Reversible Processes Involving an Ideal Gas Part 2

Constant Volume (Isometric or isochoric) Process

Changes in internal energy and enthalpy are given by:

For a constant volume process, the work associated with the displacement of system boundaries is zero. Besides, if shaft work is zero or negligible, then W = 0. The amount of transferred heat can be found from the application of the first law of thermodynamics:

Constant Pressure (Isobaric) Process

The changes in internal energy and enthalpy are given by:

Furthermore, the heat transferred and work done can be found using the following:

Constant Temperature (Isothermal) Process

Since temperature remains constant, then:

The work done in a reversible process and heat transferred are found by the following relationships:

Adiabatic Process

An adiabatic process is one in which the amount of heat transferred between the system and its surroundings is zero, i.e., Q = 0

The changes in internal energy and enthalpy are given by:

The work done in a reversible process can be calculated from:

Since temperature changes in an adiabatic process, evaluation of this integral is only possible numerically. Thus, it is more convenient to calculate work by the application of the first law, i.e.,

In some problems, we may know the values of either pressure or volume at the final state. Thus, it is necessary to develop equations between T and P, T and V , and P and V.

We can substitute the ideal gas equation of state below into the above equation to eliminate volumes terms and get a relationship between P and T. The same can also be done to eliminate T and get an relationship between P and V.

Polytropic Process

The relationship between pressure and volume during compression and expansion of gases is sometimes expressed as:

where n is a constant for any given change. Such processes are called polytropic and the equations available for adiabatic processes can also be used for polytropic ones by replacing γ with n.