Forces and dynamics - Physical Processes in Earth and Environmental Sciences - page 46

Box 3.1 For a constant volume of dilute gas, p and T are interdependent. We can write this as p = RT , where R is a
proportionality constant known as the universal gas constant. R has a value of 8.314 J mol -1 K.

Combining this expression with Boyle's Law we obtain the ideal gas law, pV = nRT , where n is the number of moles of the gas.

TO FIND THE DENSITY OF AIR FROM FIRST PRINCIPLES

We use the ideal gas law for 1 mole of substance to determine the volume, V , of air at normal Earth surface temperature
(in degrees kelvin, i.e. °C + 273) and pressure. V = RT/p = 2.41 . 10 -2 m 3
We know that the molecular weight of 1 mole of air at standard surface pressure and 20°C T is 29.2 g. The density of air is thus
29.2/ V = 1.21 kg m -3

3.4.3 Changing heat energy in Earth thermal systems

We may think of changes to thermal systems in two ways:
isothermal , temperature constant, or isobaric , pressure
constant. Rather than the absolute value of a substance's
internal/thermal energy, E , we are much more interested
in changes to that energy,

Liquid

E . A thermal system can transfer

1

energy by
changing the temperature of an adjacent system it is in
thermal contact with
changing the phase (i.e. liquid, solid, gas) of an adjacent
system
doing mechanical work on its environment
Any change in temperature,

Triple
point

Solid

Vapor

0 100

T , of a thermal system by the
first two methods must be accompanied by a flow of heat ,
Q , the change,

Temperature, (°C)

Q , being proportional to the thermal
capacity, c , for the particular substance making up the ther-
mal system. Thus we have

Fig. 3.14 Pressure-temperature (“phase”) diagram to show stability
of states of water.

T , or, equal quantities
of heat energy produce different changes of temperature in
a substance if the thermal capacities are different.
However, following on from the equation of state, the
actual heat flow depends upon how c varies according to
the path along which the change takes place, whether it is
with volume or pressure kept constant.
An interesting example of heat flow of great relevance to
Earth and environmental sciences occurs when a substance
like water changes phase. Figure 3.14 shows a phase dia-
gram , that is, a graph in p-T space in which experimental
data for the phases of water are plotted. We may again
speak of isobaric or isothermal changes and define binding
energy as the energy required to change a mole of solid or
liquid into a gas (Fig. 3.15). Importantly, there is no tem-
perature change to the phases during the change of phase;
rather a flow of heat energy arises from changing the
molecular structure of the unstable phase. This flow of
heat energy may pass from or to the ambient medium.
Heat energy is required for fusion or evaporation, but is

Q c

given out during solidification or condensation. Such heat
energy transfer is known as latent heat, L . The latent heat of
evaporation , L E , is much greater than the latent heat of
fusion , L F , because the energy required to change liquid
molecules into widely spaced gaseous molecules is much
greater than that to make solid molecules pack a little less
tightly into liquid spacing (Fig. 3.15).

3.4.4 Mechanical equivalence of heat energy

Changes in temperature may also be brought about during
the conversion of mechanical work into heat. Heat and
mechanical work are interchangeable: the flow of heat, like
work, is a transfer of energy. It follows that heat energy
must take its rightful place alongside the other forms of
energy, kinetic and potential, we encountered in
Section 3.3. The production of heat energy by mechanical
work begs the question, “How much energy from how