BIOCHEMISTRY TOPICS
The Second Law of Thermodynamics
Three scenarios. Dissipation of the coherent kinetic energy of a macroscopic object. Thermal equilibrium and the concept of temperature And... I forgot what the third one was :)
We want to be able to predict whether a process will occur spontaneously. We find that a spontaneous process is one in which the overall entropy of the universe increases, which is a statement of the Second Law of Thermodynamics. Of course, we must understand what entropy is. Succinctly stated, entropy is a measure of the dispersal of energy or matter. The details of the definition and calculation of entropy can be found within its topics page. Let us here consider a few scenarios to further illustrate the second law and entropy.
Scenario 1. In this scenario, we imagine all the laws of classical mechanics applying to the microscopic objects we'll call atoms and molecules, as well as to macroscopic objects. We know that when a bowling ball falls off the ledge of a building, its potential energy is converted into kinetic energy. As the bowling ball hurtles toward the ground, more and more of its potential energy is converted into kinetic energy. Neglecting friction, the sum of the kinetic and potential energy remains constant. This is a consequence of the conservation of energy. What happens to all of this energy when the bowling ball thuds into the ground? The impact of the ball warms the ground, and what was the macroscopic kinetic energy of the ball is converted into an increase in the microscopic kinetic energy of molecules. Now the energy, previously carried by a single object, is distributed among an astronomically large number of particles. If we imagine the reverse process, a huge number of molecules simultaneously colliding with a bowling ball at rest on the ground, launching it into the air, this is an event we know from experience to be impossible. Yet it does not violate the first law of thermodynamics. In thinking about this process, intuitively it seems extremely unlikely from a statistical standpoint for such a large number of particles to all move in the same direction, or even for there to be a significant excess of particles moving in any particular direction. (Remember, when we deal with a macroscopic number of molecules we are in the range of moles, or ~1024 molecules.) The forward process, the falling of the bowling ball to the ground seems to be spontaneous, while the reverse process does not occur, and is therefore not spontaneous. We will see that for systems consisting of a large number of discrete particles such as molecules that spontaneity can be understood as a result of the statistical behavior of these particles.
Scenario 2. A process in which two bodies initially at the same temperature and in physical contact transfer heat between them in such a way that one body becomes warmer while the other becomes colder does not violate the first law. But we all know that this does not occur. In fact, the opposite process occurs spontaneously. Two bodies in contact and initially at different temperatures will come to thermal equilibrium, exchanging heat between them until both are at the same temperature.
The spontaneous mixing of gases, liquids, or solutions can also be shown to result in an increase in entropy.
As was discussed in the entropy webpage, the definition and measurement of entropy in terms of heat and temperature is historically quite closely connected with the development of the steam engine. Heat itself was not well understood prior to Joule's careful measurements in the 1840s. The first law of thermodynamics, if universally true, meant that for any conceivable engine you could never get more work out than energy in some form that is put in. But at least one could hope to improve and perhaps maximize the efficiency of real-world engines. But, as Carnot showed, the efficiency of an ideal heat engine could never exceed the ratio (Th – Tc) / Th, where Th is the temperature of the hot reservoir, and Tc the temperature of the cold reservoir. For a steam engine (working substance water), with Th = 373 K and the low temperature ("exhaust") reservoir (condensed water, say at 4°C or 277 K), the equation yields 0.257 - not much more than 25% maximum effeciency! However, the theoretical importance of this equation is that it implies that in order for to be any possibility of conversion of heat into work, there must be a temperature difference somewhere in the system. This is actually quite close to a statement of the second law of themodynamics.
Let us consider the consequences of the statement made in the prevoius page that in an isothermal process ΔS for the system is at least as great as the heat q transferred between system and surroundings divided by the temperature T at which this transfer occurs. If the process involves no transfer of heat - e.g. the system is isolated - then ΔS for the system must be greater than or equal to zero. The equality only holds for a special theoretical case - a reversible process. All other processes are irreversible which is the same as a spontaneous process. This leads to a formulation of the second law of thermodynamics that says that ΔS > 0 for any real (spontaneous) process occurring in an isolated system.
More generally, if we consider the entire universe as an isolated system, we would have
ΔSuniv > 0 ⇔ spontaneous process
which is to say for any spontaneous process, the entropy of the universe must increase, and conversely, any process for which the entropy of the universe increases must be a spontaneous process. Since we can divide the universe into a portion of particular interest (the system) and everything else (the surroundings) by choosing a suitable boundary, and make use of the fact that the change in entropy of the universe must be the sum of the change in entropy of the system and that for the surroundings,
ΔSuniv = ΔSsys + ΔSsurr
we can state the second law of thermodynamics in the form
ΔSuniv = ΔSsys + ΔSsurr > 0 ⇔ spontaneous process
This formulation allows us to assess, for various processes, the spontanaeity criterion by looking at the entropy changes for both the system and surroundings. Ultimately, however, we would like a state function that can, when evaluated for the system alone, indicate the spontaneous direction of a process. It turns out that if we treat the transfer of energy q between system and surroundings more carefully, we can relate ΔHsys to ΔSsurr and derive a restatement of the second law as
ΔSuniv = ΔSsys − ΔHsys/ T > 0 ⇔ spontaneous process (constant P, T)
where we have specified processes for which there is no change in P or T (constant pressure and temperature). Under these conditions, we can replace ΔSsurr with −ΔHsys/T since heat transfer to or from the surroundings occurs - from the standpoint of the surroundings - reversibly, since the surroundings remains unperturbed from equilibrium. So, at constant pressure,
ΔSsurr = qrev/Tsurr = −qP/ T = −ΔHsys/ T
The last two equalities relate to the system specifically, and at constant temperature.
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