ATOC 4720: class 12 1. Enthalpy 1. Enthalpy 2. Latent heat 2. Latent heat 3.Adiabatic processes 3.Adiabatic processes.

ATOC 4720: class 12ATOC 4720: class 12

1. Enthalpy1. Enthalpy 2. Latent heat 2. Latent heat 3.Adiabatic processes3.Adiabatic processes

The first law of thermodynamics:

4. Enthalpy4. Enthalpy

If heat is added to a material at constant pressure, so that the specific volume of the material increases from a1 to a2, the work done by a unit mass of the material is p(a2-a1). Therefore, the heat dq added to a unit mass of the material at constant pressure is given by

At constant P,

Where

Enthalpy for a unit mass

Constant P,

Another form of first law of thermodynanicsBecause

In the Geopotential section,

So,

2. Latent heats2. Latent heats

Under certain conditions, heat may be supplied to a substance without changing its temperature.

Ice -- water -- vapor;

The latent heat of melting is the heat required to convert a unit mass of a material from the solid to liquid phase without a change in temperatuer.

The temperature at which this phase change occurs is called the melting point.

At normal atmospheric pressure and T, the latent heat of melting of water substance is

Latent heat of vaporization is the heat required To convert a unit mass of material liquid--vapor phase without change of T.

Normal P and 0C,

(fusion)

(condensation)

Melting & boiling points--P;Latent heat of fusion and vaporization-T;

3. Adiabatic processes3. Adiabatic processes

Concept: If a material changes its physical state (P, T, V) without gaining or losing heat--adiabatic.

A good tool to represent the process: p-V diagram.

P-V diagramP-V diagram

An air parcelAn air parcel

Mixing in the atm can be accomplished by two processes:

Below 100km; Well-defined air parcelsabove 100km.

An air parcel: An air parcel:

Thermally insulated: adiabatic (rises or Thermally insulated: adiabatic (rises or sink);sink);

Always at the environmental P; (env. Air Always at the environmental P; (env. Air assumed to be in hydrostatic equilibrium;assumed to be in hydrostatic equilibrium;

Moving slowly enough that its kinetic Moving slowly enough that its kinetic energy is a negligible fraction of its total energy is a negligible fraction of its total energy;energy;

[Real air do not satisfy all; but important to understand physical processes: z mix. & motion]

The adiabatic lapse rateThe adiabatic lapse rate

Air parcel: Adiabatic: dq=0; Hydrostatic:

=gdz

This is the adiabatic lapse rate.

Actual for moist air by radiosonde: 6-7deg/km.

Potential temperaturePotential temperatureThe potential temperature of an air parcelIs defined as the temperature which the parcel of Air would have if it were expanded or compressed adiabatically from its existing pressure and temperature to a standard pressure p0 (1000mb).

Poisson’s equation. For dry air:

In an air parcel is subjected to only adiabatic transformations as it moves through the atmosphere, its potential temperature remains constant. Or we say, conserved.

Potential temperature is a conservative Conservative quantity for adiabatic transformations.

Pseudoadiabatic chartPseudoadiabatic chart