Chapter 3: Problem 50
Perform the indicated conversions. a. 76.52 cal into kilojoules b. 7.824 kJ into kilocalories c. \(489.4 \mathrm{J}\) into calories d. \(1.598 \times 10^{4} \mathrm{J}\) into kilocalories.
Short Answer
Expert verified
a. 76.52 cal = 0.32029 kJ
b. 7.824 kJ = 1.86861 kcal
c. 489.4 J = 117.0000064 cal
d. \(1.598 \times 10^{4} \mathrm{J}\) = 3.81960 kcal
Step by step solution
01
Convert calories to joules
Using the conversion factor, 1 cal = 4.184 J, we can convert the given energy value from calories to joules:
76.52 cal * 4.184 J/cal = 320.28768 J
02
Convert joules to kilojoules
Using the conversion factor, 1 kJ = 1000 J, we can convert the energy value from joules to kilojoules:
320.28768 J * 0.001 kJ/J = 0.32029 kJ
b. Convert 7.824 kJ into kilocalories
03
Convert kilojoules to joules
Using the conversion factor, 1 kJ = 1000 J, we can convert the given energy value from kilojoules to joules:
7.824 kJ * 1000 J/kJ = 7824 J
04
Convert joules to calories
Using the conversion factor, 1 J = 0.239006 cal, we can convert the energy value from joules to calories:
7824 J * 0.239006 cal/J = 1868.611904 cal
05
Convert calories to kilocalories
Using the conversion factor, 1 cal = 0.001 kcal, we can convert the energy value from calories to kilocalories:
1868.611904 cal * 0.001 kcal/cal = 1.86861 kcal
c. Convert 489.4 J into calories
06
Convert joules to calories
Using the conversion factor, 1 J = 0.239006 cal, we can convert the given energy value from joules to calories:
489.4 J * 0.239006 cal/J = 117.0000064 cal
d. Convert \(1.598 \times 10^{4} \mathrm{J}\) into kilocalories
07
Convert joules to calories
Using the conversion factor, 1 J = 0.239006 cal, we can convert the given energy value from joules to calories:
\(1.598 \times 10^{4} \mathrm{J}\) * 0.239006 cal/J = 3819.597688 cal
08
Convert calories to kilocalories
Using the conversion factor, 1 cal = 0.001 kcal, we can convert the energy value from calories to kilocalories:
3819.597688 cal * 0.001 kcal/cal = 3.81960 kcal
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Calories to Joules
Energy conversion from calories to joules involves a simple multiplication.
The conversion factor to keep in mind is 1 cal = 4.184 J. This essentially means that one calorie is equivalent to 4.184 joules.
When you have a certain number of calories and need to know how many joules it is equivalent to, simply multiply the calories by 4.184.
The conversion factor to keep in mind is 1 cal = 4.184 J. This essentially means that one calorie is equivalent to 4.184 joules.
When you have a certain number of calories and need to know how many joules it is equivalent to, simply multiply the calories by 4.184.
- For example, if you have 76.52 calories, converting to joules would be: 76.52 cal × 4.184 J/cal = 320.28768 J.
Joules to Kilojoules
Converting joules to kilojoules is a matter of understanding the prefix 'kilo,' which stands for 1,000.
This means that one kilojoule equals 1,000 joules. Thus, to convert joules into kilojoules, you divide the number of joules by 1,000.
For instance, to convert 320.28768 joules to kilojoules, you perform the division: 320.28768 J / 1,000 = 0.32029 kJ.
This means that one kilojoule equals 1,000 joules. Thus, to convert joules into kilojoules, you divide the number of joules by 1,000.
For instance, to convert 320.28768 joules to kilojoules, you perform the division: 320.28768 J / 1,000 = 0.32029 kJ.
- This conversion is essential for working with larger energy quantities, common in various science and engineering fields.
Kilojoules to Kilocalories
When converting energy from kilojoules to kilocalories, you step into the relationship between the metric system and nutritional energy measurements.
First, convert kilojoules to joules by multiplying by 1,000 (since 1 kJ = 1,000 J).
Next, use the conversion factor that 1 J = 0.239006 cal to find the energy in calories. Finally, convert the calories to kilocalories by multiplying by 0.001 (since 1 cal = 0.001 kcal).
First, convert kilojoules to joules by multiplying by 1,000 (since 1 kJ = 1,000 J).
Next, use the conversion factor that 1 J = 0.239006 cal to find the energy in calories. Finally, convert the calories to kilocalories by multiplying by 0.001 (since 1 cal = 0.001 kcal).
- For example, 7.824 kJ becomes 7824 J, which converts to 1868.611904 cal, and finally to 1.86861 kcal.
Joules to Calories
The conversion from joules to calories is significant in various sectors, from nutrition to thermodynamics.
The conversion factor here is 1 J = 0.239006 cal, linking the joule, a unit of energy in the International System of Units, with the calorie, often used in the context of nutritional energy.
To convert, multiply the joules by 0.239006.
The conversion factor here is 1 J = 0.239006 cal, linking the joule, a unit of energy in the International System of Units, with the calorie, often used in the context of nutritional energy.
To convert, multiply the joules by 0.239006.
- So, for 489.4 J, it converts to 489.4 J × 0.239006 cal/J = 117.0000064 cal.