Energy Heat Work Enthalpy Heat Capacity · 5.07.2010 · Energy –1: Energy Heat Work Enthalpy Heat Capacity ... BTU = British Thermal Unit ... Heat and work are equivalent ways

Energy – 1:Energy

Heat

Work

Enthalpy

Heat Capacity

1 © Prof. Zvi C. Koren 21.07.10

Thermodynamics = Thermo + Dynamics

Classical “Thermo”:

empirical derivation of the laws

(this course)

Statistical “Thermo”:

theoretical derivations via statistical quantum mechanics

(if you “dare” to go there in the future …)

Laws of Thermodynaics:

0th, 1st, 2nd, and 3rd Laws


Thermodynamics, is it an “easy” subject?From: http://www.journaloftheoretics.com/Articles/2-3/tane-pub.htm

It is well known that while being very efficient in practice, the thermodynamic

tool remains difficult to understand from the theoretical point of view.

It is also well known that the difficulties encountered are not mathematical, but

rather conceptual, and that they are perceived by those who have to learn

thermodynamics as well as by those who have to teach it.

The reality of the conceptual difficulty is openly and rapidly evocated rather than

cancelled as a forbidden subject.

One of the best examples is that given by the following opinion of the great

physicist Arnold Sommerfeld about thermodynamics:

"The first time I studied the subject, I thought I understood it except for a few minor points.

The second time, I thought I didn't understand it except for a few minor points.

The third time, I knew I didn't understand it, but it did not matter, since I could use it effectively."

Arnold Johannes Wilhelm Sommerfeld Born: 5 Dec 1868 in Königsberg, Prussia (now Kaliningrad, Russia)

Died: 26 April 1951 in Munich, Germany 3 © Prof. Zvi C. Koren 21.07.10

1. What is the maximum amount of work that can be performed by an

engine?

2. Which processes are spontaneous, and which need to be “kicked”

into action?

3. Which battery system is the most efficient?

What can “Thermo” do for us?

Etc., etc., etc. …


Thermodynamics = Thermo + Dynamics

U

U (or E) = Internal Energy

What is meant by “internal” energy?

U is connected to the important (relevant) processes.

Total Energy = Internal Energy + External Energy

U (or E) f(position, velocity)

For example, if a chemical rxn occurs in a beaker, which is in a

moving train, or on somebody’s head or on the ground (different

potential energies due to height, position) what are we really

interested in?


Forms of Energy

Kinetic Energy(Energy of Motion)

Mechanical(macroscopic objects in motion)

Thermal(submicroscopic motions of atoms, molecules, and ions)

Electrical(movement of electrons through a conductor)

Radiant(electromagnetic radiation –photons – propagating through space)

Potential Energy(Energy of Position)

Gravitational(objects held in a certain position against the force of gravity)

Electrostatic(positive and negative charges held in close proximity)

Chemical(energy attractions of electrons and nuclei in molecules)


Interconversions of Kinetic Energy

Electrical

Mechanical

Thermal

Radiant

Generator

Steam

Engine

HeatLamp

Heater

LightBulb

SunlightSolarCell

Stirrer


Interconversions of Kinetic & Potential Energies

Mechanical

Kinetic Energy Potential Energy

Thermal

Electrical

Radiant

Gravitational

Electrostatic

Chemical

ElevatorWaterwheel

Fallingmeteor

Staticcling

Lightning

Car engine

Wood

burning

Battery

Fireworks

Spaceshuttle


Energy Units

SI unit = Joule (J)

1 J = 1 kg·m2/s2 = 1 V·C = 1 Pa·m3

1 cal 4.184 J (exactly), cal = calorie

1 BTU = 1054.35 J, BTU = British Thermal Unit

1 kW·h = 3.6x106 J, kWh = kilowatt hour

1 L·atm = 101.325 J (exactly)

1 cal = energy needed to raise the temperature of 1 g of water by 1oC.

1 “dietary calorie” is 1 Cal (“big calorie”) = 1 kcal.

