thermo

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Temperature Heat and the
Zeroth and First Laws of
Thermodynamics
Thermodynamics
•   A principle branch of physics and engineering is
Thermodynamics: the study and application of thermal
energy-often called internal energy of systems
•   First we study in terms of bulk properties of matter then on
the microscopic scale, ie we will define temperature in terms
of kinetic energy in ch. 19
•   One of the principle concept is temperature
•   Temperature and internal energy are related through the
concept of the transfer of this energy in the form of heat and
work done a system
•   We will quantify these notions in studying systems with many
particles
•   These systems exist in various phases: ie liquid, solid and
gas or vapor
thermodynamics & the notion of temperature
• Examples of how
thermodynamics
figures into everyday
engineering and
physics is countless
• Heating of a car engine
• Heating of your dinner in a
microwave oven or a
conventional oven
• How a thermometer works!
Thermoscope
• Based on the fact that
many bodies change as
we alter their temperature
by heating or cooling
• ie volume of a liquid
increase with heating
• A metal rod grows in
length from heating
• Expansion of volume of a      Can use any one of these
gas with heating              properties as the basis of an
• Electrical resistance of a    instrument to pin down the
wire increases with           concept of temperature
heating
MUST CALIBRATE IT TO THE
TEMPERATURE SCALE
Thermoscope to Thermometer

• Based upon the Zeroth Law
of thermodynamics and
notion thermal
equilibrium
• If two bodies A and B are
each in thermal
equilibrium with a third
body T, than A and B are
in equilibrium with each
other
• ie they have the same
temperature
Temperature scale
• To set a temp. scale pick some
reproducible thermal phenomenon and
assign a certain Kelvin temperature to
its environment.
• Called a fixed point and we give it a
fixed temperature.
• Boiling point of water, freezing point of
water …
• Triple point of water is chosen: where
Liquid water, solid ice and water vapor
coexist in thermal equilibrium at a set
temperature and pressure
T=0.01o C=273.16 K
P=0.006 Atm ….
(Recall 1atm=1.01x105 Pa)
Constant Volume Gas
Thermometer
•   Standard thermometer against which all
thermometers are calibrated is based on
the pressure of a gas in a fixed volume

T  CP
T3  CP3

P           P
T  T3       273.16
P3          P3
Calibrated temperature is independent of the gas used

in a constant volume gas thermometer
•   If you decrease the gas amount the
species of gas becomes irrelevant,
that is the temperature is
independent of the gas type… as it
must be for any reliability

•   Plot shows the boiling point
temperature of water where the
amount of gas and thus p3 was
decreased to almost zero. The
temperature values converge!
Celsius and Fahrenheit Scales
•   Zero of the Celsius scale shifted to a
more convenient value than absolute
zero

Tc  T  273.15

•   Fahrenheit scale employs a smaller
degree than the Celsius scale and a
different zero of temp

9
TF  TC  32
5
Some corresponding temperatures
• Temp                         • C        F
•   Boiling point of water     •   100    212
•   Normal Body Temp           •   37.0   98.6
•   Accepted Comfort level     •   20     68
•   Freezing point of water    •   0      32
•   Zero of Fahrenheit scale   •   -18    0
•   Scales coincide            •   -40    -40
Thermal Expansion Effects on
Materials … “Material Science”
•    Linear (solids)
•    Area (solids)
•    Volume (solids and fluids)
•    Special Case:
Water above T=4o C water expands
as the temp rises, however it
contracts as the temp rises between
T=0o and 4o
Thermal Expansion
Mechanical Properties of Materials
• Many thermostats operate on this
principle, making and breaking an
electrical contact as the
temperature rises and falls

L  LT
•      coefficient of linear expansion

• Volume expansion        V  VT

  3
Sample prob
• On a hot day in Las Vegas an oil trucker
loads V=37,000 L of diesel fuel .
Encounters cold weather on the way to the
mountains of Utah, T=23.0 K. He
delivers entire load. How many liters did
he deliver? See blackboard…
THERMAL ENERGY or
HEAT
The First Law of
Thermodynamics
Temperature and Heat
• A change in the internal or
thermal energy is due to the
transfer of “heat energy”
• Heat is the energy
transferred btwn. A system
and the environment
because of a temperature
difference that exists
between them

• Heat can be positive
increasing negative
decreasing

• Units:
• Q=[1 cal=4.1868 J ]
Definitions and Units
• Heat - Energy in transit between two
substances
- symbol Q
– Units - Joule, calorie, Btu
• calorie is energy necessary to increase
1 g of H2O by 1 degree C
• Btu is energy necessary to increase 1 lb of H2O by
1 degree F
• 1 calorie = 4.186 Joule
• 1 Btu = 252 cal = 1054 J
• 1 Calorie (food) = 1 kcal
• Internal Energy - The total energy (of the
molecules) contained within a substance;
it is a function of absolute temp.
- symbol U
Heat Capacity
• The energy required to increase the
temperature of an object
Q = CT
• SPECIFIC HEAT CAPACITY is the
energy required to increase the
temperature of each unit mass or mole
of an object
– If the specific heat capacity is constant
Q  mc T        or   Q  ncT
Heat Capacity Table
Conservation of Energy or
Calorimetry
• When heat is exchanged between
substances
– apply conservation of energy
– cannot add or subtract temperatures
– heat lost by one substance equals heat
gained by another
Heat and Work toward the 1st Law
of Thermo….

Here we consider the
thermodynamic state of a
system and the process of
energy transfer due to
heat transferred to and
and work done by the
system
Pressure versus Volume
functional relationship

 
dW  F  ds  Fds   pAds  pdV
Vf       Vf
W   dW   p(V )dV
Vi       Vi
1st Law of Thermo
The combination Q-W=constant!

