## A discussion problem of thermodynamics from University Physi

Himanshu_Shukla
Posts: 5
Joined: Sat Jul 19, 2014 10:42 am

### A discussion problem of thermodynamics from University Physi

QI9.17. 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 con-
dense and rain to fall. There is much more precipitation at the sum-
mit 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?

QI9.18. Applying the same considerations as in Question 19.17,
explain why the island of Niihau, a few kilometers to the south-
west of Kauai, is almost a desert and farms there need to be
irrigated.

blighter
Posts: 256
Joined: Thu Jan 26, 2012 6:30 pm

### Re: A discussion problem of thermodynamics from University Physi

Himanshu_Shukla wrote:QI9.17. 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 con-
dense and rain to fall. There is much more precipitation at the sum-
mit 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?

QI9.18. Applying the same considerations as in Question 19.17,
explain why the island of Niihau, a few kilometers to the south-
west of Kauai, is almost a desert and farms there need to be
irrigated.

Chiron
Posts: 9
Joined: Tue Sep 01, 2015 10:37 am

### Re: A discussion problem of thermodynamics from University Physi

I know that this is an older post, but in the hopes that others may also read this I'm posting my take on these questions.

I believe that for the first question one way to look at this is that the hot air will rise. However, as it rises the pressure decreases. Thus, assuming the gas to be ideal, using the equation $PV = N k_B T$, we see that assuming the volume of the air to be relatively constant, if the pressure decreases then the temperature must decrease as well.

For the second problem at least one way to look at it is that much of the moisture has already been expelled. However, using the same principle as before, as it goes down in elevation we see that the pressure increases, thus causing the temperature to increase. Therefore, the water vapor will not condense, and you will find a lack of rain.