The Class 5AT Advanced Technology Steam Locomotive Project

## Thermodynamic Definitions

### Page Under Development

An adiabatic process is one in which there is no transfer of heat between the system and its surroundings.  Thus in thermodynamic nomenclature, Q (heat transfer to or from a system) = 0

Adiabatic expansion can occur in a well-insulated system. Neglecting kinetic energy, electrical energy, etc, the drop in enthalpy of the system is effectively converted to work (dH = Q + W, where Q = 0). An adiabatic expanion is thus considered to be most expanion that can occur.

Adiabatic Efficiency is the ratio of the actual work output of the engine to the work output that would be achieved if the process between the inlet state and the exit state was isentropic (see below).

### Isentropic (or Isoentropic) Process

An isentropic process is one in which entropy remains constant.

For a reversible isentropic process, there is no transfer of heat energy and therefore the process is also adiabatic.

For an irreversible isentropic process, entropy will increase. Hence removal of heat from the system (cooling) is necessary to maintain a constant internal entropy for an irreversible process in order to make it isentropic. Thus an irreversible isentropic process is not adiabatic.

If a process is both adiabatic and reversible, then it is considered to be isoentropic.

### Isenthalpic (or Isoenthalpic) Process

An isenthalpic process is one that proceeds without any change in enthalpy (H) or specific enthalpy (h).  There will usually be significant changes in pressure and temperature during the process.

In a steady-state, steady-flow process, significant changes in pressure and temperature can occur to a fluid.  However the process will be isenthalpic if

1. there is no transfer of heat to or from the surroundings (i.e. it is adiabatic),
2. there is no work done on or by the surroundings, and
3. there is no change in the kinetic energy of the fluid.

The throttling process is an example of an isenthalpic process - for instance the lifting of a safety valve on a steam boiler. The specific enthalpy of the steam inside the boiler is the same as the specific enthalpy of the steam as it escapes from the valve.  Thus with a knowledge of the specific enthalpy of the steam and the pressure outside the pressure vessel, it is possible to determine the temperature and speed of the escaping fluid.

In an isenthalpic process: h1 = h2 and therefore  dh = 0.

The above definition comes from Wikipedia and also World Lingo which offers an almost identical definition.  However neither is entirely satisfactory since steam escaping through a safety valve will experience rapid cooling in its surroundings.  The diagram below (from Chemical and Process Technology) gives a clearer picture even if the accompanying explanation is less so.

An interpretation of the accompanying explanation is offered as follows:

The flow through a pressure relief valve is extremely fast.   Choked flow can occurs as far as position A inside the nozzle. The flow from the inlet to "A" will be a REVERSIBLE process and thus an ISENTROPIC process.  Beyond "A" to the outlet of the valve, the steam expands (it may even undergo a change in state if it is liquid prior to "A" resulting in a transformation energy loss) followed by a rapid loss of speed and conversion of kinetic energy to mechanical energy in the form of noise.  However the enthalpy remains constant (ISENTHALPIC).  This process is IRREVERSIBLE (i.e. entropy increases).

### Heat Capacity Ratio, Isentropic Expansion Factor, or Expansion Coefficient

[Ref Wikipedia] The Heat Capacity Ratio is sometimes also known as the "'isentropic' expansion factor".  In the 5AT FDCs, the expansion factor is termed the "expansion coefficient" and denominated by the letter 'n'.  In other texts it may be denoted by γ, κ or the letter k.

The value of n is derived from the equation:  n = Cp / Cv where, C is the heat capacity of a gas, suffix P and V refer to constant pressure and constant volume conditions respectively.

The heat capacity ratio (expansion coefficient) 'n' can be visualized from the following experiment:

A closed cylinder with a locked piston contains air. The pressure inside is equal to the outside air pressure. This cylinder is heated to a certain target temperature. Since the piston cannot move, the volume is constant, while temperature and pressure rise. When the target temperature is reached, the heating is stopped. The piston is now freed and moves outwards, expanding without exchange of heat (adiabatic expansion). Doing this work cools the air inside the cylinder to below the target temperature. To return to the target temperature (still with a free piston), the air must be heated. This extra heat amounts to about 40% more than the previous amount added.

In this example, the amount of heat added with a locked piston is proportional to CV, whereas the total amount of heat added is proportional to CP. Therefore, the heat capacity ratio in this example is 1.4.

From Steam Tables the following outputs can be found (based on a pressure of 20 bar)

 Pressure = 20 bar 200oC 300oC 400oC 450oC Cv kJ/(kg.oC) 2.06657 1.696 1.66439 1.67895 Cp kJ/(kg.oC) 2.98955 2.32035 2.2013 2.19664 n - 1.35 1.37 1.32 1.31

The coefficient is usually given the value 1.3 in SGS locomotive performance calculations.