9.10 The Laws of Thermodynamics
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the combined system has twice the internal energy of each half. Another example is
the volume V of the system itself. ‘Intensive’ variables, such as the system pressure
p or its temperature T , do not depend on how much of any subsystem is used to
make the measurement.
The work out of a system when the system pressure expands the volume of the
system can be found from
W =
pdV .
(9.29)
The amount of this work will depend on how heat is allowed into the system during
each step of the process. For this reason, we say that the integral depends on the
“path” one takes. For a small change in volume,
δW = pdV .
(9.30)
As we will see, the second law of thermodynamics will also allow us to express the
heat exchanged in terms of a path-dependent integral over thermodynamic variables.
Such expressions will no longer have meaning if the system goes nonthermodynamic, such as fluids in high chaos. One cannot use
pdV if the pressure
cannot be measured or fluctuates wildly. However, we can devise thermodynamic
paths for our integral by taking the system slowly through quasi-equilibrium states.
In this way, we can find how much a thermodynamic variable has changed.
Through logical thinking about heat engines, which are systems which run
in a cycle to take in heat and produce work, Sadi Carnot (1796–1832), laid the
foundation for the second law of thermodynamics.
Figure 9.3 shows a pair of abstract heat engines. The essence of a heat engine:
A source of energy, a ‘sink’ to discard more disordered energy, and a system
which uses some of that energy to do work, and a scheme to carry the engine in
a cycle, so that it can be used over and over. Later, we will be more specific about
the term ‘disordered’. Loosely, if all the particles in a system are moving in the
same direction and with the same speed, i.e. with coherent motion, we say they are
perfectly ordered. Such would be the case of a solid body you might push, or the
motion of the piston in your car. If the particles are moving in so-called random
directions with a distribution of speeds, they are disordered, and have incoherent
motion. Thermal motion of molecules is an example of incoherent motion.
Heat engines abound in biology, including your muscles and the operation of
flagellae in bacteria. Each takes in energy (such as through a chemical reaction
which re-arranges energy occupations), does work, and expels heat.
Carnot introduced the idea of a reversible engine. A reversible engine can not
only be made to run through each of its states in reverse order, taking heat from a
cold reservoir by doing work, and pumping that heat into a hot reservoir, but when it
does run in reverse mode, the same heats and work occur as when run in its forward
cycle, except they each are reversed in sign. Carnot realized that this kind of engine
has special idealized properties.
345
the combined system has twice the internal energy of each half. Another example is
the volume V of the system itself. ‘Intensive’ variables, such as the system pressure
p or its temperature T , do not depend on how much of any subsystem is used to
make the measurement.
The work out of a system when the system pressure expands the volume of the
system can be found from
W =
pdV .
(9.29)
The amount of this work will depend on how heat is allowed into the system during
each step of the process. For this reason, we say that the integral depends on the
“path” one takes. For a small change in volume,
δW = pdV .
(9.30)
As we will see, the second law of thermodynamics will also allow us to express the
heat exchanged in terms of a path-dependent integral over thermodynamic variables.
Such expressions will no longer have meaning if the system goes nonthermodynamic, such as fluids in high chaos. One cannot use
pdV if the pressure
cannot be measured or fluctuates wildly. However, we can devise thermodynamic
paths for our integral by taking the system slowly through quasi-equilibrium states.
In this way, we can find how much a thermodynamic variable has changed.
Through logical thinking about heat engines, which are systems which run
in a cycle to take in heat and produce work, Sadi Carnot (1796–1832), laid the
foundation for the second law of thermodynamics.
Figure 9.3 shows a pair of abstract heat engines. The essence of a heat engine:
A source of energy, a ‘sink’ to discard more disordered energy, and a system
which uses some of that energy to do work, and a scheme to carry the engine in
a cycle, so that it can be used over and over. Later, we will be more specific about
the term ‘disordered’. Loosely, if all the particles in a system are moving in the
same direction and with the same speed, i.e. with coherent motion, we say they are
perfectly ordered. Such would be the case of a solid body you might push, or the
motion of the piston in your car. If the particles are moving in so-called random
directions with a distribution of speeds, they are disordered, and have incoherent
motion. Thermal motion of molecules is an example of incoherent motion.
Heat engines abound in biology, including your muscles and the operation of
flagellae in bacteria. Each takes in energy (such as through a chemical reaction
which re-arranges energy occupations), does work, and expels heat.
Carnot introduced the idea of a reversible engine. A reversible engine can not
only be made to run through each of its states in reverse order, taking heat from a
cold reservoir by doing work, and pumping that heat into a hot reservoir, but when it
does run in reverse mode, the same heats and work occur as when run in its forward
cycle, except they each are reversed in sign. Carnot realized that this kind of engine
has special idealized properties.