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THERMODYNAMICS BASICS

INTRODUCTION
The atmosphere is a compressible fluid
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Some of the ingredients change phase (primarily
water) and there is an accompanying exchange of energy with the environment
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Electromagnetic radiation enters and leaves
the atmosphere and in so doing it warms and cools layers of air, interacting selectively with
different constituents in different wavelength bands
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) and in predicting the evolution of
these primary variables over time intervals of a few days
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Both the present state of the bulk atmosphere and
its evolution are determined by Newton’s laws of mechanics as they apply to such a
compressible fluid
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But before one can undertake the study of atmospheric
dynamics, one must be able to describe the atmosphere in terms of its primary variables
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Such parcels contract and expand, their temperatures rise and fall; water changes
phase, back and forth from vapor to liquid to ice; chemical constituents react etc
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BASIC DEFINITIONS
Thermodynamics
Thermodynamics is briefly defined as study of energy and its transformations
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We need to understand
thermodynamics to study the atmosphere for the following reasons
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Because of the Earth's
spherical shape and axial tilt, the tropics receive more energy than the poles
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Differential heating spanning a wide range of spatial scales creates
thermodynamic imbalances, which in turn create winds and ocean currents as the
atmosphere/ocean system attempts to return to thermodynamic equilibrium
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Associated with the formation of clouds and precipitation are the release of latent
heat and modifications to atmospheric radiative transfer
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c)
Accounting for heat exchanges in the atmosphere and ocean is essential in any predictive
model of the ocean and/or atmosphere, for any space or time scale that is considered
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For example, increasing the concentration of carbon dioxide in the atmosphere
tends to heat the planet
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Thermodynamic system
In thermodynamics, we regard a thermodynamic system
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Examples of systems are:
•
•
•
•
•
•

A parcel of air
A glass of water
An ice cube
The entire atmosphere
The entire Earth and atmosphere
The Universe

A thermodynamic system is a definite quantity of matter which can exchange energy with its
surroundings by performing mechanical work or by transferring heat across the boundary
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It lies
outside the system and is also called the environment of the system
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Anything that separates the system from the surroundings is known as a boundary
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The system interacts with its surroundings across the boundary
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Electrically conducting or

A given boundary can belong to various categories
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System interactions
The system exchanges matter and energy with the surroundings across the boundary
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•

•

•

An open system – the system is said to be open when it has a permeable boundary
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An open
system exchanges matter (mass, m) and energy((U)) with its surrounding
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Examples include:
o A glass of water with no lid, allowing evaporation into the air above it
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A closed system - a system is said to be closed when it has an impermeable and
diathermic boundary
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A closed system exchanges energy, but not
mass with the environment
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Examples include:
o A glass of water with a lid
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o The inside of a
ThermosTM bottle with the top screwed on
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An isolated system- a system is said to be isolated when it has an adiabatic
boundary
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An isolated system exchanges no material (matter) or
energy with its environment
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Examples include:
o The inside of a ThermosTM bottle with the top screwed on (assuming it was
perfectly insulated)
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Any matter or energy that is not part of the system is considered to be part of the
surroundings or environment
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1
...
1
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The relationship between open, closed, and isolated systems can be illustrated using a Venn
diagram
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Every system is either open or it is closed but not both
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In plain language, we can infer the following:
•
•

Any isolated system is also a closed system, but a closed system is not necessarily an
isolated system
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State of the System, fundamental equation, equation of state

The state of a system is defined by the position and momentum of every piece of matter in
the system
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56x1025 molecules in the volume
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Therefore, we
content ourselves with knowing something about the “average” or macroscopic properties
of the system as a whole
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The thermodynamic state of a simple system in thermodynamic equilibrium is completely
characterized by specifying the internal energy (U), volume (V), and the number of moles,
ni, of each of its components
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Knowledge of the fundamental equation implies complete knowledge about the
thermodynamic state of the system
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If the system is not in
thermodynamic equilibrium then additional variables are needed to describe the
thermodynamic state of the system
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The fundamental equation, (1), can also be written as

