Ton of Refrigeration to Watt Converter

The Physics of Power

Power is the rate at which work is done or energy is transferred.

Mathematical Definition: $$ P = \frac{E}{t} $$ Where:

• $P$ = Power (Watts)
• $E$ = Energy (Joules)
• $t$ = Time (seconds)

Dimensional Analysis: $$ 1 \text{ W} = 1 \frac{\text{J}}{\text{s}} = 1 \frac{\text{kg} \cdot \text{m}^2}{\text{s}^3} $$

Electrical Definition: For electrical circuits, power is the product of voltage and current: $$ P = V \times I $$ Where:

• $P$ = Power (Watts)
• $V$ = Voltage (Volts)
• $I$ = Current (Amperes)

Example:

• A device drawing 5 Amps at 120 Volts consumes:
  • $P = 120 \text{ V} \times 5 \text{ A} = 600 \text{ W}$

Watt vs. Watt-Hour (The Confusion)

This is the #1 source of confusion about watts.

• Watt (W): A unit of power (rate of energy use).
• Watt-hour (Wh) or Kilowatt-hour (kWh): A unit of energy (total amount of energy used).

The Analogy:

• Watts are like miles per hour (speed).
• Watt-hours are like miles (distance).

Example:

• A 100 W light bulb running for 10 hours uses:
  • $100 \text{ W} \times 10 \text{ h} = 1,000 \text{ Wh} = 1 \text{ kWh}$

Your electricity bill charges you for kWh (energy), not kW (power).

: James Watt and the Steam Revolution

The Man Behind the Unit

James Watt (1736-1819) was a Scottish instrument maker and inventor. While he didn't invent the steam engine, he made it vastly more efficient, enabling the Industrial Revolution.

His Key Innovation (1769): Watt added a separate condenser to the Newcomen steam engine. This kept the main cylinder hot, reducing fuel consumption by 75%. Suddenly, steam engines became economical for factories, mines, and transportation.

The Irony: Watt also coined the term "horsepower" to market his engines (see our horsepower article). Yet the unit named after him—the watt—would eventually replace horsepower as the global standard for electrical power.

Official Adoption

• 1882: The British Association for the Advancement of Science officially adopted the "watt" as the unit of electrical power, replacing the awkward "volt-ampere."
• 1889: The International Electrical Congress endorsed the watt.
• 1960: The watt was incorporated into the International System of Units (SI) as the standard unit of power.

The Original Definition

The watt was originally defined in relation to the absolute watt, based on mechanical power: $$ 1 \text{ W} = 10^7 \text{ erg/s} $$ (The erg is an obsolete CGS unit of energy.)

Today, the watt is defined in terms of fundamental SI units: $$ 1 \text{ W} = 1 \frac{\text{kg} \cdot \text{m}^2}{\text{s}^3} $$

1. Electrical Appliances

Every electrical device has a power rating in watts, indicating how much electricity it consumes when operating.

• Low Power (1-100 W): LED bulbs, phone chargers, alarm clocks.
• Medium Power (100-1,000 W): Laptops, TVs, fans, blenders.
• High Power (1,000-5,000 W): Microwaves, hair dryers, space heaters, ovens.
• Very High Power (5,000+ W): Electric water heaters, EV chargers, central AC.

2. Electricity Bills

Your utility company charges you for energy (kWh), not power (kW).

• Formula: $\text{Cost} = \text{Power (kW)} \times \text{Time (hours)} \times \text{Rate ($/kWh)}$
• Example: A 1,500 W space heater running 8 hours/day for 30 days:
  • Energy = $1.5 \text{ kW} \times 8 \text{ h/day} \times 30 \text{ days} = 360 \text{ kWh}$
  • Cost = $360 \text{ kWh} \times $0.10/\text{kWh} = $36$

3. Solar Panels & Renewable Energy

Solar panels are rated by their peak power output in watts under ideal conditions (full sun, 25°C).

• Residential Panel: 300-400 W.
• 10-Panel System: 3,000-4,000 W (3-4 kW).
• Daily Energy (sunny location): ~15-20 kWh.

4. Electric Vehicles

EV charging power determines how fast the battery charges.

• Level 1 (120V outlet): 1,400 W (1.4 kW) - adds ~4 miles/hour.
• Level 2 (240V charger): 7,200 W (7.2 kW) - adds ~25 miles/hour.
• DC Fast Charging: 50,000-350,000 W (50-350 kW) - adds 150-1,000 miles/hour.

5. Audio Equipment

Speaker and amplifier power ratings indicate maximum output.

• Bluetooth Speaker: 5-20 W.
• Home Theater Receiver: 100-200 W per channel.
• Concert PA System: 10,000-50,000 W.