# Reversible and Irreversible Expansion and Compression Processes

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.

### 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.

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