Energy, Work, and Heat

Energy and Work

Thermodynamics deals with energy in its various forms and the conversion of one form of energy into another. Energy appears in several different forms, kinetic energy, potential energy, heat, chemical energy, and so on.

Kinetic energy is energy of motion. It is written,

(1)
where m, is the mass of a moving object and v is its velocity.

Potential energy has many different forms, depending on the physical system at hand. For example,

- local gravity,

- Hook's law, compression of a spring,

- Coulomb's law,

- large scale gravity,

and so on.

Kinetic and potential energy are interchangeable and both can be converted into work.

Thermodynamics does not provide us with the expressions for kinetic energy, potential energy, or work. These must come from physics.

Mechanical work (from physics) is a force times the distance through which it acts. That is,

(2)
for one dimensional motion.

Work for a finite motion is obtained by integrating Equation (2),

(3)
where the f(x) takes into account the possibility that the force may be changing as one moves along the path from x1 to x2.

Work can increase the kinetic or potential energy of a system.

Heat

One of the great breakthroughs in the history of science was the recognition that heat is a form of energy. Since it was known that heat "flowed" from a hot body to a cold body heat was thought to be a fluid of some sort - called phlogiston. When experiment showed that the products of combustion weighed more that the object combusted, and yet the combustion process gave off heat, it was necessary to make the unlikely assertion that phlogiston had a negative mass.

Benjamine Thompson, also known as Count Rumford of the Holy Roman Empire (1753-1814) discovered the true nature of heat as a form of energy while operating a factory for boring cannon. In the process of boring the hole in the barrel of a cannon the metal got hot. Rumford was able to show that the only explanation for this phenomenon was that the work being put into turning the drill bit was being converted into heat. He even made an attempt to determine the "mechanical equivalent of heat." Joule later improved on his measurements and obtained a value close to the modern one of 4.184 J = 1 cal (in modern units).

The conclusion is that heat is a form of energy. A revolutionary conclusion for its time, but no big surprise now.

Work, kinetic energy, and potential energy can be converted into heat with no restrictions.

Heat can be converted into work, kinetic energy, and potential energy, but only with restrictions (which we will discuss in due time).

Definitions and Conventions

We define the system as the object or sample or "thing" we are interested in. The surroundings is everything else. For a given thermodynamics discussion we can say,

system + surroundings = the universe.

(Sounds a little arrogant, but it provides a useful simplification.)

We define w as the work done on the system, and q as the heat absorbed by the system. This means that w and q are algebraic quantities. They can be either positive or negative and their sign tells us which way energy is flowing. For example, if w is positive it means that work was done on the system so that the energy of the system increased, and so on. Likewise, if q is negative tahe system lost heat to the surroundings.

(In older books w was defined as the work done on the surroundings. There is a reason for this. It is sometimes easier to calculate the work done on the surroundings - see below - than to calculate work done on the system. Nevertheless, modern books use the convention given above that w is work done on the system. If you are reading an older book and there seems to be a sign error, it may be because they are using the older convention for w.)

We will define w' as work done on the surroundings. Clearly,

w' = − w.

We now define a quantity called the internal energy, U. The name of the variable, U, is self explanatory. U is the total energy contained in the system.

(Thermodynamics does not care whether or not there are atoms and molecules. Everything that we do in thermodynamics can be done without ever knowing that there are atoms and molecules. However, just to calibrate our intuition, it may be useful to say that the internal energy is the sum of all the kinetic and potential energies of all the particles in the system. We will define three other thermodynamic variables or functions which have units of energy, but none of these will have a simple description such as we have for U.

One other comment. A measurement of energy depends on where you measure the energy from. For example, the potential energy of a person standing on the surface of the earth might be considered to be zero relative to local gravity - mgh - but would be large and negative relative the large scale gravitational system such as the earth-moon system.)

The First Law of Thermodynamics

There are several word statements of the first law of thermodynamics:

Energy is conserved.

(Which is another way of saying that energy cannot be created or destroyed. You can change its form, but you cannot create it or destroy it.)

It is impossible to make a perpetual motion machine of the first kind.

(A perpetual motion machine of the first kind is a system that gives energy to the surroundings, but produces no change in the system itself and no other change to the surroundings. This statement implies that there is a perpetual motion machine of the second kind. We will find out about a perpetual motion machine of the second kind when we meet the second law of thermodynamics.)

The mathematical statement of the first law is phrased in terms of a process. Given any change or process,

initial state → final state

ΔU = UfinalUinitial ,

or

state 1 → state 2

ΔU = U2U1 .

(Initial and final states must both be at equilibrium.)

Then the first law of thermodynamics says that

ΔU = q + w.

The first law of thermodynamics is a law of observation. No one has ever observed a situation where energy is not conserved so we elevate this observation to the status of a law. The real justification of this comes when the things we derive using the first law turn out to be true - that is, verified by experiment.

(Actually there are situations were energy is not conserved. We now know that in processes where the nuclear structure of matter is altered mass can be converted into energy and vice versa. This is a consequence of special relativity were it is found that matter has a "rest energy," mc2, where m is the mass to be converted to energy and c is the speed of light. As a consequence of nuclear energy we should say that,

Energy + the energy equivalent of mass is conserved.

Then the first law would be written,

&DeltaU = q + w + Δmc2.

For chemical processes the change in energy due to changes in mass is negligible - though not zero - so we can ignore it.)

The first law can be written in differential form,

dU = dq + dw

Which is called the differential form of the first law.

(Actually, this is the differential form of the first law for a closed system, that is, for a system in which no material moves in or out of the system. Later we will write the differential form of the first law for an open system, where material can move in or out of the system.)

Note: Some writers like to use a special symbol for the d in dq and dw to indicate that these differentials are not in the same mathematical class as, for example, dU. We will not use this notation. As soon as we have learned what the difficulty is with the present d you will be expected just to remember that the d in dq and dw is different than the d in dU.

WRS

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