calories (cal) to Electronvolts (eV) conversion

What is calories?

Calories are a unit of energy, historically defined as the amount of heat required to raise the temperature of one gram of water by one degree Celsius. While the "calorie" is still commonly used, the kilocalorie (kcal), also known as the "large calorie" or "food calorie," is more prevalent when discussing dietary energy. In the International System of Units (SI), the joule (J) is the standard unit of energy.

Types of Calories

• Small calorie (cal): The amount of energy required to raise the temperature of 1 gram of water by 1°C.
• Large calorie (Cal) or Kilocalorie (kcal): The amount of energy required to raise the temperature of 1 kilogram of water by 1°C. This is the calorie commonly referred to in nutrition.

The relationship between these units is:

$1 \text{ Cal} = 1 \text{ kcal} = 1000 \text{ cal}$

Calorie to Joule Conversion

Since the joule is the SI unit for energy, it's useful to know the conversion factor:

$1 \text{ cal} \approx 4.184 \text{ J}$

$1 \text{ kcal} \approx 4184 \text{ J}$

Historical Context

While not directly related to a specific law, the development of calorimetry (the science of measuring heat) was crucial to understanding calories. Scientists like Nicolas Clément and later Wilbur Olin Atwater, a pioneer in nutrition science, contributed significantly to establishing calorie values for different foods. Atwater's work in the late 19th and early 20th centuries was instrumental in developing the calorie system used in nutrition today.

Real-World Examples and Calorie Values

• Food:

  • One medium apple (approx. 182g): ~95 kcal
  • One slice of whole wheat bread: ~70 kcal
  • A can of soda (355ml): ~150 kcal

• Energy Expenditure:

  • A 150-pound person running for 30 minutes at 6 mph burns approximately 340 kcal.
  • Sleeping for 8 hours burns roughly 50 kcal per hour, totaling around 400 kcal.

• Other Quantities:

  • Gasoline: 1 gallon of gasoline contains approximately 31,000 kcal.

Measuring Calories in Food

Calories in food are typically determined using a bomb calorimeter. This device measures the heat released when a food sample is completely burned inside a closed chamber surrounded by water. The temperature increase of the water is then used to calculate the calorie content of the food. The caloric content in the three macronutrients are as follows:

• Carbohydrates: 4 kcal/gram
• Proteins: 4 kcal/gram
• Fats: 9 kcal/gram

What is the Electronvolt?

The electronvolt is a small unit of energy used throughout atomic, nuclear, and particle physics to describe the energies of individual particles, photons, and chemical or nuclear reactions.

Definition

One electronvolt is the kinetic energy gained by a single electron accelerated through an electric potential difference of one volt:

$$1\ \text{eV} = 1.60218 \times 10⁻¹⁹\ \text{J}$$

Since the 2019 redefinition of SI units, this value is exact: 1 eV = 1.602176634 × 10⁻¹⁹ J, because the elementary charge is now a defined constant. Common multiples include the keV (10³ eV), MeV (10⁶ eV), GeV (10⁹ eV), and TeV (10¹² eV).

Origin and History

The unit arose in the early 20th century as physicists studied electrons and ions accelerated in vacuum tubes and early particle accelerators, where energy expressed in volts of accelerating potential was far more natural than joules. It became the standard energy scale as quantum and nuclear physics matured.

Law and Notable Facts

The electronvolt is accepted for use with the SI system though it is not itself an SI unit. Via mass-energy equivalence, particle masses are routinely quoted in eV/c²: the electron's rest mass is about 511 keV/c², and the proton's is about 938 MeV/c².

Real-World Examples and Conversions

• Visible-light photons carry roughly 1.6 to 3.3 eV each.
• Chemical bond energies are typically a few eV per bond.
• The Large Hadron Collider accelerates protons to about 6.5 TeV, or 6.5 × 10¹² eV, roughly 1.04 microjoules per proton.