# First Law of Thermodynamics

The first law of thermodynamics states that energy can be converted from one form to another, but cannot be created or destroyed. The most important and critical aspect of life revolves around the idea of energy. During the course of a single day, a person finds him or herself using energy in all sorts to live their lives. Whether driving a car or eating lunch, the consumption of some sort of energy is unavoidable. While it may seem that energy is being created for our purposes and destroyed during it, there is in fact no change in the amount of energy in the world at one time. Taking this a step farther, one may state the entirety of the energy in the universe is at a constant with energy just being converted into different forms.

## System and Surroundings

To obtain a better understanding of the workings of energy within the universe, it is helpful to classify it into two distinct parts. The first being the energy of a specific system, $$E_{sys}$$, and the second being whatever energy was not included in the system which we label as the energy of the surroundings, Esurr. Since these two parts are equal to the total energy of the universe, $$E_{univ}$$, it can be concluded that

$E_{univ} = E_{sys} + E_{surr} \label{1}$

Now, since we stated previously that the total amount of energy within the universe does not change, one can set a change in energy of the system and surroundings to equal

$ΔE_{sys} + ΔE_{surr} = 0 \label{2}$

A simple rearrangement of Equation \ref{2} leads to the following conclusion

$ΔE_{sys} = -ΔE_{surr} \label{3}$

Equation \ref{3} represents a very important premise of energy conservation. The premise is that any change in energy of a system will result in an equal but opposite change in the surroundings. This essentially summarizes the First Law of Thermodynamics which states that energy cannot be created nor destroyed.

 System 15 Joules of Energy flows out of the System Surroundings An equal amount of 15 Joules of Energy is added to the surroundings

## Types of Energy

Now that the conservation of energy has been defined, one can now study the different energies of a system. Within a system, there are three main types of energy. These three types are kinetic (the energy of motion), potential (energy stored within a system as a result of placement or configuration), and internal (energy associated with electronic and intramolecular forces). Thus, the following equation can be given

$E_{total} = KE + PE + U \label{4}$

where KE is the kinetic energy, PE is the potential energy, U is the internal energy, and Etotal is the total energy of the system. While all forms of energy are very important, the internal energy, U, is what will receive the remainder of the focus.

## Internal Energy, U

As stated previously, U is the energy associated with electronic and intramolecular forces. Yet, despite the abundance of forces and interactions that may be occurring within a system, it is near impossible to calculate its internal energy. Instead, the change in the U of a system, ΔU, must be measured instead. The change in ΔU of a system is affected by two distinct variables. These two variables are designated at heat, q, and work, w. Heat refers to the total amount of energy transferred to or from a system as a result of thermal contact. Work refers to the total amount of energy transferred to or from a system as a result of changes in the external parameters (volume, pressure). Applying this, the following equation can be given

$ΔU = q + w \label{5}$

If the change of ΔU is infinitesimal, then Equation \ref{5} can be altered to

$dU = dq + dw \label{6}$

Within this equation it should be noted that U is a state function and therefore independent of pathways while $$q$$ and $$w$$ are not.

Having defined heat and work, it becomes necessary to define whether a process is exhibiting positive or negative values of q and w. Table 1 describes the sign conventions of both work and heat.

Process Sign
Work done by the system on the surroundings -
Work done on the system by the surroundings +
Heat absorbed by the system from the surroundings (endothermic) +
Heat absorbed by the surroundings from the system (exothermic) -
Table 1. Sign Conventions for Work and Heat