How is mechanical energy measured?

How is energy measured? More specifically, how do we know that certain objects require or emit a certain number of Joules?

• If Joules are the basic unit of energy, how do we measure the energy output of such disparate processes and objects as the sun, photosynthesis, fermentation, the metabolism of hummingbirds, power plants, cars, etc. etc.?

• Answer:

  This is a great question. At some point in college, it also dawned on me that the very concept of energy -- and especially its conservation -- is a bizarre one. That moving objects, warm surfaces, light, chemical reactions, sound, etc. might all be intrinsically and mathematically linked is almost uncanny. I don't think I would have noticed how they're all connected if it hadn't been taught to me. But it is precisely because of this property -- the conservation of energy -- that we can measure and compare energy in its different forms. The answer to your question is already contained within the Wikipedia article on the http://en.wikipedia.org/wiki/Conservation_of_energy, but I will try my hand at an explanation of my own. It all started with the discovery that mechanical energy is conserved. This took some time to realize, but it developed out of an understanding that momentum [math]mv[/math] was conserved, combined with Leibniz' insight that squaring the velocity to get [math]mv^2[/math] produced a quantity that was more descriptive of mechanical systems in general. Momentum was used to describe colliding objects, but this new quantity (kinetic energy) had broader application in other mechanical systems such as pulleys and levers. Once we realized kinetic energy in a system is conserved, we started to build connections to other forms of energy. Dropping objects from a height makes them go fast. Fast objects have greater kinetic energy. But where did that energy come from? It must be related to the height from which the object was dropped. And so developed an understanding that there is some energy associated with distance from the ground -- what we now call gravitational potential energy, given by the equation [math]mgh[/math]. At this point, we've already produced some very valuable equations, and so it is useful to create an arbitrary unit to describe this quantity. And so we create the Joule and we define it as the energy associated with a 1 kg object lifted 1 meter off the ground. A series of experiments then began to connect these mechanical forms of energy to other recognized phenomena such as heat. James Prescott Joule (after which the Joule is named) conducted an experiment where he would drop a heavy object and have it spin a paddle immersed in water. He noticed that the water temperature would increase in proportion with the gravitational potential energy stored by the object. Thus, we start to realize that heat is also a form of energy and that it, too, is conserved. A Joule is now connected with changes in temperature - a relation we know now expressed as the heat capacity formula: [math]Q = mc \Delta T[/math] Joule's apparatus. And so, through a series of subsequent experiments, we start to learn all sorts of ways to link natural processes to movement and heat -- mostly heat, actually. We observe that combustion yields predictable changes in temperature. We observe that light does the same. We start to tie this in with our other discoveries about stoichiometry and chemical structures and photons and light intensity. And we connect all of this back to the energy stored in a 1 kg object held 1 meter off the earth. The connections turn out to be so elegant and so robust that we don't need to continue re-doing the experiments. And that's how we know how many Joules something uses or requires.