# Reversible and Irreversible Expansion and Compression Processes

Initializing live version

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

Use this Demonstration to identify isothermal, reversible-adiabatic and irreversible-adiabatic processes of an ideal gas in a step-by-step procedure. After starting and with "new problem" selected, the Demonstration shows either an expansion or a compression process, and either a pressure-temperature or pressure-volume diagram. Select your answer from the possible options (a, b, c, d, e) and then select "show solution" to see the correct answer. The "hint" button provides a hint for each step, and once "show solution" is selected, you cannot go back.

Contributed by: Neil C. Hendren (March 2011)
Additional contributions by: John L. Falconer and Rachael L. Baumann
(University of Colorado Boulder, Department of Chemical and Biological Engineering)
Open content licensed under CC BY-NC-SA

## Details

The first law of thermodynamics, representing the conservation of energy, is:

,

where is the change to internal energy of the system, is heat added to the system and is the work done by the system. In adiabatic processes, , while in isothermal processes with external pressure . Expansion-compression work for all four processes is calculated from:

,

where is the external pressure and is in units of kJ/mol. The external pressure and the gas pressure are equal for a reversible process, whereas for an irreversible process the external pressure is equal to the final pressure. Change in internal energy is calculated from:

.

Initial state:

,

where the subscript refers to the initial state, is the ideal gas constant (kJ/mol K), is volume (), is temperature (K) and is pressure (Pa).

For an isothermal process:

,

where the subscript refers to the final condition.

Reversible work:

.

Irreversible work:

.

For an adiabatic process on an ideal diatomic gas:

,

,

,

where , is the constant volume heat capacity and is the constant pressure heat capacity (kJ/(mol K)).

Reversible process:

,

.

Irreversible process:

,

.

Reference

[1] J. R. Elliott and C. T. Lira, Introductory Chemical Engineering Thermodynamics, 2nd ed., Upper Saddle River, NJ: Prentice Hall, 2012.

## Permanent Citation

Neil C. Hendren

 Feedback (field required) Email (field required) Name Occupation Organization Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback. Send