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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.