# Summary

When examining thermodynamic processes some simplifying assumptions may be applied to help describe and analyse a given system. These simplifications can be viewed as 'ideal' thermodynamic processes and include adiabatic, isenthalpic, isentropic, isobaric, isochoric, isothermal, isentropic, polytropic and reversible processes. This article provides a brief overview of each process type and suitability to a given thermodynamic system.

# Definitions

 $$C$$ : Constant $$n$$ : Polytropic index $$h$$ : Enthalpy $$k$$ : Ratio of specific heats (isentropic exponent) $$C_{p}/C_{v}$$ $$m$$ : Mass flow $$P$$ : Pressure $$Q$$ : Heat flow $$s$$ : Entropy $$T$$ : Temperature $$V$$ : Volume $$\eta$$ : Efficiency

Subscripts:

 $$a$$ : Actual or adiabatic process $$s$$ : Isentropic process $$1$$ : Initial state $$2$$ : Final state

# Summary of Process Types

Each type of thermodynamic process presented in this article has the simplifying characteristic that one or more property is held constant while the process takes place. The table below summarises the constant properties for each type of thermodynamic process.

ProcessProperties Held Constant
IsenthalpicEnthalpy
IsentropicEntropy, Equilibrium, Heat Energy
IsobaricPressure
IsochoricVolume
IsothermalTemperature
IsotropicDirection
Polytropic$$PV^{n}=C$$
ReversibleEntropy, Equilibrium

# Thermodynamic Process Descriptions

An adiabatic process is one in which no heat or mass is transferred between the system and its surroundings $$(\Delta m = 0 \text{, } \Delta Q = 0)$$. In practice this assumption is most often used for rapidly acting systems (i.e. the thermodynamic process occurs in a short period) or as a method for obtaining conservative results. For example:

• Analysing the stroke of a piston where heat transfer outside of the system can be minimal due to the short period of time analysed.
• Analysis of a combustion reaction using the adiabatic assumption to give an upper limit (conservative) estimate of the flame temperature (referred to as the adiabatic flame temperature).

## Isenthalpic

An isenthalpic process is one in which there is no transfer of heat energy to or from the surroundings as if the system were surrounded by a perfect insulator $$(\Delta h = 0 )$$. Essentially and isenthalpic system is an adiabatic system that is irreversible and extracts no work.

The isenthalpic assumption is typically applied to determine the maximum temperature change in a system with changes in pressure. For example:

• Calculating the temperature of a gas after it passed through a safety relief valve to ensure downstream components are suitably rated for the discharge temperature.

## Isentropic

An isentropic process is one in which entropy remains constant $$(\Delta s = 0)$$. Since no energy is dissipated as heat an isentropic process is both adiabatic and reversible.

Steady state fluid systems are often best represented as adiabatic, but to give an estimation of the efficiency of the process the isentropic performance of a system is often related to the adiabatic or actual performance. This is referred to as the adiabatic or isentropic efficiency:

For systems where pressure decreases, such as turbines and nozzles:

$\displaystyle \eta = \cfrac{h_{1} - h_{2a}}{h_{1}-h_{2s}}$

For systems where pressure increases, such as pumps and compressors:

$\displaystyle \eta = \cfrac{h_{2s} - h_{1}}{h_{2a}-h_{1}}$

## Isobaric

An isobaric process is one in which the pressure is held constant $$(\Delta P = 0)$$. Assuming that the quantity of gas in an isobaric process remains constant the work done by the system is directly promotional to the change in volume or temperature of the system.

The ratio of heat capacity of a gas in an isobaric system with the heat capacity of the gas in an isochoric system makes up the ratio of specific heats for gases $$k = C_{p}/C_{v}$$.

## Isochoric

An isochoric system is one in which volume is held constant $$(\Delta V = 0)$$. Isochoric processes can also be referred to as isometric or isovolumetric. For Example:

• In calorimetry the energy of a reaction may be measured in a "bomb calorimeter". This device does not change volume during the reaction so that the temperature change can be measured as a single variable, and used to calculate the energy released.

## Isothermal

An isothermal process is one in which there is no temperature change $$(\Delta T = 0)$$. There may be energy flow into and out of the system, however only the amount required to keep the temperature of the system constant. For Example:

• Phase changes - melting solids and boiling liquids of pure substances requires substantially energy transfer, but does not change temperature.

## Isotropic

An isotropic system is not strictly a thermodynamics system, however it may easily be confused for one from the name. Isotropic systems are uniform regardless of direction. For example:

• Radiation may be isotropic when the the observed intensity is the same in all directions from the source.
• A fluid may be called isotropic if the relationships between stress and rate of strain is the same in all directions.

## Polytropic

A polytropic fluid system follows the relationship:

$$PV^{n} = C$$

From this relationship we can arrive at relationships for several other types of thermodynamic process:

• When $$n = 0$$, the process is isobaric
• When $$n = 1$$, the process is isothermal
• When $$n = k$$, the process is isentropic
• When $$n = \infty$$, the process is isochoric

## Reversible

A reversible process is one which is performed as if it were always at equilibrium, and without the production on entropy. This system is purely hypothetical since entropy is increased by any process occurring in a finite time.

A reversible process is always at equilibrium as the process progresses and thus represents the maximum efficiency that is possible in the conversion between work and energy for the system.