# Power

Power is how fast energy is transformed or transmitted. To make an analogy: if energy is like money, power is a wage or salary (e.g., earning $18/hour or$50,000/year), or usage rate (e.g, spending $20/hour to rent a canoe or$1500/month on rent).

Power can be expressed in many different units, all of which can be expressed as a unit of energy divided by a unit of time. The most common unit is the watt (W), defined as 1 joule (J) of energy per second. A 40 W light bulb, then, uses 40 J of electrical energy every second to stay lit. The average power output of the human body during moderate exercise is about 100 W.

For most engines and power plants there are two different powers. The rate at which energy is coming into the system from the fuel is the thermal power. The amount of power that the engine is outputting is the mechanical power. For a power plant, this output is electricity so it's measured in megawatts electric (MWe) as opposed to the input power which is measured in megawatts thermal (MWt).

## Energy and Power

The relationship between power, energy, and time can be described by the following equation:

• P is the average power output, measured in watts (W)
• ΔEsys is the net change in energy of the system in joules (J) - also known as work.
• Δt is the duration - how long the energy use takes - measured in seconds (s)

Since power is a rate of energy use (energy divided by an interval of time), multiplying a unit of power by a unit of time will give a quantity of energy. One such example is in the energy unit kilowatt-hours (kWh). A kilowatt is equal to 1000 watts, so 1 kWh represents the amount of energy transfer that occurs over one hour from a power output of 1000 watts (i.e., joules per second). Thus 1 kWh is equal to 3,600,000 joules of energy transfer (work).

More power can accomplish a task with a given energy requirement in a shorter time. For example, lifting a 15 kg block 2 meters in the air. This task requires approximately 300 J of energy input (work). A motor and pulley system with a 5 W power output could accomplish this task in one minute. However, a more powerful motor with an output of 100 W could raise the box to the same height in just three seconds! But in the end, both motors will have done the same amount of work (energy transfer) in lifting the box.

Power output time Total energy transfer
5 W 60 s 300 J
100W 3 s 300 J

## Power Unit Conversion

Please see below to convert among various units for power: