1st Law of Thermodynamics

The 1st Law of Thermodyamics simply states that energy can be neither created nor destroyed (conservation of energy). Thus power generation processes and energy sources actually involve conversion of energy from one form to another, rather than creation of energy from nothing. For example:

terms of their energy conversion processes.

 Automobile Engine Chemical ® Kinetic Heater/Furnace Chemical ® Heat Hydroelectric Gravitational ® Electrical Solar Optical ® Electrical Nuclear Nuclear ® Heat, Kinetic, Optical Battery Chemical ® Electrical Food Chemical ® Heat, Kinetic Photosynthesis Optical ® Chemical

As you can see conversion between chemical energy and other forms of energy are extremely important, whether you are veterinarian or a mechanical engineer. That is what we will focus on for the remainder of this chapter.

System and Surroundings

The 1st Law of Thermodynamics tells us that energy is neither created nor destroyed, thus the energy of the universe is a constant. However, energy can certainly be transferred from one part of the universe to another. To work out thermodynamic problems we will need to isolate a certain portion of the universe (the system) from the remainder of the universe (the surroundings).

For example consider the pendulum example given in the last section. In real life there is friction and the pendulum will gradually slow down until it comes to rest. We can define the pendulum as the system and everything else as the surroundings. Due to friction there is a small but steady transfer of heat energy from the system (pendulum) to the surroundings (the air and the bearing upon which the pendulum swings). Due to the 1st law of thermodynamics the energy of the system must decrease to compensate for the energy lost as heat until the pendulum comes to rest. [Remember though the total energy of the universe remains constant as required by the 1st Law.]

When it comes time to work homework, quiz and exam problems (not to mention to design a power plant or computer chip) the 1st Law of Thermodynamics will be much more useful if we can express it as an equation.

DE = q + w (1st Law of Thermodynamics)

• DE ® The change internal energy of the system,
• q ® The heat transferred into/out of the system,
• w ® The work done by/on the system.

This reformulation of the 1st Law tells us that once we define a system (remember we can define the system in any way that is convenient) the energy of the system will remain constant unless there heat added or taken away from the system, or some work takes place.

Internal Energy

We have already discussed work and heat extensively, but a few comments are in order regarding internal energy. The internal energy encompasses many different things, including:

• The kinetic energy associated with the motions of the atoms,
• The potential energy stored in the chemical bonds of the molecules,
• The gravitational energy of the system.

It is nearly impossible to sum all of these contributions up to determine the absolute energy of the system. That is why we only worry about DE, the change in the energy of the system. This saves all of us a lot of work, for example:

• if the temperature doesn’t change we can ignore the kinetic energy of the atoms,
• if no bonds are broken or destroyed we can ignore the chemical energy of the system,
• if the height of the system doesn’t change then we can ignore gravitational potential energy of the system.

Our convention for DE is to subtract the initial energy of the system from the final energy of the system.

DE = E(final) – E(initial) = q + w

In a chemical reaction the energy of the reactants is E(initial) and the heat of the products is E(final).

Sign Convention

When working numerical problems we will quickly become confused if we don’t adopt a universal convention for when we use a positive sign or a negative sign.

Sign Convention for heat, q

• Heat is transferred into the system ® q > 0
• Heat is transferred out of the system ® q < 0

Sign Convention for work, w

• Work is done upon the system by the surroundings ® w > 0
• Work is done by the system on the surroundings ® w < 0

Lets look at some processes to get a better feel for defining a thermodynamic system and using the proper sign convention.

Example

Hold a piece of ice in your hand until it melts

Solution A

• System ® You
• Surroundings ® Ice + the rest of the universe
• q < 0 ® Heat flows out of the system (you) into the ice.

Solution B

• System ® Ice
• Surroundings ® You + the rest of the universe
• q > 0 ® Heat flows into the system (ice) from you.

You can see that the answer changes depending upon how you define the system, but the physical reality is exactly the same, but both solutions A and B are correct. It doesn’t matter how you define the system as long as you are consistent.

Example

Consider the evaporation of sweat from your body.

Solution A

• System ® The sweat
• Surroundings ® Your body + the rest of the universe
• q > 0 ® Heat flows into the system (sweat) from you in order to raise the kinetic energy of the sweat molecules enough to allow them to go from the liquid phase to the gas phase.

Solution B

• System ® You
• Surroundings ® The sweat + the rest of the universe
• q < 0 ® Heat flows out of the system (you) into the sweat.

Since heat leaves your body this cools you down. That’s why we sweat after all.

