T' K' Ng, HKUST

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HK IPhO Training class (thermodynamics)
T. K. Ng, HKUST
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Lecture I
(1) Introduction to fluids. (2) Zeroth and first
law of thermodynamics
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Introduction to fluids
A fluid is a substance that can flow and conform
to the boundaries of any container in which we
put them. e.g. water, air, glass.
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Basic properties of fluids
Density (mass per unit volume) - Pressure
(force per unit area) -
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Basic properties of fluids
Pressure (force per unit area) -
Notice that from definition, pressure may depend
on direction. However, this is not the case for
static fluids. (why?).
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Basic properties of fluids
Pressure (force per unit area) -
Unit of pressure 1 pascal (Pa) 1 Newton per
square meter. 1 atm. 1.01 x 105 Pa
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Fluids at rest
Pressure increases when we go deeper into water
why?
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Fluids at rest
Pressure of a fluid in static equilibrium depends
on depth only
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Example
Which one of the four container fluid has
highest pressure at depth h?
How about if (d) is move up (down) by distance h?
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Pascals Princple

• A change in the pressure applied to an enclosed
  incompressible fluid is transmitted undiminished
  to every portion of the fluid and to the walls of
  the container as a direct consequence of Newtons
  Law.

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Example Hydraulic level

• Applied force Fi ? change in pressure
  ?pFi/AiFo/Ao.
• Therefore output force is FoFiAo/Ai.
• Therefore
• Fo gt Fi if Ao gt Ai
• How about work done?

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Archimedes Principle

• Buoyant force upward force in liquid because of
  increasing pressure in liquid as one goes down
  below the surface.
• (a) a hole in water. Notice that the hole is in
  static equilibrium if it is filled with water.

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Archimedes Principle

• (a) a hole in water. Notice that the hole is in
  static equilibrium if it is filled with water.
• Therefore the upward force mfg, mf mass of
  displaced water.

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Archimedes Principle

• (b) The hole in water is replaced by a solid with
  the same shape.
• Since nothing changes in water, therefore the
  upward force mfg, mf mass of displaced water
  buoyant force

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Archimedes Principle

• (c) The solid in water is replaced by a piece of
  wood with mw lt mf..
• In this case the wood float on the surface with
  Fbmwg.

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Archimedes Principle

• When a body is fully or partially submerged in a
  fluid, a buoyant force Fb from the surrounding
  fluid acts on the body. The force is directed
  upward and has a magnitude equal to the weight
  mfg of the fluid that has been displaced by the
  body.

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Archimedes Principle

• Question Imagine a large sphere of water
  floating in outer space. The sphere of water is
  formed under its own gravity. Is there any
  buoyant force if an object enters this sphere of
  fluid?

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Flowing liquids

• The continuity equation conservation of mass in
  a incompressible liquid flow.

v velocity of fluid flowing through area A in
the tube
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Example

• What is the volume flow rate of water if
  Ao1.2cm2, A0.35cm2 and h45mm.

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Bernoullis Equation

• Bernoullis Equation is a consequence of
  conservation of energy in steady flow.

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Bernoullis Equation

• Bernoullis Equation is a consequence of
  conservation of energy in steady flow.

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Bernoullis Equation

• Adding together, we obtain

(Bernoullis Equation)
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Example

• What is the speed v of the water emerging from
  the hole?
• Show that v22gh (same as free fall)

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Thermodynamics (I)

• Temperature equilibrium
• Temperature
• - something we can all feel (hot/cold)
• - measured in Kelvin (SI unit)
• - there exists a lower limit ( 0 K) but
  apparently no upper limit. (room temperature
  300 K)

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Thermodynamics (I)

• Physics of Temperature
• Fundamental question Under what physical
  condition the temperatures of 2 objects are
  equal? (Notice this is independent of the scale
  we used to measure temperature)

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Thermodynamics (I)

• Physics of Temperature
• We assume (based on daily life experience) is
  that if two objects (in a closed environment) are
  in contact with each other for long enough time,
  they will reach thermal equilibrium (stop
  changing) ? same temperature

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Thermodynamics (I)

• Physics of Temperature
• Furthermore (zeroth law of thermodynamics) If
  bodies A and B are each in thermal equilibrium
  with a third body T, then they are in thermal
  equilibrium with each other.

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Thermodynamics (I)
Zeroth law of thermodynamics
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Thermodynamics (I)
Temperature Scales The Celsius and Fahrenheit
Scales -can relate to the Kelvin scale using
the following rules (Celsius) (Frhrenheit)
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Heat and Temperature

• Question What changes physically when the
  temperature of an object changes?

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Heat and Temperature

• We call the change heat(Q)
• Unit of heat calorie(cal) amount of heat needed
  to raise the temperature of 1g of water from
  14.5C to 15.5C, i.e. any physical process that
  can make the above change is said to provide 1
  calorie of heat.