Values & Units of R, Gas Constant:

0.0821 L·atm/mol·K

1.99 cal/mol·K

8.31 J/mol·K

James Prescott Joule (1818 - 1889)

English physicist


System & Surroundings

NO thermal or,

e.g., mechanical

links to the outside

world

Closed with respect

to matter, but there

are thermal and,

e.g., mechanical

links to the outside

world

Open to everything


Diathermic vs. Adiabatic Walls

insulation

T2 > T1


State Functions

State Variables:P, V, T, n

properties that depend only on the state itself and not on the “history” of that state

Examples

Thermodynamic Properties:U (or E) = Internal EnergyH = EnthalpyS = EntropyG = Gibbs Free EnergyA = Helmholtz Free Energy

Path Functionsproperties that depend on the process – the way the change is brought about

Examplesw (or W) = work (compression, expansion, stirring, electrical, …)q (or Q) = heat

Heat is heat!!! But work could be many things!12 © Prof. Zvi C. Koren 21.07.10

The Existence of Temperature

&

The Zeroth (0th) Law of Thermodynamics

A

B C

Thermal

Equilibrium

Thermal

Equilibrium

Thermal

Equilibrium

That is, they’re all at the same T


First Law of Thermodynamics

Infinitesimal changes (differential form): dU = đq + đw

Finite changes (integral form): U = q + w

dx = exact differential = (מסויים)דיפרנציאל שלםđx = inexact differential (“dee-slash”) or x

The system does not “know” whether q and/or w were used to change its energy, U. We can tell, but the system is “blind”.

Heat and work are equivalent ways of changing a system’s energy.The system is like a “bank”: It accepts deposits in either “currency”,

but stores its reserves as internal energy.

two methods of changing the energy of a system

For example, as Lord Rumford noticed while working in a cannon

factory, drilling into metal increased the temp, as if it was heated.

Thus, w can have a similar affect as q in raising the U.

Benjamin Thompson Rumford (1753-1814)


System

State 1 State 2

(P1,V1,T1,n1) (P2,V2,T2,n2) :גַדלים מדידים

q

w

U = U2 - U1

U1 U2

(תחילי וסופי)תלוי במצבי הקצה

U = q + w

Schematic of Energy Changes in a System


U = q + w

2. The equation is NOT any of the following:

U is a state function

q and w are path functions

U = q + w

or

U = q + w

Notes about :

3. q & w are algebraic quantities (+ or –):

A positive quantity is one that increases U, so:

q = +, heat absorbed by system from surroundings: endothermic process

–, heat released by system to surroundings: exothermic process

w = +, work done on the system by the surroundings (e.g., compression)

–, work done by the system on the surroundings (e.g., expansion)

4. While q & w are path-dependent, their sum is “amazingly” invariant.

Other examples? (length of a vector, Hess’s Law, etc.)

1. First Law is for a closed system (closed to material, but open to q and w)


Δxxxdx if

f

i

j

j

x

1

Back to First Law – Differential Form

& The Meaning of dx and đx :

dU = đq + đw

State i State fqtotal

đq1 đq2 đq3 …

= x1+x2+x3+ ··· = xi

f

i

f

dU = đq + đw dU = đq + đw U = q + w

Differential Form Integral Form

đx =(BIG x)

i

f

đx (đq, đw)dx (dU)

inexact differential exact differential

infinitesimal QUANTITY of x

đx = little bit of x: x1 đx1, etc.

infinitesimal CHANGE in x (between close states)

đx = x dx = xi

f


How can we tell

whether a differential is exact (dz) or inexact (đz)?If “z” is a state function, where z=z(x,y), then:

dyy

zdx

x

zdz

xy

partialderivative

totaldifferential

xy y

zN

x

zMNdyMdxdz

& ,

xy

z

x

z

yy

M

xyx

2

yx

z

y

z

xx

N

yxy

2

order of

differentiation

is irrelevant

aldifferentiexact an is then , and if So, dzx

N

y

MNdyMdxdz

yx

and z is a state function!!! (The reverse is also true.)18 © Prof. Zvi C. Koren 21.07.10

More Two-Way Mathematical “Streets”

For State & Path functions:

(cycle integral מסלול סגור) 0 dx(Why?)

constantdx f

i

f

i

đx f(integration path)

dx is an exact differential x is a state function (property)

If then

then If

đx is an inexact differential x is a path function (property)

x is a state function (property)

x is a path function (property)

x is a state function (property)

19 © Prof. Zvi C. Koren 21.07.10Additional Problems on Exactness

For an isolated sysytem (sys + surr), U is saved and dU = 0:

Why is U a State Function?

Energy (and mass) cannot be created or destroyed:

“Law of Conservation of Energy (and mass)”Why? Because!!! (Perpetual motion or perpetuum mobile machines do not exist.)

1 2

U = q + w

qa,wa;Ua

qb,wb;Ub

Ua = –Ub, otherwise we WILL be able to create or destroy energy

qa vs. qb, wa vs. wb, Ua vs. Ub ?

U is a State Function

dU = 0


Documents

Energy Heat Work Enthalpy Heat Capacity · 5.07.2010 · Energy –1: Energy Heat Work Enthalpy Heat Capacity ... BTU = British Thermal Unit ... Heat and work are equivalent ways