Page 50 - Geothermal Energy Renewable Energy and The Environment

Thermodynamics and Geothermal Systems 33

If we were to measure the internal energy at the end of each step in B, we would find that
E + E + E + E = E ,
B5
B2
B4
B3
f
which results in
Δ E = E + E + E + E – E . = E – E . i
1
2
f
4
5
3
Thus, regardless of the complexity of the path that is followed in getting from one set of condi-
tions to another, or to put it another way, regardless of how much work one does to a system in mov-
ing from one state to another, the internal energy will always be the difference between the initial
and final states.
pV work
The conclusion that is inescapable is that any change in the internal energy of a system is solely the
result of the work (w) done to the system, or that the system performs, and any heat (q) added to or
taken from the system:

Δ E = q + w. (3.1)

To perform mechanical work, a force is applied to a point or a surface that results in displacement
of the point or surface. An example of such a condition is the cylinder in Figure 3.1 as it moves from
position B1 to position B2. Assuming there is an external force applied to the piston, mechanical
work is performed by the gas when it increases its volume and thus moves the piston. Hence, the
element of mechanical work is defined by

dw = –P × dV. (3.2)

By convention, mechanical work done on a system is positive, thus requiring a negative sign
since there is a negative change in volume in such a case, while work done by a system is negative.
Work performed is, therefore, equivalent to the difference in volume between two states,

w = – P × (V – V ) = –P × ΔV. (3.3)
2
1
enthalpy
It follows from this that in a process in which no change in volume occurs, no mechanical work is
performed, and any change in internal energy is solely related to heat added to or removed from the
system,

Δ E = q . (3.4)
v
(The subscript v is used to indicate heat at constant volume. The subscript p refers to a constant
pressure condition). If, on the other hand, a change in volume occurs at constant pressure and heat
is also added to or removed from the system, the change in internal energy is

Δ E = q – P × ΔV. (3.5)
p
The heat added to or removed from the system at constant pressure is called the enthalpy, H, and
the change in enthalpy, ΔH, which is realized when moving from one state to another is defined as
Δ H = H – H = (E + P × V ) – (E + P × V ) = q . (3.6)
2
p
1
2
2
1
1