Matters of state and motion - Physical Processes in Earth and Environmental Sciences - page 24

is about 25 Ckm 1 and although linear for the very upper

part of the crust directly penetrated by humans, such a
gradient cannot be extrapolated further downward since
widespread lower crustal and mantle melting would result
(or even vaporization in the mantle!) for which there is no
evidence. We therefore deduce that (Fig. 2.7)
1 The geothermal gradient decreases with depth in the crust;
that is, it becomes nonlinear.
2 The high near-surface heat flow must be due to a
concentration of heat-producing radioactive elements
there.
Concerning the temperature at the 3,000 km radius
core-mantle boundary (CMB), metallurgy tells us that
iron melts at the surface of the Earth at about 1,550

Temperature (K)

1000 2000 3000 4000 5000

Lithosphere plate

410 km Discontinuity

500

Upper mantle

660 km Discontinuity

Lower mantle

1000

Curve (b)
assumes
separate
upper and
lower mantle
convection
layers

Curve (a)
assumes
whole-mantle
convection

C.
Allowing for the increase of this melting temperature with
pressure, the appropriate temperature at the CMB may be
approximately 3,000

2000

C, yielding a conveniently easy to
remember (though quite possibly wrong) mantle gradient
of c. 1 Ckm 1 .

Core-mantle interface

3000

Outer core, Fe-liquid

Fig. 2.7 Mean temperature gradient (geotherm) for solid Earth.

2.3 Quantity of matter

2.3.1 Mass

century English translation of the original Latin:
“Quantity of matter is the measure of it arising from its
density and bulk conjointly,” that is, gravity does not come
into it.

We measure all manner of things in everyday life and
express the measured portions in kilograms; we usually say
that the portions are of a certain “weight.” On old-fashioned
beam balances, for example, kilogram or pound “weights”
are used. These are of standard quantity for a given
material so that comparisons may be universally valid. In
science, however, we speak of all such estimates of bulk
measured in kilograms as mass (symbol m ). The bigger the
portion of a given material or substance, the larger the
mass. We can even “measure” the mass of the Earth and
the planets (see Section 1.4). We must never speak of
“weight” in such contexts because, as we shall see later in
this topic, weight is strictly the effect of acceleration due to
gravity upon mass. Mass is independent of the gravita-
tional system any substance happens to find itself in. So
when we stand on the weighing scales we should strictly
speak of being “undermass” or “overmass.”
Newton defined mass, what he termed “quantity of
matter” succinctly enough (Fig. 2.8). Here is a nineteenth-

2.3.2 Density

The amount of mass in a given volume of substance is a
fundamental physical property of that substance. We
define density as that mass present in a unit volume, the
unit being one cubic meter. The units of density are thus
kg m 3 (there is no special name for this unit) and the
dimensions ML 3 . The unit cubic meter can comprise air,
freshwater, seawater, lead, rock, magma, or in fact any-
thing (Fig. 2.8). In this text will usually symbolize fluid

density and , solid density (though beware, for we also

use as a symbol for stress, but the context will be obvi-

ous and well explained). Sometimes the density of a
substance is compared, as a ratio, to that of water,
the quantity being known as the specific gravity , a rather