A thermodynamic process may be defined as the energetic evolution of a thermodynamic system proceeding from an initial state to a final state. Paths through the space of thermodynamic variables are often specified by holding certain thermodynamic variables constant.
The pressure-volume conjugate pair is concerned with the transfer of mechanical or dynamic energy as the result of work.

* An isobaric process occurs at constant pressure (P=constant). An example would be to have a movable piston in a cylinder, so that the pressure inside the cylinder is always at atmospheric pressure, although it is isolated from the atmosphere. In other words, the system is dynamically connected, by a movable boundary, to a constant-pressure reservoir.
The work done by the isobaric process is $\Delta W=\int P dV=P\int dV=P(V_f-V_i)= P \Delta V$

* An isochoric process is one in which the volume is held constant (V=constant), meaning that the work done by the system will be zero. It follows that, for the simple system of two dimensions, any heat energy transferred to the system externally will be absorbed as internal energy. An isochoric process is also known as an isometric process or an isovolumetric process. An example would be to place a closed tin can containing only air into a fire. To a first approximation, the can will not expand, and the only change will be that the gas gains internal energy, as evidenced by its increase in temperature and pressure. Mathematically, ?Q = dU. We may say that the system is dynamically insulated, by a rigid boundary, from the environment.

The temperature-entropy conjugate pair is concerned with the transfer of thermal energy as the result of heating.

* An isothermal process occurs at a constant temperature (T=constant). An example would be to have a system immersed in a large constant-temperature bath. Any work energy performed by the system will be lost to the bath, but its temperature will remain constant. In other words, the system is thermally connected, by a thermally conductive boundary to a constant-temperature reservoir.
For ideal gas: $\Delta W=\int P dV=\int \frac{nRT}{V}dV=nRT \int \frac{dV}{V}=nRT ln \frac{V_f}{V_i}$
$\Delta U=\int n C_v dT=n C_v\Delta T$.
$\Delta Q=\Delta U-\Delta W=n C_v\Delta T- nRT ln \frac{V_f}{V_i}$

* An adiabatic process is a process in which there is no energy added or subtracted from the system by heating or cooling (?Q=0). For a reversible process, this is identical to an isentropic process. We may say that the system is thermally insulated from its environment and that its boundary is a thermal insulator. If a system has an entropy which has not yet reached its maximum equilibrium value, the entropy will increase even though the system is thermally insulated.
?Q=dU- ?W=0 so dU=?W.
 The first law of thermaldynamically state: [b]The internal energy[/b] change is equal to the [b]heat absorbed[/b] minus the [b] work done[/b].$\Delta U= \Delta Q -\Delta W$isothermal process: $\Delta U=0$, so $\Delta Q =\Delta W$ adiabatic process: $\Delta Q=0$, so $\Delta U =\Delta W$ isochoric process: $\Delta W=0$, so $\Delta U =\Delta Q$ net incoming change= how much you earn -  how much you spend  if net incoming change=0, how much you spend=how much you earnif how much you earn=0, net incoming change= how much you spend (-)if how much you spend=0, net incoming change= how much you earn (+)

The following let you play with different processes:
The work done, heat transfer, internal energy as well as entropy change will be shown when you change parameter with slider bar.

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Press the Alt key and the left mouse button to drag the applet off the browser and onto the desktop.

The following is a flash animation for a carnot cycle.
[flash=522,539]http://www.phy.ntnu.edu.tw/ntnujava/swf/thermal628carnot.swf[/flash]