Eint  E f ,int  Ei ,int  Q  W
dEint  dQ  dW

• Internal energy of a system tends to increase if energy is added
as heat Q and tends to decrease if energy is lost as W done on
the system
• System is not isolated as was the case in chapter 7
Special Cases of 1st Law

Q0
•   Constant Volume     W 0
•   Cyclical     Eint  0
•   Free Expansion W  Q  0

process where no
transfer of heat
occurs between
the system and
environment and
no work done on
the system.
Conservation of Energy or
Calorimetry
Example: 100 g of liquid water at 20 oC is in an aluminum
calorimeter cup having a mass of 50 g and in thermal
equilibrium. 80 g of copper at 95 oC is added to the container.
What is the final (equilibrium) temperature of the copper,
water and aluminum cup?
Hint: Apply conservation of energy
Sample 18-5
• M=1kg of H2O atT=100o C
converted to steam by
boiling at P=1Atm.
• Vi=1.0x10-3 m3 ,
• Vf=1.67 m3
• How much work done on
system?
• How much energy
transferred as heat during
process?
• What is the change in
system’s internal energy
during the process?
Ideal Gas Law Ch. 19
• When comparing sample
sizes we will uses moles or
so we can be certain we are
comparing samples that
contain the same number of
atoms.
•     N A  6.02 10 23
1
mole

M sam ple       M sam ple
n               
M m ole          mN A
M  mass of one mole of substance
m  mass of a molecule of substance
N
• Equation of state for a gas…              PV  nRT  nkN AT     kN AT
NA
or
PV  NkT
Sample Problem 19-2
•   Work done by gas during isothermal
expansion
Kinetic Theory of Gases
Pressure Temp and RMS speed
•   n moles of ideal gas in a
cubical box of volume V,
and walls of box at temp T
•   What is connection
between the pressure, p
exerted by the gas on the
walls and the speeds of
the molecules?
•   Non-interacting particles
ie no Coulomb forces and
ignore contact interactions
also……

px  p f  pi  ????
Relationship between Macroscopic
and Microscopic variables
• Speed of sound in a gas
closely related to the                   2        2
nmN Avrm s nMvrm s
molecular speeds                p           
• Sound wave cant move                 3V        3V
any faster than the fastest      Use Gas Law
moving molecule               pV  nRT
3RT   3 N A kT
vrm s      
M     mN A
3kT

m
Using Basic concepts in probability
and Equilibrium Thermo
• J.C. Maxwell 1852 derives the Maxwellian
Distribution of speeds
 Mv 2
Pv   v e
2              2 RT
Distribution of Molecular Speeds

1852 basic assumptions led J.C.
Maxwell to assume
How to find the average speed
How to find the root mean
square speed
How to find the most probable
speed?
 M  2 Mv2 2 RT
Pv   4       v e
 2RT 
Specific Heats of Gases constant V from the

standpoint of molecular particle dynamics

•   Internal Energy

1 2     1 3RT            Keep volume constant
KE  mvRMS  m
2       2  M             T  T  T
1 3RT
 m                       p  p  p
2 mN A
3                        Q  nCV T
   kT  single molecule
2                        Eint  Q  W ,
3         3
E  NkT  nN A kT  nRT
3
But W  0!!!
2         2         2
Eint  nCV T
•   n moles in a volume V and
dE            3               3
temp T                           nCV  nR, since Eint  nRT
•   Add small amount of        dT V          2               2
energy to gas as heat Q by
turning up heat of         CV  12.5 J / mol  K
reservoir
Change of Internal Energy
IS CONSERVED!!!!
3
Eint  nRT  nCvT
2

Path Independence of physical
processes
Molar Specific heat at constant p
• From First Law
E  Q  W

C p  CV  R
3
Cv  R  12.5 J / mole  K
2
5
C p  R  20.78 J / mole  K
2
Specific Heats of an Ideal Gas
Molar specific heats and Internal
Energy
• Translational
• Rotational
• Vibrational ?

• J.C. Maxwell equipartition theorem
Each kind of molecule has a certain
number of degrees of free which are the
independent ways the molecule can
store energy. On average each degree
of freedom has associated with it and
energy of
1
kT - per molecule
2
1
nRT - per mole
2
A Hint of Quantum Theory

• Note that the
specific heat
seems to
change
discretely!
Cv         Diatomic Hydrogen Gas
specific heat versus
temperature T
R
Specific Heats of an Ideal Gas

Definition - a reversible (quasistatic) adiabatic process is slow
enough to allow p and T to be nearly at
equilibrium, but fast enough that no thermal energy (Q) is
exchanged with the surroundings. Or when a process is insulated
so that no heat can escape
Adiabatic Process for an Ideal Gas
Write the First Law for the process

dE  dQ  dW
nCV dT  0  pdV
Take the total differential of the
equation of state of an Ideal Gas

pV  nRT
pdV  Vdp  nRdT
pV   Const
Cp

CV
Sample Problem 19-2 and now 19-9

• Work done by gas during
isothermal expansion

find the temperature change
consider path 3 though we
are starting at

Ti  310 K
Summary Constant…
•   p – isobaric
•   T – isothermal
•   Adiabatic    pV   const.

•   V- isochoric
pV  nRT
dE  dQ  dW                 pdV  Vdp  nRdT
What really happens ….
• Contact
interactions
The effective cross section seen by a
molecule as it traverses a volume
swept out as it travels between collions.
The length of this cylnder is the mean free
path between collisions

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 views: 26 posted: 10/20/2011 language: English pages: 44