Types of thermodynamic processes

There are a number of different thermodynamic processes that can change the pressure and/or the volume and/or the temperature of a system. To simplify matters, consider what happens when something is kept constant. The different processes are then categorized as follows :

1.Isobaric - the pressure is kept constant. An example of an isobaric system is a gas, being slowly heated or cooled, confined by a piston in a cylinder. The work done by the system in an isobaric process is simply the pressure multiplied by the change in volume, and the P-V graph looks like:
 

2. Isochoric - the volume is kept constant. An example of this system is a gas in a box with fixed walls. The work done is zero in an isochoric process, and the P-V graph looks like:
 

3. Isothermal - the temperature is kept constant. A gas confined by a piston in a cylinder is again an example of this, only this time the gas is not heated or cooled, but the piston is slowly moved so that the gas expands or is compressed. The temperature is maintained at a constant value by putting the system in contact with a constant-temperature reservoir (the thermodynamic definition of a reservoir is something large enough that it can transfer heat into or out of a system without changing temperature).
If the volume increases while the temperature is constant, the pressure must decrease, and if the volume decreases the pressure must increase.

4. Adiabatic - in an adiabatic process, no heat is added or removed from the system.
The isothermal and adiabatic processes should be examined in a little more detail.

Isothermal processes

In an isothermal process, the temperature stays constant, so the pressure and volume are inversely proportional to one another. The P-V graph for an isothermal process looks like this:

 
The work done by the system is still the area under the P-V curve, but because this is not a straight line the calculation is a little tricky, and really can only properly be done using calculus.

For an ISothermal process, the work done by the system is : W = nRT in (Y_f / Y_i)

 
The internal energy of an ideal gas is proportional to the temperature, so if the temperature is kept fixed the internal energy does not change. The first law, which deals with changes in the internal energy, thus becomes 0 = Q - W, so Q = W. If the system does work, the energy comes from heat flowing into the system from the reservoir; if work is done on the system, heat flows out of the system to the reservoir.

Adiabatic processes

In an adiabatic process, no heat is added or removed from a system. The first law of thermodynamics is thus reduced to saying that the change in the internal energy of a system undergoing an adiabatic change is equal to -W. Since the internal energy is directly proportional to temperature, the work becomes:

 
An example of an adiabatic process is a gas expanding so quickly that no heat can be transferred. The expansion does work, and the temperature drops. This is exactly what happens with a carbon dioxide fire extinguisher, with the gas coming out at high pressure and cooling as it expands at atmospheric pressure.
 

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