Structural Biochemistry/First law

Introduction
The First Law of Thermodynamics is an expression of the principle of the conservation of energy. It states that the total energy of a system and its surroundings is constant, and energy can be transformed, but may not be created or destroyed.

The First Law can be applied to living organisms by thinking of them as a system. A system cannot output more energy than it contains without an external source of more energy. Once the potential energy locked in carbohydrates and other energy sources are converted into kinetic energy (energy in use or motion) by the organism, the organism will not obtain more until energy is imputed again. This is important to understand since the variety of tasks that are performed by cells, ribosomes, proteins, etc. are only possible through the intake and transformation of pre-assembled molecules into energy.

The general equation that describes this theory is:

$$dU=\delta Q-\delta W\,$$

where dU is the change in internal energy, dq is the infinitesimal heat exchanged, and dw is the infinitesimal work performed. Work and heat are not state variables where as internal energy is. In this equation, it is demonstrated that only heat and work can lead to a change in the internal energy of a system, which is defined as the total of all kinetic and potential energy of everything within a closed system. This equation may also be described in words as: although energy assumes many forms, the total quantity of energy is constant; and when energy disappears in one form, it appears simultaneously in other forms.

In addition to work and external potential and kinetic energy, the generalization of the law of conservation of mechanical energy was made possible by the recognition of heat and internal energy as forms of energy. As a matter of fact, examples such as surface energy, electrical energy, and magnetic energy can all serve as extensions to the generalization stated above. The validity of this generalization was supported by overwhelming amount of evidence, which has raised its stature to a law of science, known as the First Law of Thermodynamics.

It is important to look at how the internal energy of system changes under constant pressure and temperature conditions because many chemical reactions take place under these specified conditions. Using the definition of the internal energy and assuming that only expansion work is done, one may write:

$$dU=\delta Q-P*\delta V\, $$

Expansion of the terms gives:

ΔU = U2 - U1 = Qp + W = Qp - P*ΔV = Qp - P*(V2 - V1)

Finally, rearrangement for Qp gives:

Q = (U2 -P*V2) - (U1 - P*V1)

Since U, P, and V are all state variables, we may define Qp, the heat transferred at constant pressure, as a new state function called the enthalpy, H. We can represent this new state function as:

H = U + PV

Where H, U, and V are molar or unit-mass values. U denotes the internal energy of a system, P denotes pressure, and V denotes volume.

When heat is added to a system, the internal energy of the system will increase, which, in turn, increases enthalpy. Work done by the surroundings on that system will produce similar (positive work) results. Conversely, heat lost to the surroundings or work done by the system are given a negative sign for enthalpy and work. In other words, any change in the energy of a system must result in a corresponding change in the surroundings. Therefore, energy is transferred from the system to the surroundings (reset of the universe), or from the surroundings to the system. And thus, energy can neither be created nor destroyed.

The sphere of influence of the process is divided into two parts when the First Law of Thermodynamics is applied to a given process. The region in which the process occurs is set apart as the system; everything with which the system interacts is its surroundings. A system may be of any size; its boundaries may be real or imaginary, rigid or flexible. A system usually consists of a single substance; however, complex systems consist multiple substances may also be found in scientific and engineering applications. In any event, the equations of thermodynamics are written with reference to a well-defined system. Attention is often focused on the particular process of interest and on the equipment and material involved in the process directly. However, the First Law of Thermodynamics applies to the system and its surroundings; not to the system alone.

Conclusion
The first law of thermodynamics is that energy can neither be created or destroyed.

General Form
 * accumulation = input - output
 * input = rate of energy (potential, kinetic, internal) is inputted into the system + rate of heat entering the system
 * output = rate of heat leaving the system + rate at which it leaves as work
 * accumulation = rate of energy in the system