First Law of Thermodynamics
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[edit] Definition
The First Law of Thermodynamics is often stated as
- The heat added to a system minus the work done by the system is equal to the increase in the internal energy of the system.
In mathematical terms:
- δQ - δW = dE
This law is essentially the law of conservation of energy as it applies to thermodynamic devices. The reader should note that we speak of heat as being input, work as being output and the internal energy increasing as a matter of convention. The equation still holds perfectly well if heat is taken out of the system, work is put in, or the internal energy decreases, in which case δQ, δW or dE respectively would have negative sign.
The First Law is adopted as an axiom in classical thermodynamics, and cannot be mathematically proven in that framework. However, experimental evidence overwhelmingly supports the First Law.
[edit] Some consequences of the First Law
Taking the law δQ - δW = dE and integrating this over the course of a thermodynamic process, we get Q - W = ΔE. That is, over the course of the process, the net heat input minus the net work output is equal to the net increase in internal energy.
An important example of a device which runs on a cycle is a heat engine. One is presented schematically in the diagram on the right. A heat engine operates in a cycle drawing a quantity of heat QH from a body at high temperature and discharging a smaller quantity of waste heat QC into a body at a lower temperature. Along the way, some of the heat is turned into work. The First Law tells us that over the course of a cycle, the net work done by the heat engine is equal to the net heat input; that is, W = QH - QC.
Another example of a machine running in a cycle is a refrigerator. A fridge is, in the abstract, a heat engine running backwards (see the diagram to the left). Work is input to the machine, heat in the quantity of QC is drawn out of the body to be cooled and a larger amount of heat QH is pumped into a hotter body (in a domestic refrigerator, it comes out at the back). The first law tells us that over a cycle, the required work input Win must be equal to QH - QC.
Again, something slightly odd may strike you about the design of a fridge. It would appear that what happens to all the work we input is that it gets turned into waste heat in the output. Yet when we operate a fridge, we have no interest at all in heating the environment into which we dump heat: we're only interested in pumping heat out of the low-temperature body. So why not have a fridge with no work input at all, which transfers no more heat into the high temperature body as it draws from the low temperature body? Again, this is a question relating to the Second Law of Thermodynamics; the First Law tells us only that the energy equation must balance.
[edit] Discussion
The law of conservation of energy is expressed more generally and is perhaps better known than the First Law. It is often stated as
- Energy can neither be created nor destroyed, only changed from one form to another.
The conservation of energy is overwhelmingly supported by evidence. Many times in science, a reaction was observed that appeared to violate the conservation of energy, but the energy has always been found. Emmy Noether demonstrated mathematically that the conservation of energy is also equivalent to time symmetry, the property of the universe such that an experiment done later in time, if nothing else changes, will produce exactly the same results as one done earlier in time.
Although energy is conserved, it is not invariant. Different observers will measure different energies based on relative motion. Furthermore, at the quantum level, fluctuations can cause extremely brief defecits and excesses of energy.
An interesting consequence of Special Relativity is that anything that is conserved is conserved locally. This means, essentially, that energy cannot move from one place to another without passing through places in-between.
[edit] Misconceptions
Because energy can never be created or destroyed, this has been used to support the idea of an immortal soul in some New Age beliefs. This, like many misuses of science, is a fallacy of equivocation and consists of taking a concept that is well established using well defined terms and assuming that it necessarily applies when the term is used in an entirely different way. "Energy" has a specific meaning in physics, and statements about energy cease to apply when the word is used in a different way, as in the mystical concept of "life energy."
