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Thermodynamics Y Y Shan

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Chapter 2 The First law of thermodynamics

2.1 Some concepts: thermodynamic Process, Quasi-static process, Reversibleprocess

A thermodynamic processmay be defined as the energetic evolution of a system

proceeding from an initial state to a final state. These processes, changing from one state

to another, can be classified as the followings depending on their specific conditions:

(i) An isobaric processoccurs at constant pressure (Constant pressure process)

(ii) An isovolumetric process is one in which the volume is held constant

(constant volume process)

(iii) An isothermal processoccurs at a constant temperature.

(iv) An adiabatic process is a process in which there is no energy added or

subtracted from the system by heating or cooling. The system is said to be thermally

insulated from its environment (surroundings) and its boundary is said to be a thermal

insulator.

(v) An isentropic process occurs at constant entropy. For a reversible process

this is identical to an adiabatic process.

(vi) An isenthalpic processintroduces no change in enthalpyin the system.

A processcan also be defined as a quasi-static one or a reversible one depending

on its evolution:

A quasistatic process is a process that happens infinitely slowly from one

thermal equilibrium state to another. It often ensures that the system will go through a

sequence of states that are infinitesimally close to equilibrium,

A reversible process (or a reversible cycle if the process is cyclic) is a process

that can be "reversed" by means of infinitesimal changes in some property of the system

without loss or dissipationof energy.

In some cases, it is important to distinguish between reversible and quasistatic

processes. Reversible processes are always quasistatic, but the converse is not always true.

For example, an infinitesimal compression of a gas in a cylinder where there exists

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friction between the piston and the cylinder is a quasistatic, but not reversible process.

Although the system has been driven from its equilibrium state by only an infinitesimal

amount, heat has been irreversibly lost due to friction, and cannot be recovered by simply

moving the piston infinitesimally in the opposite direction.

2.2 Energy transfer: Work and Heat

There are two ways of exchanging or transferring energies between a system and

its surroundings (also called environment, reservoir). One is bydoing workand the other

is byheat transfer.

2.2.1

Work

Mechanical work is the amount of energy transferred by a force. It is a scalar

quantity, measured injoules(symble: J) in SI units. Mechanical work can be taken as a

rather general definition of work:

, or

FdsdW =

Where: C is the path or curve traversed by the object; F is the force vector; s is the

position vector.

In thermodynamics, the concept of thermodynamic work is slightly more general

than that of mechanical work because it includes other types of energy transfers as well.

Forms of work that are not evidently mechanical in fact represent special cases of

this principle. For instance, in the case of "electrical work", an electric fielddoes work

on charged particles as they move through a medium. In addition to mechanical work

(moving mass), electrical work(moving charge), there are many other forms of work,

such as: polarization work(changing polarization of a dielectric solid), magnetization

work(changing the magnetization of a paramagnetic solid), etc.Electrical work:

EdQdWEdQWf

i

Q

Q== , ,

Where Qi, Qf, are the amount of charges for initial state and final state.

Polarization work:

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EddWEdW

f

i

== , ,where i, f, are the total polarization of material at initial state and final state,

respecively.

Magnetization work:

BdMdWBdMWf

i

M

M== , ,

where Mi, Mf, are the total magnetization of material at initial state and final state,

respecively.

(a) PV work and PV diagrams for gas

PV workoccurs when the volume of a gas (a fluid) changes.

For the circular piston shown below, he calculation of work for this case is

straightforward:

s.VvolumeF/A,Ppressurewhere

:bysimplydrepresentebecanworkPV

,

A

PdVW

PdVAdsA

FFdsW

f

i

f

i

f

i

f

i

V

V

s

s

V

V

s

s

==

=

===

Also, PV work is often represented by its differential form:

Eq2-1

W= work being done onto the system by environment.

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P= external pressure (which usually equals to the pressure of the system during quasi-

static process). V= volume of the system.

It should be noticed that the W or dW is defined as the work done to the system,

when

1. 0i.e.,0 = dVPdVdW , meaning the volume decreases, the system

receives work from surroundings(environment, reservoir), or to say that the

environment does work to the system.

2. 0i.e.,0 >== baV

VVVPPdVW

a

b

For a process from state a to b:

energylosessystemSot,environmenthework todoessystemor

system,thework tonegtivedoestenvironmenThe

,0)(

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In this process, the volume stays constant; V= 0. W=PV= 0. This means that there

is no PV work done in this process.

PV work in general can be visualized in PV-diagram as the area under the

pressure-volume curve(PV curve) which represents the process taking place. The more

general expression for work done is:

One important conclusionfrom the above discussion about work (read also Page 5,6):

Looking into the above examples of PV work, it can be seen that PV work is path-

dependent, but only depends on the endpoints of the initial state and final state.

From a thermodynamic perspective, this fact implies that PVwork is nota state function.

The path here in the discussion is a curve in the Euclidean space, infinitely many

such curves are possible connecting initial state and final state.

The dimension of the Euclidean space is specified by the state coordinates

(parameters) of the system. For e.g, the PV-diagrams above forms only a 2-D Euclidean

state space, because only two state coordinates, P and V are used.It must be emphasized that all thermodynamic work WC (not just the PV work

discussed above), in general, is explicitly a function of the path Cand depends on every

detail of the path C. Therefore, like PV work, all thermodynamic work functions are not

state function.

