The air parcel expands as it rises, inside the pipe

[aleksey]

The air parcel expands as it rises and this expansion, or work, causes the temperature of the air parcel to decrease.

Imagine that parcels of dry air go up inside the pipe that goes vertically from 0 to 5000 meters. Suppose that they go up because they are slightly warmer that the air outside.

Situation 1

The pipe internal diameter grows from bottom to the top so the area of cross-section grows proportionally to the decline of pressure outside. In this case the speed of parcels is constant along the pipe. The parcels expand sideways.

Which mechanical work will they do and will their temperature decrease ?

Situation 2

The pipe internal diameter is constant. In this case the speed of parcels grows along the pipe.

The parcels expand up (and down ?).

Does this mean that the parcels do mechanical work of pushing upper parcels up?

Does this mean that mechanical energy of parcels grows at the expense of their internal energy ?

Will the parcels be colder then in Situation 1 ?

[Country Boy]

2 hours ago, aleksey said:

The air parcel expands as it rises and this expansion, or work, causes the temperature of the air parcel to decrease.

Expansion is NOT work!  It might do work if the expansion is against some force. Further, the expansion as it rises is not automatic.  You apparently are assuming less air pressure at higher altitudes- so there is no force and no work done.

Quote

Imagine that parcels of dry air go up inside the pipe that goes vertically from 0 to 5000 meters. Suppose that they go up because they are slightly warmer that the air outside.

Situation 1

The pipe internal diameter grows from bottom to the top so the area of cross-section grows proportionally to the decline of pressure outside. In this case the speed of parcels is constant along the pipe. The parcels expand sideways.

Which mechanical work will they do and will their temperature decrease ?

Situation 2

The pipe internal diameter is constant. In this case the speed of parcels grows along the pipe.

The parcels expand up (and down ?).

Does this mean that the parcels do mechanical work of pushing upper parcels up?

Does this mean that mechanical energy of parcels grows at the expense of their internal energy ?

Will the parcels be colder then in Situation 1 ?

 

Edited August 31, 2018 by Country Boy

[aleksey]

15 minutes ago, Country Boy said:

Expansion is NOT work!  It might do work if the expansion is against some force. Further, the expansion as it rises is not automatic.  You apparently are assuming less air pressure at higher altitudes- so there is no force and no work done.

Then in your opinion - what will happen with temperature ?

[Country Boy]

If an air parcel rises through a pipe, NOTHING happens to the temperature.  Unless there is some other external effect that you haven't mentioned, the temperature stays the same.  

[Enthalpy]

Hi Aleksey, you're right almost everywhere.

The rising air parcel works against its neighbours. It loses internal energy, that's why its temperature drops.

Note that without any losses, energy would have to go somewhere, and the parcel isn't different from its neighbours... (Probably your next question!) The energy difference goes into kinetic energy. If the parcel was warmer than its surrounding, it becomes faster as it rises. The acceleration can happen at the bottom, the top or all along the way, depending on the profile section of the tube.

In such a case, where air packets exchange no heat with anything else, the work they provide (or receive) is the variation of their enthalpy. For air, which is almost an ideal gas under usual conditions, the enthalpy is fully determined by the temperature, or by the initial temperature and the initial and current pressure. The profile section will act on the pressure indirectly by imposing a kinetic energy and so on. It's impossible to solve locally, you must consider an distribution over the full height.

One funny thing: enthalpy is not fully contained in the considered air parcel. The internal energy is, but the additional P*V is stored in the surrounding. Despite this, (T, P, V) or the air parcel itself suffice to define its enthalpy. An extreme case is a liquid, say in a hydroelectric dam: as a water parcel goes down to the turbine, its temperature and internal energy keep constant, but it receives V*(P₂-P₁) from the neighbour water parcels, and this energy converts to speed in the injector and to work in the turbine that slows the water.