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A Treatment of the Second and Third Laws of Thermodynamics
The Second Law of Thermodynamics
Systems and the Second Law of Thermodynamics
The second law of thermodynamics states that the entropy of an isolated system is always increasing and is written in equation form in Equation 1.
A system is defined as the collection of bodies being studied; the surroundings are defined as everything in the universe that isn’t part of the system. An isolated system is a system that doesn’t exchange matter or energy with the surroundings. A closed system is one which exchanges energy, but not matter, with its surroundings. And finally, an open system is a system that exchanges both energy and mass with its surroundings.
While no exceptions to the Second Law of Thermodynamics are known, one must remember that the entropy of a closed or open system may decrease as long as the increase of the entropy of the surroundings is greater than the decrease of the entropy of the system. This is because the second law states that the entropy of an isolated system, not just any system, is always increasing. The universe is an isolated system. This means the entropy of the universe will always increase. The entropy change of the universe is the sum of the entropy change of the system and the entropy change of the surroundings. The second law mandates that this sum is positive. Therefore, the only way the entropy change of the system can be negative is if the entropy change of the surroundings is positive and the absolute value of the change in entropy of the surroundings is greater than the absolute value of the change in entropy of the system.
Second Law of Thermodynamics δS=(δq)/T>0 (Eq. 1)
S is entropy; q is work; T is temperature
The Second Law of Thermodynamics and Reversible Processes
A reversible process is defined as a process that can occur cyclically, a process that is continuously at equilibrium and a process that occurs by infinitesimally small changes. In theory, a perfectly efficient engine could be made by utilizing a reversible process by making infinitesimally small transfers of heat such that the bodies involved remained at thermal equilibrium. Unfortunately, some energy is always lost as heat and this perfectly efficient engine cannot exist in the physical world. Because energy is lost as heat, more energy must be put into the system for each additional cycle to be completed and the system is not perfectly reversible. This is a consequence of the second law of thermodynamics. In order for the entropy of the universe to be increasing, heat must be lost to the universe to create a more excited microstate.
The most efficient way for a process to occur is for it to occur in nearly infinitesimally small, finite steps that mimic a reversible process. Cells utilize this fact in glycolysis, the citric acid cycle and the electron transport chain. Each process is completed in a number of highly regulated steps. Each step produces only the number of products needed in order to not waste energy. Many of these steps can also be done in reverse to return to the “reactants” if too much “product” is obtained. This indicates that each step in these cellular processes mimics a thermodynamically reversible process, and helps the cell be as efficient as possible.
The Second Law of Thermodynamics, Gibbs Free Energy, and LeChatelier's Principle
One of the results of the second law of thermodynamics is that the change in Gibbs free energy can be used to determine whether or not a process is spontaneous. If the change in Gibbs free energy is negative, the reaction will proceed spontaneously and is said to be exergonic. If the change in Gibbs free energy is 0, neither the forward nor reverse reaction is spontaneous and the system is at equilibrium. If the change in Gibbs free energy is positive, the reverse reaction is spontaneous and the forward reaction is said to be exergonic. As stated in Equation 2, Gibbs free energy is defined as the sum of the internal energy and the energy transferred by pressure volume work minus the product of temperature and pressure. Enthalpy can be defined as the heat absorbed or released in the forming and breaking of bonds during a chemical process. It can be calculated by finding the sum of the internal energy and the energy transferred by pressure volume work. This means the change in Gibbs free energy can also be defined as the change in enthalpy minus the product of temperature and the change in entropy.
Gibbs Free Energy ∆G=U+pV-TS=∆H-T∆S (Eq. 2)
G is Gibbs free energy, p is pressure, v is volume, T is temperature, S is Entropy, H is Enthalpy
In biological system, the enthalpic term of the Gibb’s free energy is related to the changes in bonding. It is affected by van der Waals forces, Hydrogen bonding and charge interactions. The entropic term is related to changes in the arrangement of the solvent, counter ions, and rotational and translational changes.
Related to the idea of Gibb’s free energy is Le Châtelier’s principle. As previously explained, Le Châtelier’s principle states that if a system at equilibrium is disturbed that system will undergo a process to return to equilibrium. This concept is utilized by cells in glycolysis, the citric acid cycle, and the production of amino and nucleic acids. Successive steps in glycolysis and the citric acid cycle keep the buildup of product from inhibiting previous steps when the cell needs that process to continue. As soon as enough products from one step in glycolysis are formed they can be used in a following step as needed. This utilization allows for the previous step to continue. The citric acid cycle creates products that are not only used in successive steps in the citric acid cycle, but are used in production of amino acids and nucleic acids. The interconnectedness of these processes further allows for careful control of the cell’s energy and metabolites. The first and second laws govern these processes in ways that allows the cell to most efficiently produce the compounds it needs for life, growth, and reproduction, without producing excess.
Equation 2 also explains why body temperature must be closely regulated. Because Gibb’s free energy is temperature dependent, certain reactions are only spontaneous at specific temperatures. If one’s body was to stray too far outside of the preferred temperature range, not only would one’s proteins be denatured (cooked), but some reactions required for cell life and reproduction may no longer be spontaneous.
The Third Law of Thermodynamics
The Third Law of Thermodynamics states that the entropy of a perfect crystal, whose atoms are fixed and don’t move, vibrate or rotate, is zero when temperature is zero as measured in Kelvin. The Third Law serves to define zero entropy. It also serves to say that zero entropy cannot be reached by a finite number of steps because at 0 K there is no entropy difference, so an infinite number of steps would be needed. The Third Law is most commonly applied to systems at temperatures much lower than human body temperatures or in support of the first two laws of thermodynamics.