# Does it make sense to compare mechanical wattages to electrical wattages?

A smartphone might produce 1 watt of power. A voltage of 1 volt producing 1 ampere of current over 1 second is 1 watt of power. (Did I do that right?)

Or a kid pushing a toy block might produce 1 watt of power. Accelerating one kilogram one meter-per-second every second, moving it one meter in the direction of force, in one second — that’s also 1 watt of power.

These come from different definitions of power. In what sense does it make sense to say it is the "same" amount of power? Are they convertible or comparable?

• Energy has several form : Thermal,Mechanical,etc.Similarly as power = (energy emitted)/time or (work)/time it has different forms... – user74370 Sep 27 '16 at 6:25
• Joule showed the equivalence of mechanical and thermal prior to 1850. It has since been shown for all forms: first law of thermodynamics. – Peter Diehr Sep 27 '16 at 11:49
• Consider two cars, one is driven by a gasoline engine and the other by battery power. The power output of the two engines (in kilowatts) is directly comparable, in its effect on acceleration time, maximum speed, etc. Of course in the USA people often state the power output of gas engines in horsepower not kilowatts, but that's no different from measuring lengths in inches not millimeters. – alephzero Sep 27 '16 at 14:51
• @PeterDiehr— Ah! I think this is exactly what I sought: "In the history of science, the mechanical equivalent of heat states that motion and heat are mutually interchangeable and that in every case, a given amount of work would generate the same amount of heat, provided the work done is totally converted to heat energy. The mechanical equivalent of heat was a concept that had an important part in the development and acceptance of the conservation of energy and the establishment of the science of thermodynamics in the 19th century." en.wikipedia.org/wiki/Mechanical_equivalent_of_heat – Toph Sep 27 '16 at 16:57

In what sense does it make sense to say it is the "same" amount of power? Are they convertible or comparable?

Yes, mainly due to the conservation of energy, which can be translated to a conservation of power in many situations (as power is only energy per time). Two examples:

• In many practical situations, energy or power is eventually converted to heat. E.g., if you have a server cluster that consumes 10 kW of electrical power, it will generate 10 kW of thermal power, which you would have deduct with your cooling system.

• If it takes 1 kW of mechanical power to move a vehicle under some given conditions (speed, friction, slope), you need to feed it at least 1 kW of electrical, chemical or other power. However, since electrical and chemical power cannot be converted to mechanical power without loss, you actually need to feed it more power. The amount of loss for a given power-conversion device (motor) is actually an important characteristic, namely the energy conversion efficiency.

Power is simply the energy consumed (or produced, in other cases) by a component of the system. 1 watt means a dissipation of 1 joule every second, it has nothing to do with the nature of what consumes the energy. The unit of measure watt is defined exactly that way: $W = \frac{J}{s}$.

Power has the units

${\rm watt} = \dfrac {{\rm joule}}{{\rm second}} = \dfrac {{\rm newton}\times {\rm metre}}{{\rm second}} = \dfrac {{\rm kilogramme}\times {\text{ metre second}}^{-2} \times{\rm metre}}{{\rm second}}$

${\rm watt} = {\rm volt} \times {\rm ampere} = \dfrac{{\rm joule}}{{\rm coulomb }} \times \dfrac{{\rm coulomb}}{{\rm second}} =\dfrac {{\rm joule}}{{\rm second}}$

So it is the same unit in both mechanical and electrical usage.