Example

Consider the combustion process that occurs in the cylinder of an automobile:

2C8H18(l) + 25O2(g) ® 16CO2(g) + 18H2O(g)

because the reaction produces a greater amount of gas than is consumed, not to mention gives off excessive heat which causes the product gases to expand, the reaction pushes the piston upward against the force of gravity and the tension of the camshaft (or something like that, to be honest I’m really stretching my knowledge of an automobile engine here). The point is that this process involves some work.

• System ® The reactants and products
• Surroundings ® The piston, cylinder, engine + the rest of the universe
• q < 0 ® The reaction gives off heat which is dissipated in the engine (thus the need for radiator coolant).
• w < 0 ® The system (octane, oxygen, CO2 and H2O) does work on the surroundings by pushing the piston upwards.

Exothermic and Endothermic Reactions

Since heat transfer is an important component of many processes special words have been created to describe the direction of heat flow in a process. Primarily we will use these terms when referring to chemical reactions.

Exothermic Reactions

• q < 0
• reaction releases heat (heat leaves the system)
• heat is a product of the reaction (i.e. explosions, combustions, etc.)

Endothermic Reactions

• q > 0
• reaction absorbs heat (heat enters the system)
• heat is a reactant in the reaction

P-V Work

Most chemical reactions either give off or absorb heat, but not all chemical reactions do a significant amount of work. By far the most common types of work associated with chemical reactions are:

• Electrical work (i.e. batteries, fuel cells, etc.)
• Mechanical work done by an expanding or contracting gas

At this point in the course we will not concern ourselves with electrical work (until chapter 20). Therefore, we only have to worry about work when a gaseous product or reactant is involved (for example the previous example of the reaction that takes place in the automobile cylinder).

Let us return to 1st Law equation with the restriction that the only type of work we will consider is done by the expansion/ contraction of a gas (think of the cylinder example).

DE = q + w = q - (F ´ d) = q - FDh

where F is the force opposing the upward push of the cylinder, and Dh is the distance we move the cylinder upwards against this force. The negative sign in front of the second term comes from the sign convention for work. If the gas expands then Dh will be positive and the system will do work on the surroundings (the piston), and when that happens work must be negative. Now we use the relationship:

P = F/A ® F = PA

where F = force, P = pressure, and A = Area, so that:

but the cross sectional area of the cyliner (piston) multiplied times Dh is simply the change in the volume of the cylinder:

DE = q - PDV

Of course this expression is only useful if the pressure is constant throughout the reaction. Under such conditions we will call the heat transfer by a special name, enthalpy (H). The first law then becomes:

DE = DH - PDV

Where DH is the change in enthalpy that occurs at constant pressure

DH = H(final) – H(initial) = qp

At first you might think that constant pressure reactions are a special case, so that enthalpy isn’t a terribly useful concept. As it turns out any reaction which is carried out in an open container (such as a beaker or a test tube) is a constant pressure reaction. Therefore, as you will soon see enthalpy is a concept that we will use over and over again.

State Functions

State Function ® Any quantity whose value is independent of its history.

The concept of a state function is a very simple one, which is best illustrated through a few examples.

Example

Lets say I move two bricks from the sidewalk outside McPherson Hall to the roof of the building so that the change in elevation of both bricks is exactly the same. However, lets say I don’t take the same route to get to the roof in each case.

Brick A ® I carry this brick directly up the stairs to the roof.

Brick B ® I first carry this brick over to high street because I have to stop by the bank. Then having some money I stop into BW-3 to get a pint of beer. Then I wander over to my office in Newman and Wolfrom to check my e-mail. Finally I go back outside and then take the stairs up to the roof of McPherson.

The change in height, and thus the change in gravitational potential energy is exactly the same for both bricks, whereas the amount of work expended to complete the task is much greater for brick B. Now if you come along the next day and see that the bricks have been moved to the roof, by measuring the change in elevation you can immediately determine what the change in gravitational potential energy was. However, unless you know exactly what I did you cannot know the work involved in the process of moving the bricks. Thus, DEpot = mgDh is a state function, while work is not.

Example

Consider two beakers of water. I raise the temperature of beaker A to 80° C using a bunsen burner. I attempt to raise the temperature of beaker B in the same manner, but accidentally heat up to 90° C instead. At this point I turn the burner off to let the water cool. I unexpectedly get called away and when I return the temperature of beaker B is now 50° C, so I have to heat it again to get to 80° C.

You can see that while the temperature is a state function (a sample at 80° C is at 80° C regardless of what temperature it was 2 hours ago), while the amount of heat transferred into or out of a system is very dependent upon the history of the system, so that heat is not a state function.

Generally we will not know the history of the system, so it becomes imporant to work with state functions whenever possible.

Quantities which are state functions ® DE, DH, DV

Quantities which are not state functions ® w, q