Conservation of energy is the first law of thermodynamics, and one of several conservation laws.
It is stated as follows:
Meanwhile, in 1843 James Prescott Joule independently discovered the law by an experiment, now called the "Joule apparatus", in which a descending weight attached to a string caused a paddle immersed in water to rotate. He showed that the gravitational potential energy lost by the weight in descending was equal to the thermal energy (heat) gained by the water by friction with the paddle.
Unfortunately for Mayer, his work was overlooked in favour of Joule's, and Mayer attempted to commit suicide. Later, Mayer's reputation was restored by a sympathetic account in John Tyndall's Heat: A Mode of Motion (1863).
A similar law was written in the privately published Die Erhaltung der Kraft (1847) by Hermann von Helmholtz.
With the discovery of special relativity by Albert Einstein, conservation of energy was shown to be a special case of a more general rule. According to special relativity, mass and energy are interchangable with the famous equation E = mc2.
Conservation of energy can be shown through Noether's theorem to be the result of the time-invariance of the laws of physics.
If all the heat is used to do work ( and
) then the system
is undergoing an isothermal process, which means that its
temperature remains constant. This is because the system's internal
energy is proportional to its temperature.
If all the heat is used to increase internal energy,
( and )
then the system is undergoing an
isochoric process, also called isometric process. This is
a process in which the system's volume is constant:
It is also possible for the heat energy to be used up partially by
doing work and partially by increasing internal energy. Examples of
such processes are the isobaric process and the adiabatic process.
Equation (1) is the one preferred by engineers. Another convention preferred by chemists is
The law of conservation of energy excludes the possibility of perpetuum mobile of the first kind.
Formulae
One formulation for the first law of thermodynamics is
where Q is heat transferred into the system from the surroundings, W
is work done by the system, and E is the internal energy of the system.
This energy is mostly kinetic energy: the potential energy can be assumed to
be negligible. Pressure-volume work (e.g. done by a gas on a piston) is
defined to be
Equation (1) can be interpreted as follows: Q is heat energy being
input into the system. The system the can use this incoming energy
to do two things: (1) do work, or (2) increase its own internal energy.
Here is an analogy: Q is income, which can then be spent to buy
things (W), or it can be saved in a bank account ().so that, according to equation (2),
W = 0.
where W is work done on the system by the surroundings. In this
case pressure-volume work is defined to be
Equation (3) can be interpreted to mean thus: that heat Q and
work W are energies being transferred into or out of the system.
The system then responds by increasing or lowering its internal energy
accordingly. Equation (3) is more symmetric in the sense that
internal energy E is a state function (it is conservative; independent
of the chosen path (process) between initial and final thermal states) whereas
neither Q nor W are state functions: they do depend on which particular (thermodynamic) process is chosen to connect the initial and final thermostatic states.References