The overall shaft work or exergy required by any process consists of the minimum reversible work — plus the work to offset irreversible losses. The latter is exergy which is completely destroyed in achieving the objectives of the process or piece of equipment — within the constraints of real equipment of finite size.

Certain processes or process steps arise very frequently:

• Separation of a feed into two or more products of given purities.
  
  
• Liquefaction of a normally gaseous substance.
  
  
• Compression of a gas stream.
  
  
• Carrying out a reaction.

A. Reversible work of separation

A mixture of different chemical species has a greater degree of randomness or disorder — a higher entropy — than the pure components of which it is comprised under the same temperature and pressure. “Un-mixing” this stream into its pure components results in a reduction in entropy. The 2^nd Law tells us this cannot occur spontaneously but requires a minimum input of work: