Page 51 - Geothermal Energy Renewable Energy and The Environment

34 Geothermal Energy: Renewable Energy and the Environment

Enthalpy is an important system property in geothermal power applications because it provides
a means for establishing the behavior of a system in the subsurface and allows for evaluation of the
useful energy that can be extracted from a working fluid. It has units of J/kg. We will consider this
in more detail in Chapter 9.

The second law oF ThermodynamIcs: The
IneVITable Increase oF enTropy

efficiency
At the same time as the concept of conservation of energy was being formulated, advances in steam
engine technology were flourishing. By 1769 James Watt, building on early work of Thomas Savery,
Thomas Newcomen and others, had developed the steam engine to the point that it began to be the
dominant driver of the Industrial Revolution. As the steam engine was adopted and modified, inter-
est grew in the factors that determined the efficiency of steam engines.
The issue, at its core, was how much work could be done for a given amount of heat. The ideal,
of course, would be a situation in which all of the energy contained in a given amount of heat would
be converted to work with 100% efficiency. Mathematically, the efficiency of any situation involving
heat and work can be expressed as
e = –w/q,

where w is the amount of work output (to reiterate, by convention we assign work done by a system
a negative sign, and work done to a system a positive sign) for a given amount of heat input (q). In
this expression, e is the efficiency. For the ideal case, e = 1.0 and q = –w.

carnoT cycle
In 1824 Nicolas Léonard Sadi Carnot, a young French engineer, provided the definitive concept
that allowed efficiency to be rigorously determined. Carnot’s conceptualization of the problem was
further developed by Èmile Clapeyron and Rudolf Clausius, such that by the 1850s, the concept was
available in the form we generally use today.
A Carnot engine is an imaginary engine that cycles through a series of four steps. By the end
of the fourth step the engine has returned to its initial state. Each step must be carried out revers-
ibly, meaning that equilibrium is achieved continuously throughout each step of the process. In
reality, it is impossible to carry out a series of completely reversible steps, since achieving com-
plete equilibrium requires that no pressure or temperature gradients develop during action of
the engine. The only means by which such a state can be achieved is if each step is carried out
infinitely slowly. Hence, the Carnot engine is an ideal that cannot be realized. But, as a means for
understanding the relationship between heat, work, and efficiency, it is indispensable as a refer-
ence frame.
In its simplest form, assume the engine is composed of a gas-filled cylinder with a frictionless
piston. The gas we will consider follows the ideal gas law, which states

P × V = n × R × T, (3.7)

where P is the pressure of the gas, V is the volume of the gas, n is the amount of gas (in moles), T is
the temperature in Kelvins (K), which is the thermodynamic temperature scale in which absolute
zero is equivalent to 273.16˚C, and R is the universal gas constant (8.314 J/mol × K). In the first step