

1 kcal = 4184 J x J = 1 kcal

To solve for x, you can divide both sides by 4184:

x = 1 kcal / 4184 J/kcal x ≈ 0.00024 J

Q: What is the relationship between kilocalories and kilojoules?

A: Kilocalories (kcal) and kilojoules (kJ) are both units of energy, but they are not interchangeable. 1 kilocalorie (kcal) is equal to 4.184 kilojoules (kJ). You can use the conversion factor to convert between these units.

Q: How do I convert kilocalories to joules?

A: To convert kilocalories to joules, you can use the conversion factor: 1 kilocalorie (kcal) = 4184 joules (J). You can set up a proportion to solve for the number of joules:

1 kcal = 4184 J x J = 1 kcal

To solve for x, you can multiply both sides by 4184:

x = 1 kcal × 4184 J/kcal x ≈ 4184 J

Q: What is the difference between kilocalories and calories?

A: Kilocalories (kcal) and calories (cal) are both units of energy, but they are not interchangeable. 1 kilocalorie (kcal) is equal to 1000 calories (cal). You can use the conversion factor to convert between these units.

Q: How do I convert calories to kilojoules?

A: To convert calories to kilojoules, you can use the conversion factor: 1 kilojoule (kJ) = 239.006 calories (cal). You can set up a proportion to solve for the number of kilojoules:

1 kJ = 239.006 cal x cal = 1 kJ

To solve for x, you can divide both sides by 239.006:

x = 1 kJ / 239.006 cal/kJ x ≈ 0.0042 cal

Q: What is the relationship between joules and kilojoules?

A: Joules (J) and kilojoules (kJ) are both units of energy, but they are not interchangeable. 1 kilojoule (kJ) is equal to 1000 joules (J). You can use the conversion factor to convert between these units.

Conclusion

In this Q&A article, we addressed some common questions and concerns related to energy unit conversions. We reviewed the conversion factors and provided step-by-step solutions to common problems. By mastering these conversions, you will be able to accurately calculate and convert energy values in various contexts, from chemistry to physics and beyond.

Key Takeaways

  • 1 calorie (cal) = 4.184 joules (J)
  • 1 kilocalorie (kcal) = 1000 calories (cal) = 4184 joules (J)
  • 1 kilojoule (kJ) = 1000 joules (J) = 239.006 calories (cal) = 0.239006 kilocalories (kcal)
  • To convert joules to calories, divide by 4.184
  • To convert calories to kilocalories, divide by 1000
  • To convert calories to kilojoules, divide by 239.006
  • To convert kilocalories to kilojoules, divide by 0.239006

Additional Practice Problems

Try converting the following values:

  • 2500 J to cal
  • 120 kcal to kJ
  • 4500 cal to kJ
  • 3.5 kcal to kJ

Remember to use the conversion factors and set up proportions to solve for the desired unit.