Energy Density

Note: This activity refers to energy density as the ratio of energy to mass. This is more commonly referred to as specific energy. Energy density usually refers to the ratio of energy to volume.

Preparation and points to note

This activity builds on the ideas in the activities in Food Energy and develops in a more formal way the idea of energy density*. Given the nature of the calculations, it is preferable that students use calculators (or spreadsheets). They can then focus on what they are trying to achieve, look for patterns, and maintain enthusiasm and involvement, without being tied up by the calculations themselves.

For Activity Two, the students need to dehydrate food items. You may need to discuss with them what items are suitable and whether they are able (with permission) to bring them from home. It may be impractical for the whole class to use an oven or dehydrator. If this is an issue, consider assigning different foods to different groups, dehydrating the foods over a period of time, and sharing the results.

These activities are ideal for focusing on the key competency thinking because students will be exploring energy density by using their own experiences and ideas and the information that they research.

Points of entry: Mathematics

This activity focuses students’ attention on a real-life problem: “What food should Henry pack to go on a 3 day tramp?” The food that students think Henry should take on the tramp should be based on sound mathematical and scientific evidence, from both what the students have calculated and any research they may have done.

The students should fill in the blank columns on their copy of the water content and energy density table as they work through the questions in Activity One, rounding appropriately. You may need to review rounding principles.

Question the students about what the table is showing and how they should use the data. Ask What do the columns actually show and mean? Make sure all the students understand why energy is the product of mass and energy density (column D = B x C). You can use the idea of ratio to help students, for example, If 1 g of apple has 1.5 kJ, how many kilojoules do 670 g have?

See the notes in the bottom row of the water content and energy density table for question 4 for explanations of the equations used.

Ensure that the students also set up the calculation properly for question 5 because the questions invert the relationships in the table. For example, beef is 54% water, so dry beef is 100 – 54 or 46% of the original. If 300 g of dehydrated beef is 46% of the original amount, that amount equals 300 ÷ 0.46. This is not intuitive and needs to be taught with care. A diagram can help:

If 46% of the original beef equates to 300 g, then 1% of the original beef must equate to a tiny part of that, namely 300/46 g. If this is 1% of the original, then the original must weigh 100 times as much, namely 100 x 300/46 = 652 g.

There is huge scope to develop this topic further. You could encourage the students to produce graphic displays that show, for example, energy levels compared with food types or water content as a percentage for a variety of foods.

Points of entry: Science

Find out what your students already know. Ask Which foods are probably high in water content? (Most fruits and vegetables)

Water provides absolutely no food energy, so removing water does not reduce the available energy. Energy density is energy divided by mass, so when mass is reduced, energy density increases. Water is surprisingly heavy (1 L weighs 1 kg). This means that any reduction in water content can be helpful where mass is an issue.

Like potential energy, energy density is an abstract quantity (energy per gram). Abstractions tend to be hard to understand. Clear-cut examples can help: Will you have more energy after eating 500 g of celery or 500 g of sugar?

As an extension, ask the students to research the energy densities (kJ ÷ 100 g) of a variety of foods and drinks from the supermarket, especially those that are marketed as good sources of energy. Link the amount of energy Henry uses while hiking (11 000 kJ per day) to the suggested intakes from the previous activity (Food Energy). Compare the level of activity and the amount of energy in sports foods and discuss the implications of eating or drinking high-energy foods without exercising.

At the end of these activities, the students should be able to clearly identify good choices of foods to take on a tramp (high in energy, low in mass). Make sure you have enough time for a closing session to ensure that all students are clear about this.

Answers

Activity One
1. a. Yes. (Henry needs 11 000 kJ and has 11 426 kJ, which is the total from column D in the table for question 4.)

b. Beef, at 4 860 kJ

2. 8.7 kg (his menu of 2 900 g x 3 days)

3. Dehydrated foods have more energy per gram than the same food with its normal water content. Water is not a source of energy, but it does have mass, so if you remove the water, the energy stays the same but the number of grams goes down.

4. a. The completed table (including column H from question 6a) is: 

Columns A, B, C, and E are given.

Column D is the total energy provided by the food in kilojoules. Find it by multiplying the energy density (number of kilojoules per gram) by the number of grams.

Column F is the dry mass (mass once water is removed). Calculate how much of the food is not water (using the normal water content percentage) and then multiply the dry percentage by the original mass (column B). For example, if apples are 85% water, then the dry mass is 15% (100 – 85). Multiply 450 g by 0.15 (15%) to get a dry mass of 68 g.

Column G is the mass of the water content. Find it by subtracting the dry mass (column F) from the original mass (column B). For example, if the apples were originally 450 g and now weigh 68 g, Henry saves 450 – 68 = 383 g of mass by dehydrating them.

Column H is the energy density of the dried food. Energy density is how much energy each food contains per gram. As water contributes no kilojoules, the foods contain the same energy as before. To find the energy density of the dehydrated food, divide the energy (column D) by the new mass (column F).

b. 5.8 kg over 3 days (1 937 x 3, rounded, using daily total from column G in the table above)

5. a. About 600 g. (Beef is 54% water, which means it’s about half (50%) water and half dry mass. You can work out the amount of normal beef required by estimating: if about half of normal beef is dry mass, then to get 300 g of dehydrated beef, you’ll need about 600 g of normal beef because 300 is 1/2 of 600. Calculating exactly, the mass of dehydrated beef is 46% [100 – 54] that of normal beef. Dividing 300 by 46% [0.46] gives 652 [reverse to check: 0.46 x 652 = 299.92].)

b. 88%. (24/200 = 12%. 100 – 12 = 88)

6. a. Rice. (See the calculated values on the table above.)

b. Bananas have a higher energy density than peas, but peas contain relatively more water (89% compared with 76%). When you remove the larger amount of water, the remaining dry mass actually has more energy per gram.

c. Beef, peas, and bananas

Activity Two
1. a. Suggestions and predictions will vary.

2. a. Practical activity

b. In order to find the water content, you need to measure the normal mass of the food, remove the water, and then measure its mass with the water taken out. Methods may vary, for example, you can dry food in an oven, in the sun, in a microwave, or freeze-dry it.

i. Percentage loss of water = (original mass – final mass) ÷ (original mass) x 100

ii. When there is no further change in mass if you continue drying

3. a.–b. Answers will vary.

Activity Three
Menus and discussion will vary. Your food choices need to have good food value in relation to their mass (because they are to be carried).