# Why does air get cooler in wind turbines?

And in general why it becomes cooler in example the steam that go past a turbine cannot be used indefinitely because first or later it start to condensate into water again.

The R.M.S velocity of the gas is given by,

$$v = \sqrt{\frac{3RT}{M}}$$

where R is the universal gas constant, $T$ is the temperature and $M$ is the average molecular mass of the gas.

As you can clearly see, the higher the temperature, the more shall be the velocity of the gas.

When these gas molecules hit the wind turbine, they transfer part of their energy (or momentum) to the turbine which causes the turbine to rotate (the blades of the turbine are bent so that the energy taken from the gas molecules can be maximised). The remaining energy is retained by the gas molecule and obviously lesser kinetic energy implies that its velocity is slower.

Go back to the equation stated earlier, with $R$ and $M$ remaining unchanged, a decrease in the velocity would mean a decrease in temperature.

Hence the air leaving a turbine appears to be cooler than it initially was.

The same steam cannot be reused again because the used steam has already given away most of the energy it could give. If reused, the steam would still transfer some energy but it would eventually settle down at the room temperature and stop supply energy to the turbine. The purpose of using steam is basically lost if it cannot rotate the turbine.

The open system (control volume) version of the first law of thermodynamics tells us that, for an insulated turbine operating at steady state, $$\dot{W}_s=-\dot{m}\Delta h$$ where $\dot{m}$ is the mass flow rate through the turbine, $\dot{W}_s$ is the rate at which shaft work is being done by the turbine, and $\Delta h$ is the change in specific enthalpy of the fluid passing through the turbine. Since the turbine is doing positive work, the change in specific enthalpy is negative.

• For readers, enthalpy goes down because air actually lose energy (see other answer) – GameDeveloper Aug 12 '16 at 14:00