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Energy - need a proper definition please

  1. Mar 7, 2014 #1
    Energy -- need a proper definition please

    Please could someone give me a proper definition of energy. My teacher said in class today that "there is no such thing as different types of energy". He said that although we learn this in introductory physics, a physicist would not agree there are different types and would define it in a much different way. He said something about it being "the ability to do something" which therefore means the notion of having different types of energy isn't quite right. Is he right? From researching the internet I can see that energy is very abstract but could someone give me a proper physics definition of what it is. I found a video clip from professor Brian Cox who says that he defines energy as:

    "the length of a space-time four vector in the time direction"

    What does that mean?

    Thanks for any help!
  2. jcsd
  3. Mar 7, 2014 #2


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    Energy is an abstraction of what we otherwise call "work". In physics we take work done = force x distance in the direction of the acting force. For mechanical systems this results in the Work-Energy theorem: Kinetic energy is equal to the work done.

    All other types of energy can be shown to be equivalent to mechanical energy by means of appropriate processes. For example, Joule showed that the energy used to stir a fluid ends up as heat - with a precise conversion factor. Thus we have heat energy.

    The kinetic theory of heat allows us to build up from the (hidden) kinetic energy (motion) of molecules/atoms to the measurable temperature of large bodies. The history of thermodynamics is bound up with these ideas.

    The First Law of Thermodynamics thus states that energy cannot be created or destroyed, but only changed in form. The forms are mechanical, thermal, chemical, nuclear, electromagnetic, etc.

    But physicists have also found that there is no such thing as "pure energy" - energy cannot be found independent of some other physical entity.

    And one cannot make use of energy except by taking into account "how it is physically present".
  4. Mar 7, 2014 #3
    Thanks for the answer. I get what you mean by its not a physical thing and therefore can't be isolated but can you still not talk about different types of energy? In class we were going through mechanical, thermal, nuclear as you said and he was saying that its not really true that there are different types of energy?
  5. Mar 7, 2014 #4


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    I should think that may be too advanced for your level. But you can believe what he says, which is that the full formula for the Energy associated with an object involves its Kinetic Energy and its Potential Energy and its Mass.
    Normally, we talk in terms of the KE formula, the PE formula or, getting cleverer, we say E=mc2. Often, one of the above counts more than the others.
    Look at this link ( let it wash all over you without worrying about the details). If you search for "energy" on the page, you will see some formulae that Cox refers to.
  6. Mar 7, 2014 #5
    I wouldn't say energy is not a physical thing. In Newtonian physics it appears to be just a bookkeeping device, but if we look at special or general relativity, energy is something with direct consequences.

    There isn't just one definition of energy. It appears in many different subfields of physics with different definitions, and only when we combine the fields, we find this quantity works out to be the same thing.

    Your typical object has two forms of energy: rest energy and kinetic energy. In special relativity, the total energy is given by
    ##E = \sqrt{m^2 c^4 + p^2 c^2}##
    This is approximately equal to
    ##E = m c^2 + \frac{1}{2} m v^2##
    The more commonly seen expression ##E = m c^2## is just the rest energy, which you get by setting the velocity ##v## to 0. The kinetic energy is (approximately) ##\frac{1}{2} m v^2##.
    The kinetic energy is the energy in the motion of objects. When multiple objects are interacting, you can convert between rest energy and kinetic energy. One crude way to look at energy is that it is a storage that can be converted into the motion of objects. It's a useful concept because the total energy in a closed system is conserved. So, if you know the energy, you can figure out how much motion is possible.
  7. Mar 7, 2014 #6
    For example, a battery contains a very specific amount of energy which is available to be harnessed. If you installed it into a car, the energy tells you how much motion (calculated as ##\frac{1}{2} mv^2##) you could put into the car by draining the battery, if the motors were 100% efficient (which they aren't).
  8. Mar 7, 2014 #7


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    I agree with everything you said - except for this first part.

    There is no "single thing" which represents energy - it is always associated with other physical entities: force fields have sources (charges), heat has something moving (particles), chemical energy is ultimately due to electromagnetic (and atomic/molecular arrangements), and the energy in E=mc^2 comes from the particles that make up the mass.

    Hence there is no energy independent of "the things"; nor can you isolate something called "energy". That is why I called it an abstraction - this is also how Richard Feynman introduces the topic in his "Lectures on Physics", volume I.
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