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Lost Work

Watch the sign convention ! This equation applies to both turbines and compressors.

Where :

actual rate at which work is done by a real process operating between states 1 and 2.

rate at which work is done by a completely reversible process operating between the same initial and final states.

Such a process must be internally reversible and all heat exchange must be reversible as well.

Heat exchange only occurs with the surroundings, not a thermal reservoir.

Lesson 8D: page 2 of 15

A completely reversible process operating between initial and final states 1 and 2 would produce or consume Wdot,S,rev.
The sign convention applies. Wdot,S,rev > 0 when the system does work on the surroundings, as in a turbine.
A real process operating between the same initial and final states 1 and 2, produces less work (or consumes more if it is a pump or compressor). This amount of work is Wdot,S,actual.
The lost work is the work that we did not get out of the turbine because it is not reversible.
Alternatively, the lost work is the EXTRA work we had to put into the compressor because it was not reversible.
Either way, the lost work is equal to the reversible work minus the actual work.
The sign convention makes this equation work for both turbines and compressors.
Remember, lost work is always a positive number.
Now, let’s see if we can figure out how to calculate lost work.