The Carnot's cycle was
proposed by Sadi Carnot (1796-1832), who is considered to be the founder of
thermodynamics. The cycle describes a sequence of steps that can be performed
only in an ideal engine, which transforms heat into work. The Cycle was a
culmination of the research done by Carnot in thermodynamics. By the end of the
eighteenth century, many engineers were doing experiments on engines used to
perform especialized work, using heat as the source of energy. For example, many
engines were designed using as source or energy the heat produced by combustion
of coal or wood. A common goal of all those engineers were to create machines
that could be as effcient as possible in using the heat provided. Based on the
study of these machines, Carnot discovered the cycle as an ideal model, and
demonstrated that this could not be improved.
Phases of the Carnot's Cycle A diagram of the Carnot's Cycle
is shown in the figure down there. The sequence of steps in the
Carnot's cycle are the following: І Adiabatic compression from temperature
T1 to T2, where T2 < T1; І Isothermal expansion at the temperature T1 І
Adiabatic expansion to T2 І Isothermal compression We describe each of
these phases of the cycle next.
The first phase of Carnot's cycle consists of an adiabatic
compression of the material in the engine. An adiabatic transformation is one in
which no heat is gained or lost. In this kind of process, the energy is
conserved inside the boundaries of the system. This condition can be described
in mathematical therms as dQ = 0; where Q is the variable representing the
amount of heat in the system. However, according to the first law of
thermodynamics, dE = dQ-dW; i.e., the variation of internal energy is
equal to the variation of temperature minus the variation of work done by the
system. Therefore dE = -dW = -pdV; where V is the volume of the system.
Thus, to have an adiabatic process we must have change in volume of the
A diagram of
the Carnot's Cycle, with a measure of its eficiency.
first phase of the Carnot's Cycle is defined by a change in volume of the
system. This change is made in such a way that energy is transformed from heat
into movement, and that will result in the change of volume. The temperature in
the system, consequently, changes from T1 to T2. However, the process of
changing heat into work cannot be done indefinitely, due to restrictions from
the 2nd law of thermodynamics. This implies that the system will at some point
loose e±ciency, and heat energy cannot be further transformed into work.
These two phase are complementary to the phases described
above. An isothermal process is one in which the temperature remains constant.
To have expansion, or compression at isothermal conditions, some energy must
exchanged with other systems, and therefore work can be done. In the second
phase of the Carnot's cycle, the system will expand at a the same temperature.
This will promote the transformation of energy from heat to a mechanical form.
It is important to mention that this process is not reversible, and it is there
that the limitation is, acording to the 2nd law of thermodynamics. The last
phase of the Carnot's cycle is similar, but here a contraction is done, instead
of an expansion. This makes the system go back to the same state it was at the
beginning of the cycle, and a new cycle can start.
Importance of the Carnot's Cycle
The Carnot's cycle is important since it describes an
optimal system, where heat energy is used at its best. However, it has
consequences beyond the simple study of engines. It can be also used to describe
theoretical limits of the transformation of heat into physical work. In this
sense it is applicable not only to mechanical models, but also to other kinds of
energy. One of the consequences of the second law of thermodynamics is that
heat cannot be transformed completely in work. Heat is a type of energy that has
high entropy. Acording to the 2nd law of thermodynamics, entropy in a system can
only increase with time. Thus, this gives a limit on the amount of energy that
can be tranfered from heat to work. Carnot's cycle is a physical expression
of the consequence of the 2nd law of thermodynamics for engines and other
related physical systems. It quantiЇes the loss of energy that must occur
whenever we try to convert heat into other types of physical energy.