/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 84 A pound of plain \(\mathrm{M\&am... [FREE SOLUTION] | 91影视

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Chapter 5: Problem 84

A pound of plain \(\mathrm{M\&M}\) candies contains \(96 \mathrm{~g}\) fat, \(320 \mathrm{~g}\) carbohydrate, and 21 g protein. What is the fuel value in \(\mathrm{kJ}\) in a \(42-\mathrm{g}\) (about 1.5 oz ) serving? How many Calories does it provide?

Short Answer

Expert verified
A 42-g serving of plain M&M's provides approximately \(899.4 \mathrm{~kJ}\) and 215 Calories.

Step by step solution

01

Calculate the energy provided by fat, carbohydrate, and protein in one pound of M&M's

Each macro has a different energy contribution: Fat has 37 kJ/g, carbohydrates have 17 kJ/g, and protein has 17 kJ/g. So, for one pound of M&M's: Energy from fat = \(96 \mathrm{~g}\) x \(37 \mathrm{~kJ/g}\) = \(3552 \mathrm{~kJ}\) Energy from carbohydrates = \(320 \mathrm{~g}\) x \(17 \mathrm{~kJ/g}\) = \(5440 \mathrm{~kJ}\) Energy from protein = \( 21 \mathrm{~g}\) x \(17 \mathrm{~kJ/g}\) = \(357 \mathrm{~kJ}\) Total energy = Energy from fat + Energy from carbohydrates + Energy from protein Total energy = \(3552 + 5440 + 357 \mathrm{~kJ}\) = \(9349 \mathrm{~kJ}\)
02

Calculate the total energy per gram

To find out the energy provided by one gram of plain M&M's, we need to divide the total energy by the weight of the candy. Total energy per gram = Total energy 梅 Total weight Total energy per gram = \(9349 \mathrm{~kJ}\) 梅 \(437 \mathrm{~g}\) = \(21.40 \mathrm{~kJ/g}\)
03

Calculate the energy in a 42-g serving

Now we can calculate the fuel value in a 42-g serving by multiplying the energy per gram by the serving size. Energy in a 42-g serving = Total energy per gram 脳 Serving size Energy in a 42-g serving = \(21.40 \mathrm{~kJ/g}\) 脳 \(42 \mathrm{~g}\) = \(899.4 \mathrm{~kJ}\)
04

Calculate the energy value in Calories

To convert the energy value to Calories (dietary/caloric), we need to know that 1 Calorie is equal to 4.184 kJ. Energy in a 42-g serving (Calories) = Energy in a 42-g serving (kJ) 梅 4.184 Energy in a 42-g serving (Calories) = \(899.4 \mathrm{~kJ}\) 梅 4.184 = 215 Calories So, a 42-g serving of plain M&M鈥檚 provides approximately 899.4 kJ and 215 Calories.

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Key Concepts

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

Fuel Value Calculation
Understanding the fuel value of food is akin to assessing the energy that a specific quantity of that food provides when consumed. This concept is crucial for determining caloric intake and managing dietary needs.

Let's begin by considering a real-world example - a serving of M&M candies. The fuel value can be calculated by multiplying the amount of each nutrient (fat, carbohydrates, and protein) in a serving by the energy that each of those nutrients contributes. For instance, fats are generally more energy-dense, with a standard fuel value of approximately 37 kJ/g. Carbohydrates and proteins offer less, about 17 kJ/g each.

To calculate the fuel value for a serving, we would follow these steps:
Energy Content of Nutrients
Fuel values for nutrients are based on the amount of energy they provide, typically measured in kilojoules per gram (kJ/g) or Calories per gram. The three primary macronutrients have standard energy values:
  • Fat: 37 kJ/g (about 9 Calories/g)
  • Carbohydrates: 17 kJ/g (about 4 Calories/g)
  • Protein: 17 kJ/g (also approximately 4 Calories/g)
These values are average estimates and can differ slightly based on the exact composition of a particular food item. In our M&M example, the total energy content is calculated by combining the individual contributions from fats, carbohydrates, and proteins. It is the sum of these components that provides the overall caloric content of the food.
Dietary Calories
In the context of nutrition, Calories (with a capital 'C') refer to kilocalories, which are units used to measure the energy in food. One dietary Calorie is equal to 4.184 kilojoules (kJ). This conversion is vital when reading nutritional information and in calculating energy intake for dietary planning.

When evaluating the calorie content of a serving of M&M's, we convert the measured energy from kilojoules to Calories to align with common dietary standards. This allows individuals to relate the energy content to dietary recommendations and daily calorie allowances.

Remember that counting Calories can help with managing weight and ensuring a balanced diet, but it is also essential to consider the quality and nutritional value of the foods consumed, not just the caloric content.

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Most popular questions from this chapter

For the following processes, calculate the change in internal energy of the system and determine whether the process is endothermic or exothermic: (a) A balloon is cooled by removing \(0.655 \mathrm{~kJ}\) of heat. It shrinks on cooling, and the atmosphere does \(382 \mathrm{~J}\) of work on the balloon. (b) A 100.0 -g bar of gold is heated from \(25^{\circ} \mathrm{C}\) to \(50{ }^{\circ} \mathrm{C}\) during which it absorbs \(322 \mathrm{~J}\) of heat. Assume the volume of the gold bar remains constant. (c) The surroundings do \(1.44 \mathrm{~kJ}\) of work compressing gas in a perfectly insulated cylinder.

At \(20^{\circ} \mathrm{C}\) (approximately room temperature) the average velocity of \(\mathrm{N}_{2}\) molecules in air is \(1050 \mathrm{mph}\). (a) What is the average speed in \(\mathrm{m} / \mathrm{s}\) ? (b) What is the kinetic energy (in J) of an \(\mathrm{N}_{2}\) molecule moving at this speed? (c) What is the total kinetic energy of \(1 \mathrm{~mol}\) of \(\mathrm{N}_{2}\) molecules moving at this speed?

Under constant-volume conditions, the heat of combustion of glucose \(\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right)\) is \(15.57 \mathrm{~kJ} / \mathrm{g}\). A 3.500 -g sample of glucose is burned in a bomb calorimeter. The temperature of the calorimeter increased from \(20.94^{\circ} \mathrm{C}\) to \(24.72^{\circ} \mathrm{C}\). (a) What is the total heat capacity of the calorimeter? (b) If the size of the glucose sample had been exactly twice as large, what would the temperature change of the calorimeter have been?

The air bags that provide protection in autos in the event of an accident expand because of a rapid chemical reaction. From the viewpoint of the chemical reactants as the system, what do you expect for the signs of \(q\) and \(w\) in this process?

Imagine a book that is falling from a shelf. At a particular moment during its fall, the book has a kinetic energy of \(24 \mathrm{~J}\) and a potential energy with respect to the floor of \(47 \mathrm{~J} .\) (a) How does the book's kinetic energy and its potential energy change as it continues to fall? (b) What is its total kinetic energy at the instant just before it strikes the floor? (c) If a heavier book fell from the same shelf, would it have the same kinetic energy when it strikes the floor? [Section 5.1]
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