Question

5. The Santa Ana winds, also known as "devil winds", are strong and dry high-pressure masses of air that begin in the Great Basin mountains and then affect coastal areas in Southern California. Assume that these winds consists of a mixture of nitrogen and oxygen gases that behave ideally and that they begin at a pressure and temperature of 0.705 atm of 22.0 0C, respectively, and that this mass of air is then adiabatically and reversibly compressed to a pressure of 1.00 atm when it descends to the coastal regions. Calculate the final temperature.

Answer 1

Step-by-step explanation:

Given that;

The initial pressure = 0.705 atm

The initial temperature = 22.0° C

The final pressure = 1.00 atm

The objective is to calculate the final temperature,

Since the change occurs adiabatically and reversibly, the final temperature can be calculated by using the thermodynamics equation:

`((T_2)/(T_1))^r= ((P_2)/(P_1))^(r-1)`

where;

r = 7/5 = 1.4

`((T_2)/(22.0^0))^(1.4)= ((1.00)/(0.705))^(1.4-1)`

`((T_2)/(22.0^0))^(1.4)= (1.418)^(0.4)`

`T_2 = 22 * 1.418 ^{^{(0.4)/(1.4)}`

`T_2 = 22 * 1.418 ^{{0.286}`

`T_2 =24.31^0 \ C`