Chapt. 17. Work, Heat, and the First Law of Thermodynamics - PowerPoint PPT Presentation

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Chapt. 17. Work, Heat, and the First Law of Thermodynamics

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Chapt. 17. Work, Heat, and the First Law of Thermodynamics Mechanical Energy Emech = K + U If there are only conservative forces ( ex. Gravity force, spring force) in ... – PowerPoint PPT presentation

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Title: Chapt. 17. Work, Heat, and the First Law of Thermodynamics


1
Chapt. 17. Work, Heat, and the First Law of
Thermodynamics
  • Mechanical Energy Emech K U
  • If there are only conservative forces ( ex.
    Gravity force, spring force) in the system ?Emech
    ?K ?U 0
  • If there is friction forces ?Emech ?K ?U
    Wfric lt 0
  • General case ?Emech ?Eth Wext
  • ?Eth is the change of thermal energy and Wext is
    the work done by the external force.
  • The systems we want to study in thermodynamics
    are stationary containers gases or liquids, whose
    center-of mass mechanical energy does not
    change. Thus ?Emech 0

2
Stop to think 17.1 page 508Stop to think
17.2 page 513Stop to think 17.3 page 516Stop
to think 17.5 page 521Stop to think 17.6 page
529
  • Example 17.2 page 512
  • Example 17.3 page 520
  • Example 17.4 page 521
  • Example 17.7 page 524

3
Thermal Energy
  • Thermal energy Eth is associated with the
    systems temperature. We now need to be a bit
    more specific
  • During a phase change, from solid to liquid or
    from liquid to gas, a systems thermal energy
    increases but its temperature does not.
  • If there are no phase changes, increasing the
    systems temperature increase its thermal energy.
  • A systems thermal energy does not change
  • (?Eth 0) during an isothermal process (?T
    0)

4
0.10 mol of a montomic gas follows the process
shown in the Figure, What is the total change in
thermal energy of the gas?
5
Work
  • Work is the energy transferred between a system
    and environment when a net force acts on the
    system over a distance.
  • The sign of the work
  • Work is positive when the force is in the
    direction of motion
  • Work is negative when the force is opposite to
    the motion

6
Heat
  • The energy transferred in a thermal interaction
    is called heat
  • The symbol for heat is Q
  • The energy equation now becomes
  • ?Esys ?Emech ?Eth Wext Q
  • Quick quiz A gas cylinder and piston are covered
    with heavy insulation. The piston is pushed into
    the cylinder, compressing the gas. In the
    process. The gas temperature
  • Increases
  • Decreases
  • Doesnt change

7
Work in Ideal-Gas Processes
  • The work done on the system
  • When we press the gas, the gas volume becomes
    smaller, so the total work done by the
    environment on the gas

8
Work in some special processes
  • Isochoric Process W 0
  • Isobaric Process W -P?V
  • Isothermal Process

Work depends on path
9
Finding work from the P-V diagram
  • W the negative of the area under the PV curve
    between Vi and Vf

W lt 0
W gt 0
10
Heat and Thermal interactions
  • Heat is the energy transferred during a thermal
    interaction
  • Units of heat
  • The SI unit of heat is joule.
  • Historically, unit for measuring heat, is calorie
  • A cal the quantity of heat needed to change the
    temperature of 1 g of water by 1 oC.
  • 1cal 4.186 J
  • 1 food calorie 1 Cal 1000 cal 1 kcal

11
Distinguish between heat, temperature, and
thermal energy
  • Thermal energy is an energy of the system due to
    the motion of its atoms and molecules. Thermal
    energy is a state variable, it may change during
    a process. The systems thermal energy continues
    to exist even if the system is isolated and not
    interacting thermally with its environment
  • Heat is energy transferred between the system and
    the environment as they interact. Heat is not a
    particular form of energy, nor is it a state
    variable. Heat may cause the systems thermal
    energy to change, but that does not mean that
    heat and thermal energy are the same thing.
  • Temperature is a state variable, it is related to
    the thermal energy per molecule. But not the same
    thing.

12
The first Law of thermodynamics
  • ?Esys ?Emech ?Eth W Q
  • Here we assume the system mechanical energy does
    not change ?Emech 0
  • ?Eth W Q work on system heat to system (
    first law of thermodynamics)
  • The first law of thermodynamics is the law of
    conservation of energy.
  • The first law of thermodynamics doesnt tell
    us anything about the value of Eth only how Eth
    changes, doing 1 J of work changes the thermal
    energy
  • by ?Eth 1 J.
  • The systems thermal energy isnt the only thing
    that changes. Work or heat that change the
    thermal energy also change the pressure, volume,
    temperature, and other state variables. The first
    law tells us only about ?Eth . Other law and
    relationship must be used to learn how the other
    state variables change.

13
First-Law bar chart
  • The isochoric process.
  • The final point is on a lower isotherm than the
    initial point, that is Tf lt Ti. No work is done
    (W0) in this process. Heat energy was
    transferred out of gas (Q lt 0) and thermal energy
    of gas decreased (?E lt 0) as the temperature
    fell.
  • ?Eth E (th f) E( th i) W Q
  • The isothermal process. ?T 0
  • ?Eth 0 , therefore W -Q
  • The heat energy is transfered, causes the
    gas to expand and do the work to environment

14
Specific Heat
  • What happens to a system when you change its
    thermal energy?
  • The temperature of the system changes
  • The system undergoes a phase change, such as
    melting or freezing
  • Specific Heat C The amount of energy that
    raises the temperature of 1 Kg of
  • A substance by 1 K ( or 1C) is called specific
    heat. In other words, the
  • thermal energy of the system changes by
  • ?Eth Mc ?T ( Kelvin and Celsius temperature
    scales have the same step size. )
  • The first law of thermodynamics ?Eth W Q ,
    In working with solids
  • And liquids, we almost always change the
    temperature by heating, so W 0,
  • Then the heat needed to bring about a temperature
    change ?T is Q Mc ?T .
  • Molar specific heat The amount of energy that
    raises the temperature of 1 mol
  • of a substance by 1K. It depends on the molar
    mass.
  • Table 17.2 (page 527) list few specific heat and
    molar specific heats of solids and
  • Liquids.

15
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16
Phase change and heat of transformation
  • A phase change is characterized by a change in
    thermal energy without change in temperature
  • Heat of fusion Lf the heat of transformation
    for 1 Kg substance between a solid and liquid.
  • Heat of vaporization Lv the heat of
    transformation for 1 Kg substance between a
    liquid and gas.
  • Q M Lf melt/freeze
  • Q M Lv boil/condense
  • Table 17.3 list few melting/boiling temperatures
    and heat of transformation.
  • For systems that undergo a temperature change, Q
    Mc (Tf Ti).
  • For systems that undergo a phase change Q ML,
    Supply the correct sign by observing whether
    energy enters or leaves the system during the
    transition.

17
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18
Problem 44 your 300 ml cup of coffee is too hot
to drink when served at 90 C. what is the mass of
an ice cue, taken from a 20C freezer, that will
cool your coffee to a pleasant 60 C
  • There are two interacting systems coffee (i.e.,
    water) and ice. Changing the coffee temperature
    from 90C to 60C requires four steps (1) raise
    the temperature of ice from -20C to 0C, (2)
    change ice at 0C to water at 0C, (c) raise the
    water temperature from 0C to 60C, and (4) lower
    the coffee temperature from 90C to 60C.
  • Solve For the closed coffee-ice system,Q
    Q(ice) Q(coffee) 0
  • Q (ice) Q (ice, -20C 0) Q ( melting)
    Q(water, 0 60c)
  • Q (coffee) m(cof)C(water) (60-90)
  • Q (coffee) 0.3 Kg (4190 J?kg) ( -30) -37,710
    J
  • Suppose the mass of ice is M
  • Q (ice) 41800 M 330,000 M 251,400 M 37710
    J
  • M 0.0605 kg 60.5 g

19
Quiz Objects A and B are brought into close
thermal contact with each other, but they are
well isolated from their surroundings. Initially
TA 0 oC and TB 10 0 oC. The specific heat of
A is less than the specific heat of B. The two
objects will soon reach a common final
temperature Tf . The final temperature is
  • a. Tf gt 50 oC
  • b. Tf 50 oC
  • c. Tf lt 50 oC
  • Answer a
  • QA QB 0
  • MACA(Tf 0) MBCB(Tf 100)0
  • CA(Tf 0) CB(100-Tf)

20
The specific heats of gases
  • The heat required to cause a specified
    temperature change depends on the process by
    which the gas changes

Process A and B, which start on the Ti And end on
the Tf, have the same temperature Change ÄT
Tf-Ti, But different amount of Heat is required.
ÄT at constant volume
ÄT at constant pressure
Cv is the molar specific heat at
constant Volume. Cpis the molar specific heat at
constant pressure
21
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22
Cp and Cv
  • ?Eth (constant volume process) W Q 0
    nCv?T nCv?T
  • ?Eth (constant pressure process) W Q -p?V
    nCp?T
  • If both have the same ?T, ?Eth in tow process is
    the same
  • -p?V nCp?T nCv?T
  • Using the ideal gas law, in constant-pressure
    process
  • p?V nR ?T
  • -nR ?T nCp?T nCv?T
  • Cp Cv R
  • ?Eth nCv?T (any idea-gas process)
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