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

Answer:

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:

$(\dfrac{T_2}{T_1})^r= (\dfrac{P_2}{P_1})^{r-1}$

where;

r = 7/5 = 1.4

$(\dfrac{T_2}{22.0^0})^{1.4}= (\dfrac{1.00}{0.705})^{1.4-1}$

$(\dfrac{T_2}{22.0^0})^{1.4}= (1.418)^{0.4}$

$T_2 = 22 \times 1.418 ^{^{\frac{0.4}{1.4}}$

$T_2 = 22 \times 1.418 ^{{0.286}$

$T_2 =24.31^0 \ C$