Gibbs equations

Cryogenics is the production of materials or parts at very low temperature. There is not a clear definition of it, but we can assume as distinguishing the gas liquefaction temperature of −150 °C (123 K; −238 °F).
In the Natural-gas processing for example, the raw gas, coming from under-ground, is processed in order to improve the quality (purification from sulfur gas, mercury, ecc…) and, at the end, it’s necessary to transform it in a liquified state for a convenient transportation (for example, the Prelude FLNG, a bluk carrier ship, would carry about 56.200m^3 of liquid methane at -162°, but only 37t of of the gaseous one at 25°: the density changes of about 650 times!).
Ed. about 1/260 times the daily production of oil barrel.

A common step in the process from gas wells to the car tank may need a sudden pressure lowering. Basically this can be done using a valve for pressure drop. The final result is good, but if we install a turbine, the result is better: we can recover energy.
Let’s see how to approach the final saving. A good approximation is to consider 0.075/kWh as electricity cost.

The first principle of the termodynamics says that \delta Q-\delta W=dU. Obviously positive heat is the one absorbed by the system, and work is produced by the system.

That equation becames Tds-Pd\nu=du if we referer to the unit mass/energy.
Remembering the entalpy definition h=u+pv and differentiating it, we obtain the Gibbs equations:

ds=\frac{du}{T}+\frac{Pd\nu}{T}
ds=\frac{dh}{T}-\frac{\nu dP}{T}

These are useful for finding the limit efficiency in a process: If the entropy change is 0, all the variation in internal energy is used for a volume variation (considering first equation). If it`s >0, /eta<

If you want to find that ship, it’s transforming