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Heat and Temperature

• Unit of heat calorie(cal) amount of heat needed
  to raise the temperature of 1g of water from
  14.5C to 15.5C, i.e. any physical process that
  can make the above change is said to provide 1
  calorie of heat.
• Notice that nowadays we know heat is a form of
  energy and 1 cal. 4.186 Joule.

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Heat and Temperature

• Heat Capacity (C) of an object
  - is the proportionality constant between an
  amount of heat and the change in temperature that
  it produces in the object.
• Usually Q C(Tf-Ti), Ti, Tf are initial and
  final Temperatures of the object.

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Heat and Temperature

• Specific Heat (c)
• Heat Capacity per unit mass of a material
• Unit cal/g.K or J/kg.K
• Molar Specific Heat (c)
• Heat Capacity per mole of material (1 mole
  6.02x1023 elementary units)
• Units J/mol.K

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Heat and Temperature
Almost constant
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Heat and Temperature
In general we have to specify the
conditions under which heat transfer occurs to
define specific heat, since different conditions
may lead to different values of specific heat.
For example, cV and cP are specific heats
measured at constant volume and pressure,
respectively. For gases, the difference between
the two is large.
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Heat and Temperature
When heat is absorbed by a solid or liquid,
the temperature may not rise. Instead, heat may
simulate a transformation of the sample from one
state, or phase, to another. For example, ice to
water or water to water vapor. The temperature of
the sample remains unchanged in the process. The
amount of heat per unit mass that must be
transferred when a system undergoes a phase
change is called Heat of Transformation L. The
total heat transferred by a sample of mass m is
QLm
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Heat as a form of energy
Question How do you know that heat is a form of
energy as used in mechanics? Ans If heat is a
form of energy, we expect that there should be a
way to use heat to do work (heat engine).
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A simple Heat-Work System

• Work- controlled by lead shots which exert
  pressure on the system.
• Heat - controlled by thermal reservoir which
  changes temperature.
• System - characterized by Pressure (P),
  Temperature (T) and Volume (V).

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A simple Heat-Work System

• Work- adding or removing lead shots ? piston
  displaced by amount ds.

dVchange in volume
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A simple Heat-Work System

• Total Work done in changing volume from Vi to Vf

Notice temperature remains fixed.
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A simple Heat-Work System

• Notice we can also change the volume by heating
  the system. This is an example of converting heat
  energy (raising temperature) to work done (change
  in volume)

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P-V diagram

• To find out what is the work done in a general
  thermodynamics process we use P-V diagram.
• E.g.

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P-V diagram

• Total Work done area under curve.
• (a) Wgt 0, Q (Heat) unknown?
• (b) (ia) W gt 0, Q gt 0 (system heats up),
• (af) W 0, by adjusting Pressure and
  Temperature together
• (c) (b) in reverse order
• (d) Wighf gt Wicdf
• (e)W lt 0, when volume decreases, but keeping
  pressure gt0.
• (f) Thermodynamic cycle, net work done gt 0.
• Problem How about Q?

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First Law of Thermodynamics

• When a system changes from a given initial state
  to a final state, the work done W and the heat Q
  are different for different path of changes.
  However, the quantity Q -W always remains the
  same for all paths. It depends only on what are
  the initial and final states.

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First Law of Thermodynamics

• The change in (internal) energy of the system is
  given by

or in differential form,
Indicating that there are two ways to change the
(internal) energy of a system.
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First Law of Thermodynamics

• Example The figure at the right shows four paths
  on a p-V diagram along which a gas can be taken
  from state i to state f. Rank the paths according
  to (a)the change ?Eint, (b)The work done W by the
  gas, and (c) the magnitude of the heat transfer
  Q, greatest first.

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First Law of Thermodynamics

• Example Ideal gases.
• For all gases, when the densities of the gases
  are low, they all tend to obey the same law,
  PVnRT (Ideal gas law) where n is the number of
  moles of gas present, and R is a universal
  constant, called gas constant, with value R
  8.31J/mol.K.
• the number of elementary units (atoms/molecules)
  in one mole of the material 6.023 x 1023
  (Avogadros number).

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Work done by Ideal gases (examples)

• (1)Isothermal processes (Temperature kept
  constant) ? PnRT/V

(2) Constant Pressure processes
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Example
Initially, containers A and B are kept at
temperatures and pressures PA,PB and TA,TB,
respectively, with VB4VA. What will be the final
pressure of the system if the valve is opened
with TA and TB kept the same?
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Example
Initially,
After valve opened
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Example
Using the Ideal Gas Law and Archimedes
Principle, estimate what is the minimum
temperature needed to heat up a hot air balloon
with volume 1m3 and mass 2.0g such that the
balloon rises at atmospheric pressure and room
temperature (300K). (R8.31J/mole.K. Take molar
mass of air to be 29g/mole ). How about if the
volume is (0.1m)3?
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Example
buoyant forcemmolar(n1-n2)g 0.002g
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