Question

An Oreo cookie has 53 food calories and weighs 11 grams \([17] .\) A ton (2000 pounds) of TNT contains approximately \(4.184 \cdot 10^{9} \mathrm{~J}\) of energy |7]. Calculate the specific energy of the cookie in joules per kilogram, and calculate the specific energy of the TNT in joules per kilogram. (Yes, the value for the cookie is higher.)

Short answer

The specific energy of the Oreo cookie is higher than that of TNT when measured in joules per kilogram.

Step-by-step solution

Convert Calories to Joules

One food calorie is equivalent to 4184 joules. Therefore, the energy of one Oreo cookie in joules is calculated by multiplying the number of calories by 4184. Energy of Oreo in Joules = 53 calories \(\times\) 4184 J/calorie.

Calculate Specific Energy of Cookie

The specific energy is defined as the energy per unit mass. We must convert the mass of the Oreo cookie from grams to kilograms for this calculation. Mass of Oreo in kg = \( \frac{11}{1000} \text{ kg} \). Now, calculate the specific energy:Specific Energy of Oreo = \( \frac{53 \times 4184}{0.011} \) J/kg.

Convert Weight of TNT

Since specific energy is also needed for TNT, we need to express the mass in kilograms. The total mass of one ton (2000 pounds) is converted into kilograms as follows: 1 pound is approximately 0.453592 kg.Mass of TNT in kg = \( 2000 \times 0.453592 \) kg.

Calculate Specific Energy of TNT

Use the mass of TNT in kilograms to find the specific energy. The energy content for one ton of TNT is approximately \(4.184 \times 10^9\) joules. Specific Energy of TNT = \( \frac{4.184 \times 10^9}{2000 \times 0.453592} \) J/kg.

Key concepts

Calories to Joules Conversion

In physics and nutrition, energy is commonly expressed in both calories and joules. The term "Calorie" with a capital C is used for food and is equivalent to 1000 small "calories" (or "gram calories"). In the specific context of food energy, 1 Calorie is also equal to 4184 joules. This means that to convert food calories to joules, you multiply the number of Calories by 4184.

• For example, if an Oreo has 53 Calories, its energy content in joules is calculated as: \( 53 \times 4184 = 221752 \text{ J} \).
• This conversion is essential for comparing energy values across different units and systems, ensuring consistency in energy-related calculations.

Mass Conversion

Mass conversion primarily involves changing units of weight or mass from one system to another, such as from grams to kilograms or pounds to kilograms. This is crucial in physics and engineering to maintain a standard unit of measurement when computing quantities like specific energy.
For instance, when converting the mass of an Oreo cookie from grams to kilograms:

• The mass of the Oreo is 11 grams, which must be divided by 1000 to convert it into kilograms.
• Thus, the mass of an Oreo in kilograms is \( \frac{11}{1000} = 0.011 \text{ kg} \).

Similarly, when dealing with a larger mass such as the weight of TNT expressed in pounds:

• Convert pounds to kilograms using the conversion factor where 1 pound equals approximately 0.453592 kilograms.
• Hence, \( 2000 \times 0.453592 = 907.184 \text{ kg} \).

Energy Per Unit Mass

Energy per unit mass, or specific energy, is an important concept in physics and engineering. It measures how much energy is stored or expended per kilogram of a substance. Calculating specific energy involves dividing the total energy by the total mass.
In the example of the Oreo cookie:

• The total energy calculated in joules is divided by the mass of the Oreo in kilograms.
• This yields a specific energy of: \( \frac{53 \times 4184}{0.011} = 20159272.72 \text{ J/kg} \).

For TNT:

• The stored energy of 4.184 billion joules is divided by the mass of one ton of TNT in kilograms.
• The specific energy is therefore: \( \frac{4.184 \times 10^9}{907.184} = 4610151.27 \text{ J/kg} \).

Unit Conversion

Converting units is a fundamental skill in science, ensuring that measurements are consistent and comparable. This skill includes converting between measurement systems (e.g., metric and imperial) and between different units within the same system.
Here's how you can apply unit conversion:

• Ensure you understand the equivalence between units, such as 1 Calorie = 4184 joules or 1 kg = 1000 grams.
• Apply conversion factors directly to the measurements to change them to a common unit, which supports calculation accuracy, especially in mixed unit problems.
• Use conversion to derive specific quantities, such as specific energy, which is calculated in units of joules per kilogram (J/kg) to provide a basis for further comparison between different substances.

Consistent and accurate conversions allow for clear communication and reliable results in scientific research and practical applications.