Page 48 - Geothermal Energy Renewable Energy and The Environment

3 Thermodynamics and

Geothermal Systems

Effective use of geothermal energy requires the ability to move heat efficiently. In some instances,
heat is used to do work, as in the generation of electricity. In other cases, heat is either concentrated
or dissipated. Regardless of the application, an understanding of the behavior of fluids and materials
when heated or cooled, and the implications for energy balances, is the foundation for achieving an
economically successful outcome for any geothermal application. This chapter provides an intro-
duction to the elements of thermodynamics that are important for such considerations.

The FIrsT law oF ThermodynamIcs: The eqUIValence oF
heaT and work and The conserVaTIon oF enerGy

conservaTion of enerGy
By the second half of the 1700s, the engineering community had become intrigued by the repeat-
edly observed fact that doing work on some materials generated heat. It was noted by Benjamin
Thompson in 1798 that, in the process of making cannons, boring into metal resulted in the metal
becoming very hot. A series of experiments he conducted (followed shortly by experiments by
Humphrey Davy in 1799) demonstrated that mechanical work and heat were directly related. They
and others eventually demonstrated that a given amount of mechanical work would result in the
generation of a predictable amount of heat.
However, it wasn’t until Julius Mayer published a seminal paper in 1842 that the concept of
conservation of energy, as embodied in the equivalence of heat and mechanical work, was articu-
lated. Although Mayer’s paper was the first to present the concept directly, it lacked sufficient
experimental grounding and mathematical rigor to be considered an adequate demonstration
of the equivalence of work and heat. In 1847 Hermann von Helmholtz developed a mathemati-
cal basis for the concept. Then, in 1849 the thorough experimental and observational work of
James Prescott Joule was presented to the Royal Society, in a paper entitled “On the Mechanical
Equivalent of Heat.” These achievements established the concept that mechanical work and heat
are equivalent and that, invariably, energy is conserved. This principle became the First Law of
Thermodynamics.
Simple statements of the First Law of Thermodynamics have been numerous, two of which are:

Energy can neither be created nor destroyed
All forms of energy are equivalent

Internal energy
The most rigorous description relies on the concept of internal energy, E. The E is a characteristic
of a specific, defined system. A system can be a cylinder of gas, a bottle of water, a bar of steel, a
rock—anything that can be physically described by parameters of state (such as temperature, T;
pressure, P; volume, V; etc.). If a system is completely isolated from its surroundings (that is, it is
a closed system, meaning no mass can move into or out of it) then at any given set of conditions
(T, P), the internal energy E of the defined system is fixed and only depends on the properties of the
materials of which the system is composed. The internal energy, E, will solely change in response to

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