Microbial Thermodynamics

The study of the relationships between heat and other forms of energy is called thermodynamics. All living things utilize heat, therefore, the science of thermodynamics may be used to evaluate life processes. An example of a life process is the growth of bacteria when wastewater is fed to them to treat the waste. Knowledge of microbial thermodynamics is therefore important to professionals involved in cleaning up wastewaters.

Variables involved in the study of the relationship of heat and energy are called thermodynamic variables. Examples of these variables are temperature, pressure, free energy, enthalpy, entropy, and volume. In our short discussion of thermodynamics, we will address enthalpy, entropy, and free energy. As mentioned, whether or not a particular reaction, such as a biological reaction, is possible can be determined by the free energy change between products and reactants. Free energy, in turn, is a function of the enthalpy and entropy of the reactants and products.

15.3.1 Enthalpy and Entropy

Let H represent the enthalpy, U the internal energy, P the pressure, and - the volume of a particular system undergoing a process under study. The enthalpy H is defined as

Internal energy refers to all the energies that are present in the system such as kinetic energies of the molecules, ionization energies of the electrons, bond energies, lattice energies, etc. The system possesses all these energies by virtue of its being and are all integral (that is, internal) with the system.

Let us derive the relationship between enthalpy and the heat exchange during a biological reaction, where biological reaction is a chemical reaction mediated by organisms. Biological reactions are carried out at constant pressure; hence, the heat exchange is a heat exchange at constant pressure. Designate this exchange as Qp. The first law of thermodynamics states that any heat added to a system minus any work W that the system is doing at the same time manifests itself in the form of an increase of the internal energy. In differential form, dU = dQp - dW = dQp - PdV (15.2)

The only work done in biological reactions is the work of pushing the surroundings (the atmosphere) in which the reaction is occurring. This is a pressure-volume work; hence, the PdV term.

Because the biological reaction is at constant pressure, differentiate the enthalpy equation at constant pressure. This produces dH = dU + PdV (15.3)

This may be combined with Equation (15.2) to eliminate dU producing dH = dQp (15.4)

This equation concludes that change in enthalpy is a heat exchange at constant pressure between the system under study and its surroundings.

Before we discuss entropy, define reversible process and reversible cycle. A reversible process is a process in which the original state or condition of a system can be recovered back if the process is done in the opposite direction from that in which it is currently being done. To perform a reversible process, the steps must be conducted very, very slowly, in an infinitesimal manner, and without friction. From the definition of a reversible process, the definition of a reversible cycle follows. A reversible cycle is a cycle in which the reversible process is applied in every step around the cycle.

Heat added to a system causes its constituent particles to absorb the energy resulting in the system being more chaotic than it was before. If the heat is added reversibly, the ratio of the infinitesimal heat added to the temperature T during the infinitesimal time that the heat is added defines the change in entropy. If this addition is done around a reversible cycle, the state or condition of the system at the end of the cycle will revert back to its original state or condition at the beginning of the cycle. This must be so, since the whole process is being done reversibly in every step along the way around the cycle. Hence, the change in entropy around a reversible cycle is zero.

Let S be the entropy and Qrev be the reversible heat added. In a given differential step, the heat added is dQrev. The differential change in entropy in every differential step is therefore dS = dQrev/I. Around the cycle, the change in entropy is the integral, thus dS = Se - Sb = AS = °-dQev = 0 (15.5)

The symbol $ means that the integrand is to be integrated around the cycle and subscripts e and b refer to the end and the beginning of the cycle, respectively. If the process is not around a cycle, the previous subscripts simply mean the end and beginning of the process. In this case, the integral will not be zero and the equation is written as the integral

Interpretations of enthalpy and entropy. The heat absorbed by the system causes more agitation of its constituent elements. This increased agitation and chaos is the entropy increase and is calculated by Eqs. (15.6) and (15.7). The entropy increase is an increase in disorder of the constituents of the system. The energy state of the system is increased, but because the energy supporting this state is nothing more than supporting chaos, this energy is a wasted energy. The equations therefore calculate the loss in energy of the system as a result of increased chaos or disorder.

Consider a fuel such as coal, and burn it in a furnace. The burning of the coal occurs under constant atmospheric pressure. As the coal burns, heat is released; this heat is energy Qp, which may be used to produce electricity by using a boiler and a turbine generator. From Equation (15.4), Qp is equal to the enthalpy change AH. We therefore conclude that before the coal was burned, it possessed an enthalpy H which, by virtue of Equation (15.4), is its energy content. By the entropy change during the process of burning, however, all this energy is not utilized as useful energy but is subtracted by the change in entropy. The electrical energy that is ultimately delivered to the consumer is less by an amount equal to the overall entropy change in the transformation of coal to electricity.

In biological reactions, the fuel is the food. In biological nitrogen removal, nitrogen in its appropriate form is fed to microorganisms to be utilized as food. This food possesses enthalpy as does coal; and, similar to coal, its energy content cannot all be utilized as useful energy by the microorganism as a result of the inevitable entropy inefficiency that occurs in the process of consuming food.

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