Exergy balance for a closed system can be developed by combining the energy and entropy balances for a closed system. When a closed system undergoes a process from state 1 to state 2, its energy and entropy balances are

Energy Balance:             
Entropy Balance:       

Multiplying the second equation by T₀ and subtracting it from the first one yields,

 (1)

A closed system contains internal, kinetic, and potential energies. At state 1 and state 2, the total energy in a closed system is,

The exergy of the mass in the closed system at state 1 and state 2 are:

Subtracting X₁ from X₂ gives,

Replacing (E₂ - E₁) in equation (1) with the above equation, and rearranging it gives,

     

The above expression is the exergy balance of a closed system undergoing a process from state 1 to state 2. The terms on the right hand are:

• The first term is the exergy transfer by heat.
• The second term is the exergy transfer by work.
• The third term is the exergy destruction.

There is a third term in the exergy balance because exergy can not be created, but only can be destroyed. Therefore, the exergy change of a system equals the difference between the net exergy transfer through the system boundary and the exergy destroyed in the system. For a closed system, exergy transfer through the system boundary is due to exergy transfers by heat and work.