Question

1a: We eat food to gain energy. Some foods provide energy more efficiently than others. The established energy value for three food types is given: carbohydrates, 17 kJ/g; fats, 38 kJ/g; and proteins, 17kJ/g. Look at the nutrition label on your favorite candy bar. Calculate the energy gained by eating this candy.

1b: If the same amount of heat is added to equal masses of aluminum, lead, zinc, and iron, which metal would experience the greatest increase in temperature? Explain.

Answer 1

Question 1a.

​In "m&m's" milk chocolate bar label, amount of total carbohydrates, total fats and proteins, listed are, 34 g, 10 g, and 2 g respectively. Total energy value due to each nutrient in one pack of the candy bar is listed in the table below.

Nutrient	Energy value per gram (given in question) (kJ / g)	Amount of Nutrient (given in label) (g)	Total energy value (calculated here) (kJ)
Carbohydrate	17	34	34 * 17 = 578
Fat	38	10	38 * 10 = 380
Protein	17	2	17 * 2 = 34

Total energy value of the candy is, (578 + 380 + 34) kJ = 992 kJ

Hence, energy that can be gained by eating the candy is 992 kJ.

​Image of the candy label:

ANSWER: 992 kJ ( for the candy label in image uploaded)

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Queation 1b.

Relation between heat change and change in temperature of a substance is given by the equation,

q = c * m * T

where, q is heat gained or lost by the substance; c is specific heat capacity of the substance; m is mass of the substance and T is change in temperature of the substance.

So, change in temperature, T = [q / (m * c) ]

T = [(q / m) * (1/ c) ] ............................(1)

In the given case, heat is added to metals and hence temperature of the metals increases. So, T​ gives the increase in temperature. Given that, amount of heat added (q) and mass (m) of the metals is same for all given metals. From equation (1), it follows that, when q and m are constant,

T = [(constant) * (1/ c) ]​ where, (constant) is (q / m) in the given context.

then T varies inversely as specific heat capacity(c) of the metals.

Hence, the metal with lowest specific heat capacity(c) will experience the greatest increase in temperature (T).

Specific heat capacity of the given metals are listed in the table below.

Metal	Specific heat capacity (c) in J / g.oC
Lead	0.126
Zinc	0.377
Iron	0.460
Aluminum	0.921

Lead has the lowest specific heat capacity and hence experiences the greatest increase in temperature, among the given metals.

ANSWER: Lead