Work, Heat, and the First Law of Thermodynamics

1
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
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)

3
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

4
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

5
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

6
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
7
Work in some special processes

• Isochoric Process W 0
• Isobaric Process W -P?V
• Isothermal Process

Work depends on path
8
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

9
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.

10
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.

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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 transforred, causes the
  gas to expand and do the work to environment

12
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.

13
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.

14
Problem 45 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

15
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)

16
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 ?T
Tf-Ti, But different amount of Heat is required.
?T at constant volume
?T at constant pressure
Cv is the molar specific heat at
constant Volume. Cpis the molar specific heat at
constant pressure
17
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)