Each process is one of the following:
 isothermal
(at constant temperature, maintained with heat added or removed from a heat source or sink)
 isobaric (at constant pressure)
 isometric/isochoric (at constant volume)
 adiabatic (no heat is added or removed from the working fluid)
Some examples are as follows:
Ideal cycle
An ideal cycle is constructed out of:
 TOP and BOTTOM of the loop: a pair of parallel isobaric processes
 LEFT and RIGHT of the loop: a pair of parallel isochoric processes
An illustration of an ideal cycle is provided below.
Carnot cycle
A Carnot cycle is constructed out of:
 TOP and BOTTOM of the loop: a pair of quasiparallel isothermal processes
 LEFT and RIGHT of the loop: a pair of quasiparallel adiabatic processes
The adiabatic processes are described by Q=0
so they are impermeable to heat. Heat flows into the loop through the top isotherm and some
of that heat leaves the loop through the bottom isotherm. The heat which remains is equal to the
work done by the process, which equals the area enclosed by the loop.
Otto cycle
An Otto cycle is constructed out of:
 TOP and BOTTOM of the loop: a pair of quasiparallel adiabatic processes
 LEFT and RIGHT sides of the loop: a pair of parallel isochoric processes
The adiabatic processes are impermeable to heat: heat flows into the loop through the left pressurizing process and some of it flows back out through the right depressurizing process, and the heat which remains does the work.
Stirling cycle
A Stirling cycle is like an Otto cycle,
except that the adiabats are replaced by isotherms.
 TOP and BOTTOM of the loop: a pair of quasiparallel isothermal processes
 LEFT and RIGHT sides of the loop: a pair of parallel isochoric processes
Heat flows into the loop through the top isotherm and the left isochore, and some of this heat flows back out through the bottom isotherm and the right isochore, but most of the heat flow is through the pair of isotherms. This makes sense since all the work done by the cycle is done by the pair of isothermal processes, which are described by Q=W. This suggests that all the net heat comes in through the top isotherm. In fact, all of the heat which comes in through the left isochore comes out through the right isochore: since the top isotherm is all at the same warmer temperature T_{H} and the bottom isotherm is all at the same cooler temperature T_{C}, and since change in energy for an isochore is proportional to change in temperature, then all of the heat coming in through the left isochore is cancelled out exactly by the heat going out the right isochore.
State Functions and Entropy
If Z is a state function then the balance of Z remains unchanged during a cyclic process:
 .
If entropy is defined as
so that
 ,
then it can be proven that for any cyclic process,
Demonstration
Part 1
Draw a rectangle on a PV diagram, such that the top and bottom are horizontal isobaric processes and the left and right are vertical isochoric processes. Such a rectangle should be made really small, so that change in temperature can be averaged out, and so that the cycle will enclose an area Δarea.
Let the top left corner be labeled A, then label the rest of the corners clockwise starting from A as ABCD.
Assume that the system is a monatomic gas. Then
 W_{AB} = P_{
A}(V_{B} − V_{A})
Process BC:
 W_{BC} = 0

Process CD:
 W_{CD} = P_{C
}(V_{A} − V_{C})

Process DA:
 W_{DA} = 0
Process ABCDA (cyclic):
Part 2
Any loop can be broken up into a rectangular grid of differential areas.
The line integral of the entire loop is equal to the sum of the line integrals of each of the constituent differential areas.
Let all these integrals be done clockwise. Then any pair of adjacent differential areas will be sharing a
process as a common border, but one area will add that process in one direction while the adjacent area adds
that process in the reverse direction, so that process is cancelled out.
Therefore all processes internal to the loop cancel each other out
(see Green's theorem),
and the result of the summation is equal to the line integral of the contour of the loop: