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					Temperature Heat and the
 Zeroth and First Laws of
•   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
•   These systems exist in various phases: ie liquid, solid and
    gas or vapor
     Questions that are addressed in
thermodynamics & the notion of temperature
                     • Examples of how
                       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!
• 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
                               MUST CALIBRATE IT TO THE
                               TEMPERATURE SCALE
   Thermoscope to Thermometer

• Based upon the Zeroth Law
  of thermodynamics and
  notion thermal
• 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
• ie they have the same
               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
•   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

          Tc  T  273.15

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

                 TF  TC  32
    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…
    The First Law of
          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

• Units:
• Q=[1 cal=4.1868 J ]
         Definitions and Units
• Heat - Energy in transit between two
  - 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
  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
• When heat is exchanged between
  – 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
   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

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

                  An adiabatic
                  process where no
                  transfer of heat
                  occurs between
                  the system and
                  environment and
                  no work done on
                  the system.
     Conservation of Energy or
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
• How much energy
  transferred as heat during
• 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
  Avagadro’s number of things
  so we can be certain we are
  comparing samples that
  contain the same number of
•     N A  6.02 10 23

         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
• Equation of state for a gas…              PV  nRT  nkN AT     kN AT
                                            PV  NkT
              Sample Problem 19-2
•   Work done by gas during isothermal
       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

                         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
 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
                                              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
                                 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
    Change of Internal Energy
      IS CONSERVED!!!!
Eint  nRT  nCvT

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

C p  CV  R
Cv  R  12.5 J / mole  K
C p  R  20.78 J / mole  K
Specific Heats of an Ideal Gas
 Molar specific heats and Internal
• 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
                     kT - per molecule
                     nRT - per mole
    A Hint of Quantum Theory

• Note that the
  specific heat
  seems to
       Cv         Diatomic Hydrogen Gas
                  specific heat versus
                  temperature T
Specific Heats of an Ideal Gas
       Adiabatic Process Q=0

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
   Sample Problem 19-2 and now 19-9

• Work done by gas during
  isothermal expansion

• Work done adiabatically and
  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
  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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