Warm winds called Chinooks sweep across the plains just east...

Warm winds called Chinooks sweep across the plains just east of the Rocky Mountains. They carry air from high in the mountains down to the plains so fast that the air has no time to exchange significant heat with its surroundings (Figure GP1 4.93). On the day of a Chinook, pressure and temperature high in the Alberta Rockies are $62.0 \mathrm{kPa}$ and $-11.0^{\circ} \mathrm{C},$ respectively. (a) What will the air temperature be once it's reached the city of Calgary, where the pressure is $86.5 \mathrm{kPa}$ ? (b) How much work is done on what was initially a cubic meter of air as it descends to the plain?

Warm winds called Chinooks sweep across the plains just east of the Rocky Mountains. They carry air from high in the mountains down to the plains so fast that the air has no time to exchange significant heat with its surroundings (Figure GP1 4.93). On the day of a Chinook, pressure and temperature high in the Alberta Rockies are $62.0 \mathrm{kPa}$ and $-11.0^{\circ} \mathrm{C},$ respectively.
(a) What will the air temperature be once it's reached the city of Calgary, where the pressure is $86.5 \mathrm{kPa}$ ? (b) How much work is done on what was initially a cubic meter of air as it descends to the plain?

Key Concepts

Adiabatic Process

An adiabatic process is one in which no heat is exchanged with the surroundings. In thermodynamics, if a gas undergoes a rapid change such that there is little time for heat transfer, its internal energy change is solely due to work done on or by the gas. This concept is central to understanding temperature changes in quickly moving air masses, such as those influenced by Chinook winds.

Isentropic Process (Poisson’s Relation)

When an adiabatic process is also reversible, it is termed an isentropic process, meaning entropy remains constant. For an ideal gas undergoing an isentropic process, Poisson’s relations connect the pressure and temperature by the formula T?/T? = (P?/P?)^((?-1)/?), which is key to determining new temperatures after pressure changes.

Ideal Gas Law

The ideal gas law, expressed as PV = nRT, links pressure, volume, temperature, and the amount of gas. This law provides the foundational relationship needed to analyze changes in state for gases undergoing processes such as adiabatic compression and is essential when applying Poisson’s relations.

Work Done in Adiabatic Compression

In an adiabatic process, the work done on or by the system results in a change in internal energy since no heat is exchanged. The work can be computed by considering the specific heat capacities of the gas and the temperature change, reflecting how compression elevates the energy state of the gas. This concept is crucial when calculating the amount of work performed as air moves from a high altitude to a lower one under changing pressures.

Transcript

Please give Ace some feedback