2

where the only difference between Eqs
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U, V, and n are not the only possible state variables
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These variables are known as state variables because the state of the system
changes when one or more of these variables change
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Such equation or equations are called equations of state for the system
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In general:
For a one-component system in equilibrium we need 3 state variables
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For a three-component system in equilibrium we need 5 state variables
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Thermodynamic Process
It is any operation or process that brings about a change in the state of the system
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The
initial state of the system is defined by the pressure, temperature, volume, and amount of the
system before the change takes place
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A
process is said to have taken place whenever there is a change in any one or more of the state
variables
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If the change is infinitesimal (very small) it is represented by dY
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These categories are
as follows:
i
...
ii
...

iii
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iv
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v
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The series of changes taking place is known as a
cycle
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The path can
consist of a single or more steps
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Reversible process: A process is said to be reversible if the system undergoes a change in
the state through a specified sequence of intermediate states, each one of which is an
equilibrium state
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That is, a process is said to be reversible if it can
proceed in forward and backward directions by a small change in state variables
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That is, the process is said to be reversible only if the system can retrace its steps without any net
change in the system and the surroundings
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Each reversible process is slow (quasi-static) but each slow (quasistatic)
process may or may not be reversible
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At
null point the external potential applied is equal but in the opposite direction to the cell emf
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Irreversible process: A process is said to be irreversible if the change takes place without
the system being in equilibrium with its surroundings at any stage during the change
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Hence, the system can
attain its initial state by some change in the surroundings
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Equilibrium and Steady State
Equilibrium: A system exists in a state of equilibrium if its macroscopic properties such as
temperature, pressure, volume, and mass remain constant without the help of an external
source
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Mechanical equilibrium: The external forces on the system are equal to internal forces in the
system
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The pressure acting on the system

is equal to the pressure exerted by the system
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This also implies that there is no turbulence within the system
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This means that there is no
net transfer of matter from one phase or component of the system to another
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Even if one of the equilibrium is not achieved the system is not in
thermodynamic equilibrium
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For example, Ethanol kept in a
closed container having adiabatic walls
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After some time equilibrium is attained between the liquid and vapour
phases of ethanol
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Another example of steady state is the water taken in a tank that has an
inlet and an outlet of water
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As a result the level of water in the tank does not change with time
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A quasi-static process is almost always nearly in
equilibrium
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A
quasi-static process must proceed infinitesimally slow, so that the system is always nearly in
equilibrium
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However, if the curve is magnified, it would be apparent that it is not
continuous, but consists of a series of infinitesimally spaced dots
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For a reversible
process, at any point the transformation can be stopped and then made to proceed in the exact
opposite direction
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Note the following rules about quasi-static and reversibility of a process:

•
•
•

All reversible processes are also quasi-static processes
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An irreversible process may also be quasi-static
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We often assume, however,
that some real processes are quasi-static or reversible because it makes doing
thermodynamics so much easier, and the errors are often not significant
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They are
additive in nature
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Some
of the important extensive properties are: mass, volume, amount (number of moles), energy,
enthalpy, entropy, free energy, and heat capacity
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These
properties are not added up to get the total value of a given property of the system
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Some of the important intensive properties are:
pressure, temperature, density, concentration, mole fraction, refractive index, surface
tension, viscosity, and specific heat capacity
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These
are based on the facts that many of the physical properties are related to other physical
properties
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The sum of two extensive properties is an extensive property
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Dividing an
extensive property by another extensive property results in an intensive property
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In atmospheric science, two ways are used to convert an
extensive property into an intensive property:
a
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The result is a property that is normalized by the mass
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For example, the
specific internal energy u is defined as U/m
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Divide by the number of moles
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We add the term molar specific to indicate we’ve divided
by the number of moles
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iii
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In general, extensive properties are denoted using upper-case letters, while intensive properties
are denoted using lower-case letters
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State and Path Functions
A state function is a property whose value does not depend on the path taken to reach that
specific value
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Both path and state functions are often encountered in thermodynamics
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The
change in the state property does not depend upon how the process is carried out
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A function that depends only on the state variables is known as a state
function
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The changes in these properties depend
upon the initial and final states of the system
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Therefore, these thermodynamic properties are also state properties or state
functions
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Characteristics of state functions: Let z be a state function that depends upon two variables x and
y
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Using enthalpy as an example and assuming that the
parameter that changes is temperature, then this can be expressed through integrals, as

