calories (cal) to Milliwatt-hours (mWh) 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 Milliwatt-hours?

Milliwatt-hours (mWh) are a unit of energy, commonly used to express the capacity of small batteries and the energy consumption of low-power electronic devices. Understanding mWh helps in comparing battery life and energy efficiency.

Understanding Milliwatt-hours

A watt-hour (Wh) is a unit of energy equivalent to one watt of power sustained for one hour. A milliwatt-hour (mWh) is simply one-thousandth of a watt-hour. Mathematically:

$$1 \text{ mWh} = \frac{1}{1000} \text{ Wh} = 0.001 \text{ Wh}$$

Since a Watt is defined as Joules per second ($J/s$) and an hour is 3600 seconds, 1 Wh can also be represented in joules ($J$).

$$1 \text{ Wh} = 1 \frac{J}{s} \cdot 3600 s = 3600 \text{ J}$$

Therefore, converting mWh to Joules ($J$)

$$1 \text{ mWh} = 3.6 \text{ J}$$

Formation of Milliwatt-hours

Milliwatt-hours represent the amount of energy a device consumes or a battery provides over a period of time. It is derived by multiplying power (in milliwatts) by time (in hours):

$$\text{Energy (mWh)} = \text{Power (mW)} \times \text{Time (h)}$$

For example, a device consuming 10 mW of power for 5 hours uses 50 mWh of energy.

Real-World Examples and Applications

• Coin Cell Batteries: Small electronic devices like watches, calculators, and some sensors use coin cell batteries with capacities often measured in mWh. For example, a CR2032 battery might have a capacity of around 200-240 mWh.
• Wearable Devices: Smartwatches and fitness trackers use batteries with capacities expressed in mWh. A typical smartwatch battery might be rated at 300-500 mWh.
• Hearing Aids: These devices require very small, energy-efficient batteries. Their capacity is naturally expressed in mWh.
• IoT (Internet of Things) Devices: Many IoT sensors and devices designed for long-term deployment and low power consumption rely on batteries measured in mWh to operate for extended periods.
• Low-Power Integrated Circuits: Evaluating the power consumption of a chip in milliWatts gives engineers an idea about heat dissipation, battery life and other metrics.

Milliwatt-hours and Battery Capacity

Battery capacity is often specified in mWh. A higher mWh rating indicates that the battery can supply more energy and power a device for a longer time, assuming a constant power draw. When comparing different batteries for the same device, look for the higher mWh rating for longer usage. For an in-depth understanding, refer to resources on battery capacity.