Question

Adiabatic wind. The normal airflow over the Rocky Mountains is west to east. The air loses much of its moisture content and is chilled as it climbs the western side of the mountains. When it descends on the eastern side, the increase in pressure toward lower altitudes causes the temperature to increase. The flow, then called a chinook wind, can rapidly raise the air temperature at the base of the mountains. Assume that the air pressure depends on altitude acording to p=p₀ exp(-ay) where p₀=1.00 atm and a=1.16×10⁻⁴m⁻¹. Also assume that the ratio of the molar specific heats is ⋎=4/3. A parcel of air with an initial temperature of -5.00⁰C descends adiabatically from y₁=4267m to y=1567m .What is its temperature at the end of the descent?

Answer 1

The temperature of the air at the end of the descent will be -25.94⁰C.

Step-by-step explanation:

The temperature of the descending air can be calculated using the adiabatic lapse rate.

The adiabatic lapse rate is defined as the rate at which the temperature of a parcel of air changes as it descends or ascends without exchanging heat with its surroundings.

The adiabatic lapse rate is given by the equation:

Γ = (g / Cp) * (1 - (R / Cp))

Where:

• Γ: Adiabatic lapse rate
• g: Acceleration due to gravity (9.8 m/s²)
• Cp: Specific heat capacity at constant pressure (1004 J/kg·K)
• R: Gas constant for air (287 J/kg·K)

Substituting the values into the equation, we get:

Γ = (9.8 / 1004) * (1 - (287 / 1004)) = -0.0098 K/m

Since the air is descending, the temperature will increase at a rate of 0.0098 K/m.

The change in temperature of the parcel of air can be calculated by multiplying the lapse rate by the change in altitude:

ΔT = Γ * Δy = -0.0098 * (4267 - 1567) = -20.94 K

Therefore, the temperature of the air at the end of the descent will be:

T = -5 - 20.94 = -25.94⁰C