# free adiabatic expansion

My question is mainly an engineering question. Assume I have a turbine in which I adiabatically expand compressed air. The air cools down and does work to its surroundings, which is captured by the blades of the turbine and then is transformed into rotational energy/electricity.

When instead I let the compressed air flow through a nozzle into open space (no vacuum) and it expands adiabatically, it also cools down. But where is the internal energy of the air going? It does work to its surroundings, but where does this work end up? Does the surrounding heat up? Does it produce wind, i.e. kinetic energy in the surrounding air?

Feel free to replace adiabatic with polytropic. Whenever the gas cools down, I ask: Where does the energy end up, when I do not capture it with a turbine?

## 1 Answer

Adiabatic expansion in a nozzle results in internal energy being converted into kinetic energy. A generic steady-state energy balance is:

\begin{align} \Delta (H + \frac{1}{2}{v^2} + zg) = Q + W \end{align}

• ok, thanks (by the way, when this was edited, the equation got wrong). – Till B May 9 '11 at 10:47
• You're right. I'm not sure how to edit Latex here, I'll look into it. – Whelp May 9 '11 at 12:48
• Then if the nozzle is fixed no work is done on it. Instead, the energy is dissipated in heating the surrounding fluid. Even if the nozzle is a rocket, some of the energy is dissipated in turbulence in the surroundings. – Ross Millikan Jan 28 '14 at 4:45