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2.2.2 Heat

Heat, symbolized by Q, is a form of energy. It is defined as the kind of energy

transferred from a high temperature object (system) to a lower temperature object

(system). Heat can be transferred between objects by radiation, conduction and

convection.

In thermodynamics, Q is said to be the heat absorbed from the surroundings

(environment) by a system. Its conventional sign is that:

Q>0, means a system absorbs heat from its surroundings,

Q

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In a classic experiment in 1843, James Joule showed the energy equivalence of

heating and doing work by using the change in potential energyof falling masses to stir

an insulated container of water with paddles. Careful measurements showed the increase

in the temperature of the water to be proportional to the mechanical energy used to stir

the water. At that time calories were the accepted unit of heat and joules became the

accepted unit of mechanical energy. Their relationship is found to be:

Joule's apparatus for measuring the mechanical equivalent of heat.

2.3 Internal energy

The above examples indicate that a system in a low temperature state can get to a

high temperature state (or vise verse) through different thermodynamic processes.

Starting from the initial low temperature state to reach the final temperate state does not

depend on what specific forms of processes are. This fact tells us that we can define a

state function to describe the possible states. Therefore, a state function, namely the

internal energy is introduced.

Internal energy, microscopically defined, is the sum of all microscopic forms of

energy of a system, referring to the invisible microscopic energy on the atomic and

molecular scale. It is related to the molecular structure and the degree of molecular

activity and may be viewed as the sum of kinetic and potential energies of the molecules

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For example, a room temperature glass of water sitting on a table has no apparent

energy, either potentialor kinetic . But on the microscopic scale it is a seething mass of

high speed molecules traveling at hundreds of meters per second.

Internal energy, symbolized by U, is a state function of a system, and an

extensive quantity. Strictly speaking, the internal energy cannot be precisely measured.

This is because only changes in the internal energy can be measured, and the total

internal energy of a given system is the difference between the internal energy of the

system and the internal energy of the same system at absolute zero temperature. Since

absolute zero cannot be attained, the total internal energy cannot be precisely measured.

2.3.1 More discussion and clarification among temperature, heat, and internal energy

From the zeroth law, we know that when a high temperatureobject is placed in

contact with a low temperature object, then energy will flow from the high temperature

object to the lower temperature object, and they will approach an equilibrium temperature.

When the details of this common-sense scenario are examined, it becomes evident that

the simple view of temperature is embodied in the commonly used kinetic temperature.

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The above figures illustrate faster molecules striking slower ones at the boundary

will increase the velocity of the slower ones and decrease the velocity of the faster ones,

transferring energy from the higher temperature to the lower temperature region. With

time, the molecules in the two regions approach the same average kinetic energy (same

temperature) and in this condition of thermal equilibrium there is no longer any net

transfer of energy from one object to the other. A higher temperature simply implies

higher average kinetic energy.

A theoretical definition of temperature says:

"Temperature is a measure of the tendency of an object to spontaneously give up energy

to its surroundings. When two objects are in thermal contact, the one that tends to

spontaneously lose energy is at the higher temperature.

To describe the energy that a high temperature object has, it is not a correct use of

the word heat to say that the object "possesses heat", it is better to say that it possesses

internal energyas a result of its molecular motion. The word heat is better reserved to

describe the process of transfer of energy from a high temperature object to a lower

temperature one.

Surely you can take an object at low internal energy and raise it to higher internal

energy by heating it. But you can also increase its internal energy by doing work on it,

and since the internal energy of a high temperature object resides in random motion of

the molecules, you can't tell which mechanism was used to give it that energy.

Internal energy involves energy on the microscopic scale. Molecules in materials have

not only kinetic energy but also potential energy associated with the intermolecular

attractive forces. A simplified visualization of the contributions to internal energy can be

helpful.

Systems with the same temperature do not have the same internal energy:

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Internal Energy Example

When the sample of water and copper are both heated up by 1C, the addition to

the kinetic energy is the same, since that is what temperature measures. But to achieve

this increase for water, a much larger proportional energy must be added to the potential

energy portion of the internal energy. So the total energy required to increase the

temperature of the water is much larger, i.e., its specific heat is much larger.

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2.4The first law and its differential form

The first law of thermodynamics is an expression of the universal law of

conservation of energy, and identifies heat transfer as a form of energy transfer. The

most common enunciation of the first law of thermodynamics is:

The change in the internal energyof a thermodynamic system is equal to the amount of

heat energy added to the system minus the workdone by the system on the surroundings

Eq.2-2

The first law makes use of the key concepts of internal energy, heat, and system work. It

is used extensively in the discussion of heat engines. It is typical to see in other

references the following expression of the first law:

WQU += Eq.2-3

It is the same law, of course, just that W is defined as the work done on the system

instead of work done by the system.

Clarification of two definitions of work, W:

Systemwork( Wsys): work done by the system on the environment, the W in Eq.2-2 is

the Wsys.

Environment work(Wenv): work done by the environment on the system. The W in

Eq.2-3 is the Wenv.

envsysWW =

The differential form of the mathematical statement of the first law is:

WQdU = , Eq.2-4

if W denotes the system work, or it can be expressed as:

WQdU += ,

if Wdenotes the environment work.

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Where dU , Q and W express the infinitesimal amount. The infinitesimal heat and

work are denoted by rather than d because, in mathematical terms, they are inexact

differentials rather than exact differentials. In other words, there is no function Qor W

that can be differentiated to yield Qor W

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