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Chapter 7: Problem 5

Express 1,265 cal in kilocalories and in joules.

Short Answer

Expert verified
1,265 cal = 1.265 kcal and 5,293.36 J.

Step by step solution

01

Convert Calories to Kilocalories

To convert calories (cal) to kilocalories (kcal), use the conversion factor: \( 1 \, \text{kcal} = 1000 \, \text{cal} \). Therefore, divide 1,265 cal by 1000. \[ \text{kcal} = \frac{1,265 \, \text{cal}}{1000} = 1.265 \, \text{kcal} \]
02

Convert Calories to Joules

To convert calories to joules, use the conversion factor: \( 1 \, \text{cal} = 4.184 \, \text{J} \). Multiply the number of calories by this factor:\[ \text{Joules} = 1,265 \, \text{cal} \times 4.184 \, \text{J/cal} = 5,293.36 \, \text{J} \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Calories to Kilocalories
When converting calories to kilocalories, it's important to understand the difference between these two units. While they sound similar, their relationship simply involves a factor of 1000. One kilocalorie (kcal) is equivalent to 1000 calories (cal). This conversion is often used in nutritional contexts, where dietary energy is typically expressed in kilocalories. For our specific case, we want to convert 1,265 calories to kilocalories. The calculation is straightforward: simply divide the number of calories by 1000.

That means:
  • Number of calories: 1,265 cal
  • Conversion factor: 1 kcal = 1000 cal
  • Result: \(\frac{1,265 \text{ cal}}{1000} = 1.265 \text{ kcal}\)
Thus, 1,265 calories is equal to 1.265 kilocalories.
Calories to Joules
The conversion of calories to joules involves understanding how these units measure energy. Calories are commonly used in nutritional settings, while joules are more scientific and standard units of energy. The conversion factor between these two is 1 cal = 4.184 J. This means that one calorie is equal to 4.184 joules. To convert calories to joules, multiply the number of calories by this factor.

For instance, with 1,265 calories:
  • Number of calories: 1,265 cal
  • Conversion factor: 1 cal = 4.184 J
  • Result: \(1,265 \text{ cal} \times 4.184 \text{ J/cal} = 5,293.36 \text{ J}\)
Hence, 1,265 calories equals 5,293.36 joules.
Energy Conversion Factors
Understanding energy conversion factors is essential in transitioning between different units of energy. These factors help convert measurements from one unit to another, allowing for universal application across different fields such as chemistry, physics, and nutrition.

Some common energy conversion factors include:
  • Calories to Kilocalories: 1 kcal = 1000 cal
  • Calories to Joules: 1 cal = 4.184 J
  • Joules to Kilojoules: 1 kJ = 1000 J
Knowing these conversion factors ensures that you can calculate and interpret energy measurements accurately no matter the context.

Whether you're analyzing a food label or solving a physics problem, recognizing these relationships between energy units is fundamental to comprehensive energy understanding.

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Most popular questions from this chapter

How much energy in calories is required to heat \(150 \mathrm{~g}\) of \(\mathrm{H}_{2} \mathrm{O}\) from \(0^{\circ} \mathrm{C}\) to \(100^{\circ} \mathrm{C} ?\)

A large, single crystal of sodium chloride absorbs \(98.0\) cal of heat. If its temperature rises from \(22.0^{\circ} \mathrm{C}\) to \(29.7^{\circ} \mathrm{C}\), what is the mass of the \(\mathrm{NaCl}\) crystal?

Determine the heat capacity of a substance if \(23.6 \mathrm{~g}\) of the substance gives off 199 cal of heat when its temperature changes from \(37.9^{\circ} \mathrm{C}\) to \(20.9^{\circ} \mathrm{C}\).

Does a substance that has a small specific heat require a small or large amount of energy to change temperature? Explain.

Sulfur dioxide \(\left(\mathrm{SO}_{2}\right)\) is a pollutant gas that is one cause of acid rain. It is oxidized in the atmosphere to sulfur trioxide \(\left(\mathrm{SO}_{3}\right)\), which then combines with water to make sulfuric acid \(\left(\mathrm{H}_{2} \mathrm{SO}_{4}\right)\). a. Write the balanced reaction for the oxidation of \(\mathrm{SO}_{2}\) to make \(\mathrm{SO}_{3}\). (The other reactant is diatomic oxygen.) b. When \(1 \mathrm{~mol}\) of \(\mathrm{SO}_{2}\) reacts to make \(\mathrm{SO}_{3}, 23.6 \mathrm{kcal}\) of energy are given off. If \(100 \mathrm{lb}(1 \mathrm{lb}=454 \mathrm{~g})\) of \(\mathrm{SO}_{2}\) were converted to \(\mathrm{SO}_{3}\), what would be the total energy change?
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