Geoscience Reference
In-Depth Information
An adiabatic transformation is one of the most impor-
tant aspects of work done by thermal systems. Here the
substance can do work but it is treated as being thermally
isolated from its surrounding environment. In other
words, no heat can flow from or into the substance, rather
in the fashion of an imaginary super-efficient thermos
flask. Thus
Mass
Mass
0 for such systems. However, it is most
important to realize that T can change within the adiabatic
volume as it rises or falls, it is just that none of the heat
energy can escape or be exchanged with the ambient envi-
ronment. The process is best illustrated by reference to air
masses once more, for air is a reasonably efficient thermal
insulator. Our rising, expanding air mass must therefore
increase in T as it does work against its surroundings, vice
versa for descent. Another example is the adiabatic rise of
deep mantle rock undergoing convection, a key solid
Earth process; here the rising hot rock loses so little of the
extra heat energy arising from decompression that it even-
tually melts to cause midocean ridge volcanism and plate
creation (Sections 5.1 and 5.2).
Q
piston
Total mass, m , of piston ring
d x
Expanding gas
exerts pressure, p ,
on area, A, of piston ring
and changes volume by A dx
,
Fig. 3.17 Mechanical work done by expanding gas on its
surroundings, illustrated here by a thought experiment with a
cylinder and piston apparatus. Expanding gas exerts force, F
pA ,
and does work W
pA d x . Generally, dW
p d V .
3.4.6 Internal thermal energy, energy conservation,
and the First Law of Thermodynamics
B
Molecules making up a thermal system have their own
intrinsic energy, called internal thermal energy, denoted
by the symbol U or E . This is easiest to comprehend with ref-
erence to an adiabatic transformation since here work is
being done by the isolated thermal system. The system
may be thought of as changing its internal thermal
energy in proportion to the amount of this work, that is,
d W = p d V
v 2
W = v 1 p d V
A
work done
= area under
p : V curve
W . The minus sign indicates that W refers to
the work being done by the system on its environment.
In an expanding atmospheric air mass or gaseous volcanic
column (Fig. 3.19), the system is doing work and losing
internal energy, with the converse being true for contrac-
tion. Internal energy arises due to the motion of mole-
cules as described by kinetic theory (Section 4.18) and is
a function of the variables of state, p , V , and T . Just like
potential energy but unlike work or heat flow,
U
V 1
V 2
Volume
Fig. 3.18 To illustrate path dependence. Path A to B; from the
integral the net work done in an expanding gas is positive and the
gas does work on its surroundings. Path B to A; the net work done
in a compressing gas is negative; the ambient medium has done
work on the gas.
U is
path independent. In the special case of ideal gases,
U
is only a function of T . The First Law of Thermodynamics
recognizes the mechanical equivalence of heat energy.
Any change in a substance's internal energy must be
equal to work done plus any heat flow into the system.
Thus,
and thermal systems. Isobaric systems can do work
because, by Boyle's Law, the constant pressure must be
accompanied by a change in temperature. The resultant
heat flow is then given by
T , where C p is the
thermal capacity at constant pressure. Systems where
volume is kept fixed while pressure changes are known as
isochoric . Since there is no volume change no work can be
done by the system, but despite this a heat flow exists of
magnitude
Q
C p
Q . In reversible isochoric sys-
tems, the first term on the right-hand-side of the First
Law is zero, since no work is done and
U
W
U
Q
C v
T .
In reversible isobaric systems,
U
W
Q
Q
C v
T , where C v
is the thermal capacity
p
V
C p
T .
at constant volume.
 
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