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==[[First Law of Thermodynamics]]==

==[[First Law of Thermodynamics]]==

Joule continued in other experiments, noting the pressure changes caused by electrically-heated gasses, and achieved similar results.  This in turn led to a number of other scientists to research in this area, among them the German physicist Rudolf Clausius, who stated in 1850:

Joule, and others, continued in other experiments, noting the pressure changes caused by electrically-heated gases, and achieved similar results.  This in turn led to a number of other scientists to research in this area, among them the German physicists Rudolf Clausius and Hermann von Helmholtz in the 1840's.  This led to the general acceptance of [[Conservation of Energy]] as a clear and precise principle.  Clausius stated in 1850:

:''"In any process, energy can be changed from one form to another, but it is never created or destroyed."''

:''"In any process, energy can be changed from one form to another, but it is never created or destroyed."''

What Clausius discovered was the first law of thermodynamics, which states that energy is conserved, and heat and work are transfers of energy. The formula can be summed up as this:

This principle notably included heat as a form of energy, which was the first law of thermodynamics.  Hot objects contain potential energy in the form of their heat, and all the usual rules of transformation between potential and kinetic energy apply.  When an electric current is passed through a resistor, the electrical energy is converted to heat energy, and the resistor gets hotter.  Everything seemed to work out accurately.

Where the change (<math>\Delta</math>) in the system's internal energy (<math>E</math>), <math>q</math> is the heat added to the system, and <math>w</math> is the work done.  In thermodynamics a system is defined as having isolation from the remaining universe, and one with defined boundaries.  This would include a cup filled with hot tea, a human body, or an engine cylinder.  The internal energy of such a system - defined as <math>E</math> - is dependent on the state of the system itself, and not how that system state was achieved.

Of course, in all experiments that attempt to tally energy (or other properties) accurately, one must be careful to avoid outside interference.  Newton's formula <math>F = ma\,</math> requires that no unaccounted-for forces are acting on the object.  Similarly, in thermodynamics, one must take into account any possible sources of heat into or out of the entity under test.  This is often described by saying that the law of thermodynamics apply only to "isolated", or "closed", systems.  If a system can interact with some external entity, that entity's properties must be taken into account.

==[[Second Law of Thermodynamics]]==

==[[Second Law of Thermodynamics]]==