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

This problem aims to familiarize us with the daily consumption of calories using the fuel value of daily macronutrients. The concept required to solve this problem is mostly related to the fuel value or calorific calculation, and the energy values of macronutrients.

The calorie range, or the calorific value, of an edible substance is the part of the energy that is released when the compound is fully “burned,” or experiences complete combustion. Combustion usually happens in the existence of oxygen gas, with a reacting agent such as fuel.

The calorific value of a compound is mostly given based on per amount, that is, per mole or gram of compound burned.

Expert Answer

The caloric value of a substance can be resolved by calculating the heat produced when a given amount is fully fumed in oxygen. The energy received as an effect of full combustion is the potential energy but the energy released in the body is not identical.

According to the given information, a pound of candies contains:

Fat $=96g$,

Carbohydrates $=320g$,

Protein $=21g$,

The mass of serving is $m = 42g$

We are asked to find the value of one serving.

For this, we will first find the fuel value of candies per pound:

\[Fat \space= 98g \space \times \space 38 \dfrac{kJ}{g} \]

\[= 3648 kJ \]

\[Carbohydrates \space= 320g \space \times \space 17 \dfrac{kJ}{g} \]

\[= 5440 kJ \]

\[Protein \space= 21g \space \times \space 17 \dfrac{kJ}{g} \]

\[= 357 kJ \]

Total fuel value per pound is the sum of the fuel values of Fat, carbohydrates, and protein.

\[= 3648 kJ + 5440 kJ + 357 kJ \]

Total fuel value comes out to be: $9445 Kj$ per pound.

After calculating the total fuel value per pound, calculate the total fuel value per gram.

The total fuel value per gram is given as the total fuel value per pound into $\dfrac{1lb} {453.6g}$

That is:

\[=9445 \times \dfrac{1lb}{453.6}\]

The total fuel value per gram comes out to be $20.82 \space \dfrac{kJ}{g}$.

Now calculating the fuel value of one serving:

That is given as the total fuel value per gram times the mass. That is:

\[= 20.82 \dfrac{kJ}{g} \times 42g \]

\[= 874.44 kJ \]

Numerical Answer

The total fuel value per pound is $9445 Kj$.

The total fuel value per gram is $20.82 \space \dfrac{kJ}{g}$.

The fuel value of one serving is $874.44 kJ$

Example:

a) A $45-g$ golf ball is moving at $61 m/s$. Calculate its kinetic energy in joules.

b) Convert this energy to calories.

c) When the ball lands in a sand trap, what happens to this energy?

Part a:

\[ 1 J = (1 kJ) (m^2/s^2) \]

\[ E_k = \dfrac{1}{2} mv^2 \]

\[ E_k = \dfrac{1}{2} (45) (\dfrac{1kg}{1000g}) (61 \dfrac{m}{s})^2 \]

\[ = 84 kg (\dfrac{m^2}{s^2}) \]

\[ = 84 J \]

Part b:

\[ Calories = \dfrac{84}{4.184} \]

\[ Calories = 20 Cal \]

Part c:

The speed and the kinetic energy of the ball drop to zero as it hits the sand.

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