# First Law of Thermodynamics

The first law of thermodynamics is the conservation of energy principle.  This provides us with the statement that energy cannot be created or destroyed.  As a result, the first law of thermodynamics allows us to to form relationships between various forms of energy as well as energy interactions.

### The First Law of Thermodynamics

The first law of thermodynamics will allow us to see how energy will change form through different processes of a system.  First, let’s take a look a couple of examples.

##### Potential Energy & Kinetic Energy

The first example is the transformation of potential energy to kinetic energy.  Lets say you are holding a ball up in the air at a certain height.  If you know the mass of the ball and its height you can calculate the potential energy.

(Eq 1) $P.E.=mgΔh$ (kJ)

$m$ = mass

$g$ = gravitational constant

$h$ = height

Next if you were to drop the ball its velocity will continue to increase until it hits the ground.  The reason for this is because the potential energy is converted to kinetic energy.

(Eq 2) $K.E. =\frac{1}{2}m(v^2_2-v^2_1)$ (kJ)

$v_2$ = final velocity

$v_1$ = initial velocity

In fact because of the first law of thermodynamics, the decrease in potential energy will exactly equal the increase in kinetic energy.

(Eq 3) $K.E.=P.E.$

##### Adiabatic Process

Next let’s consider a system that is undergoing an adiabatic process. Recall that if a process is adiabatic than the heat transfer across the boundary layer must be negligible.  Instead an increase or decrease in energy is due to a work interaction.

From experimental data the following statement has been concluded.  “For all adiabatic processes between two specified states of a closed system, the net work done is the same regardless of the nature of the closed system and the details of the process.”  This statement was derived from experiments performed by Joule during the nineteenth century.  In turn, It is also the fundamental principle that the first law of thermodynamics is derived from.

The first law of thermodynamics allows us to define the property “total energy” $E$.  Let’s take a look at an adiabatic process again. During the process the net work is the same between two specified states.  As a result, the net work is dependent on the end state of the system.  In turn, it also  corresponds to a change in property of the system.  This property is the total energy of the system.  Hence, per the first law, the change in total energy for an adiabatic process is equal to the net work done.  Due to this fact an arbitrary value can be assigned to the total energy as a reference point.

##### Heat Transfer

The first law of thermodynamics is a statement of the conservation of energy principle.  As a result, we must also consider how heat transfer will affect the total energy.  For example it is well known that if you put a potato in the oven or a pot of water on a lit stove their temperature will increase.  The reason for this is because  heat transfer into the potato or the pot of water increases their energy.  In turn, this will increase the total energy, which will be equal to the amount of heat transferred into these two items.

To further this example let take a look at heater that is in a well insulated room.  This means the room, which represent the system, can be considered adiabatic.  As a result, since heat cannot transfer across the boundary layer of the room, energy introduced to the room from the heater will remain in the room.  Hence, the increase in total energy of the room will be equal to the amount heat transferred from the heater.

### Energy Balance

From the conservation of energy principle the following can be concluded.  The net change of energy within a system is equal to difference between the total energy leaving the system and entering the system during a process.  In other word,

(Eq 4) $E_{in}-E_{out}=ΔE_{system}$

This relationship is referred to as the energy balance.  Energy balance is applicable to any system undergoing a process.  As a result, the energy change of a system can be determined.  In order to do this you will need to know what the energy was at initial state of the system and what it is at its final state.  Than by taking the difference, the energy change of the system can be determined.

(Eq 5) ΔE_{system}=E_{final}-E_{initial}=E_2-E_1$Finally, there are numerous forms of energy. To name a few there is internal energy, kinetic energy, potential energy, electric, and magnetic. The sum of all of these forms of energy within the system will equal the total energy of the system. As a result, if we were to focus on potential, kinetic, and internal energy and assume the other forms of energy are negligible, than we would obtain the following equation. (EQ 6)$ΔE=ΔU+ΔKE+ΔPE$In addition, if the system is stationary, there will be no change in the kinetic energy or potential energy of the system. In turn, equation 6 will than become the following. (Eq 7)$ΔE=ΔU$### Mechanisms of Energy Transfer There are three forms of energy transfer into and out of a system. They are heat, work, and mass flow. All of these forms of energy transfer are recognized and the system’s boundary as energy crosses it. In addition, if the system has a fixed mass or is a closed system than only heat transfer and work will apply. ##### Heat Transfer Heat is represented by the symbol$Q$. This type of energy transfer will only occur when there is a temperature difference between the system and its surroundings. This type of energy transfer occurs by increasing or decreasing the energy of the molecules within the system. As a result, it changes the internal energy of the system. ##### Work Transfer Work,$W$, is a type of energy transfer that does not result from a temperature difference between the system and its surroundings. There are many examples of work transfer. A hydraulic jack is an example of work energy. A hydraulic jack uses work energy to raise heavy objects such as a car. Work can transfer to a system, which in turn increases the energy of that system. It can also be transferred out of the system lowering the systems total energy. For example, turbines produce work, pumps and compressors consume work. ##### Mass Flow Mass flow,$m$, is the movement of a mass, such as a fluid, through a system. This provides an additional mechanism of the energy transfer. The reason why is because when a mass enter a system the energy within the system will increase since the mass itself carries energy. Likewise, as the mass exits the system, the system energy will decrease. All three forms of energy can occur on a system. As a result, the following equation is used to calculate the change in energy within the system. (Eq 8)$E_{in}-E_{out}=(Q_{in}-Q_{out}+(W_{in}-W_{out})+(E_{mass,in}-E_{mass,out})=ΔE_{system}$For the above equation heat transfer,$Q$will be zero if the system is adiabatic. In addition, work,$W$will be zero if there are no work interactions. Finally, if there is no mass flow within the system than$E_{mass}\$ will zero.

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