This is equivalent to

Such a relation cannot be written for path functions, especially since these cannot be defined for
the limiting states
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Two examples of
path functions are Work and heat
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Heat exists only as it crosses the boundary of a system and the
direction of heat transfer is from higher temperature to lower temperature
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Work is the energy transfer associated with a force acting through a distance
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Path functions are inexact differentials, that is,
they cannot be integrated
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w is the work done when the system goes from an initial state to
the final state
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dq and dw where ever they are mentioned do not mean change in heat or change in
work
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The correct symbol for small amount of heat exchanged is δq and for
small amount of work done is δw, where, δ represents an inexact differential
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Using similar reasoning the first law of thermodynamics
can be written as ΔU = Q + W or dU = δQ + δW
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This is referred to as a quasi-static processit is reversible
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1
The total work for a quasi-static process is readily calculated by integrating:

We can only integrate -PdV when the process is reversible
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1:

We can clearly see from the graphical representation that the work done along path 1 will be
significantly different from that along path 2: the total work is path dependent
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Most of the time the individual molecules are in
free flight out of the range of influence of their neighbors
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All collisions are elastic (between each other and the walls of the container)
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The molecules are in rapid random motion

The equation of state for ideal gasses is known as the ideal gas law
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The form of ideal gas law that we
are most familiar with is:

2
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3145 Jmol-1K-1, and n is the number of moles (not molecules)
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Real gasses in the atmosphere, such as O2 and N2, are diatomic, and some gasses such as CO2
and O3 are triatomic
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Even though the gasses that make up the atmosphere
aren’t monatomic, they still closely obey the ideal gas law at the pressures and temperatures
encountered in the atmosphere, so we can still use the ideal gas law
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We will, therefore, start by first stating
these two laws
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2)
Where P0α 0 denotes the product of the initial state of pressure P, and specific volume α, while
P1 α1 denotes the final state of the product of P and α
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e
...
3)

where subscripts 0 and 1 denote initial and final conditions respectively
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The corresponding value of α at pressure Po and temperature To will be α (To, Po)
Then using Charles’ law (constant pressure):

α1=α (T, P0) and α0=α (T0, P0) and using equation 2
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4)

We keep Po constant in equation 1
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If we now use Boyle’s law (constant temperature):

α1=α (T, P) and α0=α (T, P0) and using equation 2
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(2
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From Equation 2
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(2
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6) into (2
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(2
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13 mb) and α (To, Po) is the specific volume (volume of
1 gm of gas at To, Po); To = 273
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13 mb
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⸫P

𝛼(𝑇0 , 𝑃0)

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(2
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1
Since

𝜌

=

α

Then
P = 𝜌RT

2
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Equation 2
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Equation of state for Mixture of gases
Air is a mixture of gases which is observed to behave in a nearly ideal fashion, so long as
condensation does not take place
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Dalton’s law
It states that the total pressure exerted by a mixture of gases is equal to the sum of the partial
pressures which would be exerted by each constituent if it alone filled the entire volume at the
temperature of the mixture
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According to the law, the total pressure is the sum of the partial pressures
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+𝑃𝑘 = ∑ 𝑃𝑛

………………………………… (2
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Let the volume of the mixture be V and
the mass of the kth component be Mk and its molecular weight be mk
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It follows from this hypothesis that provided we take the same
number of molecules of any gas, the constant R in (2
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However, 1 mol of any
gas contains the same number of molecules as 1 mol of any other gas
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8) for 1 mol is the same for all gases; it is called the universal gas constant (R*)
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3145 J K_1 mol_1
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The specific gas constant is unique for each gas
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11
and the ideal gas equation f for n moles of a gas can be written as

2
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13a
Or

2
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13 can be written as

2
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15

Divide each side of 2
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For RHS, M=ΣMk if we divide both sides of 2
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Equation 2
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It
exactly of exactly of the same form as the ideal gas law if we define a mean molecular weight
(𝑚
̅)
1
̅
𝑚

𝑀
∑ 𝑘

=∑

𝑚𝑘

𝑀𝑘

… … … … … … … … … … … … … … … 2
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16 becomes

2
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18) is the equation of state for a mixture of gases
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If
we have a mixture of Md gms of dry air and Mv gms of moisture
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622

(m and m are molecular masses)

We can express 2
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18 becomes

2
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19

becomes
Pα = Rd (1 + 0
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20a

We define virtual temperature Tv as

Hence equation 2
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20b

Equation 2
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17 using Md and md

Equation 2
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21)

Equation 2

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