Milliwatt-hours (mWh) to Electronvolts (eV) conversion

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.

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.