When strong winds rapidly carry air down from mountains to a lower elevation, th

Question

When strong winds rapidly carry air down from mountains to a lower elevation, the air has no time to exchange heat with its surroundings. The air is compressed as the pressure rises, and its temperature can increase dramatically. These warm winds are called Chinook winds in the Rocky Mountains and Santa Ana winds in California. Suppose the air temperature high in the mountains behind Los Angeles is 0 degrees Celsius at and elevation where the aire pressure is 60 kPa. What will the aire temperature be, in degrees Celsius and degrees F, when the Santa Ana winds have carried this air down to an elevation near sea level where the air pressure is 100kPa?

Explanation / Answer

Adiabatic compression of the gas leads to increase in temperature. so the adiabatic equation for change in temperature and pressure is

P1(1-) T1 =P2(1-) T2

Given that for air = 1.41, P1 = 60kPa, P2 = 100kPa , T1 = 0+273

on substitution for the temperature

   T2 = (273)(1.67)(0.286)

= 316K

Change in centrigrade is

   t = 316- 273 = 43 oC

In fahrenheit scale

43/100 = (Ft - 32 ) / 180

   Ft = 109.4 oF

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