Question

The prevailing winds on the Hawaiian island of Kauai blow from the northeast. The winds cool as they go up the slope of Mt. Waialeale (elevation 1523 m), causing water vapor to condense and rain to fall. There is much more precipitation at the summit than at the base of the mountain. In fact, Mt. Waialeale is the rainiest spot on earth, averaging 11.7 m of rainfall a year. But what makes the winds cool?

Short answer

The work done by the winds system will decrease its internal energy and hence the temperature. The winds cool down to the point where water vapours condensates and leads to rain.

Step-by-step solution

Understanding the condensing phenomenon

It is the phenomenon in which the gas/ vapour is transformed/ changed into liquid. This process is known as condensation. It involves the moisture contents of vapour condenses to form the water droplets or fog.

Analysis of the reason behind the cooling of wind

The elevation of Mt. Waialeale is 1523 m. When winds blow, they must go to the mountain's top to pass through the slope. In this process, winds work a lot. But this process is fast and comes under an adiabatic process.

In an adiabatic process, there is no heat exchange, it can be given as:

$∆Q=0$

Here,$∆Q$is the change in the heat energy.

According to the first law of thermodynamics, we have:

$∆Q=∆U+W$

Here,$∆U$ is the internal energy change and W is the work done.

Substitute the values in the above equation.

$$\begin{gathered} 0=∆U+W \\ W=-∆U \end{gathered}$$

Here, the internal energy change is negative and the internal energy is related to temperature change.

Therefore, the work done by the winds system will decrease its internal energy and hence the temperature. The winds cool down to the point where water vapours condensates and leads to rain.