Fluid dynamics

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Liquid thermometers
Based on thermal expansion of liquids. The
liquids are held in little vessels at the bottom.
At higher temperatures they expand and climb
toward the top of narrow capillaries.
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How to calibrate a liquid thermometer?
You need some reference temperatures. You may
want to stick the thermometer into boiling water
and melting ice, hoping that those set two
well-defined temperatures. You will find the
liquid expended and its column risen. What next?
We can divide the column height difference into N
(say, N 100) even intervals and call them
degrees. Would it be a good temperature
scale? Would it be the same, no matter what
liquid we use?
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Liquid thermometers
Coefficients of thermal expansion
b fractional increase of volume per one degree

• Problems
• Liquid is a rather complex state of matter.
  Molecules in liquids are held together by
  cohesive forces, different for different liquids.
• The coefficients of thermal expansion vary a lot
  between liquids, and may depend on temperature in
  an extreme fashion.
• Liquids freeze at low temperatures and boil at
  high temperature. So the ranges of operation of
  the liquid thermometers are restricted.

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Gas thermometer
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Gas thermometer
Gasses are much simpler than liquids. The
molecules are moving freely most of the time, and
only once in a while suffer short term
collisions. The collision events are still
different for different molecules.
BUT when the gasses are rarified (low density)
and the collisions are rare behavior of different
gasses in the gas thermometer becomes very much
the same!
In order not to change the gas density, it is
preferable to keep the gas volume constant and to
measure the gas pressure.
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Gas thermometer
Level of the mercury in the right tube is varied
to keep the level in the left tube
constant. Pressure of the gas is measured as P
rgh
The absolute temperature of the system is defined
as
P3 is pressure of the gas at a special reference
point called triple point, which is unique and
can be reproduced in every laboratory.
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Gas thermometer
To set the temperature scale we need some
convenient reference points. 273.15 K, the same
as 0 C is the temperature of ice melting at
normal pressure 373.15 K, the same as 100 C is
the temperature of water boiling at normal
pressure
1K temperature difference is the same as 1 C
temperature difference, but 0 K corresponds to
-273.15 C.
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Temperature scales
Fahrenheit
Celsius
Lord Kelvin
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Thermometers summary.

• Thermometers always measure their own
  temeparature.
• For a thermometer to measure the temperature of
  the system of interest, it needs to be brought
  into thermal equilibrium with the system (and
  better insulated from everything else).

• A thermometer must be much smaller than system.
• For fast temperature measurements, it should be
  small and have low heat capacity.

An array of miniature thermometers
An array of bolometers
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Heat is not a material or a from of matter.
Heat is energy in transit!
When pouring water you transfer it from one
vessel to another and you get more water in the
second vessel.
In thermodynamics you transfer heat but you
usually end up having more or less internal
energy.
Heat is positive when the system of interest
obtains it.
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What are common results of heat transfer?

• Growth of temperature.
• A phase transition (melting ice).
• Mechanical work.
• In cases 2 and 3 there may be NO temperature
  variation.

Case 1, no phase transition or work done. How
much does the temperature vary?
Heat capacity of the object C, measured in J/K
tells you how much Joules of heat you need to
transfer to increase the temperature of the
object by 1 K (or 1 ºC).
Heat is energy in transit! Positive, when
obtained.
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Heat capacity of the object C, measured in J/K
tells you how much Joules of heat you need to
transfer to increase the temperature of the
object by 1 K (or 1 ºC).
The term heat capacity is used for historic
reasons and is confusing! It sounds as if the
object contains heat, whereas by definition
heat is energy in transit. An object contains
some internal energy (not heat!) and its
temperature is a measure of this internal energy.
An analogy from mechanics you do some work on an
object and the object gains the same amount of
energy (kinetic, potential) as a
result. Mechanical work also relates to a
process, not state.
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Heat capacity is an extensive (integral)
parameter When you bring two objects together,
heat capacity of the system of the two objects
becomes the sum of the two individual heat
capacities.
It is convenient to introduce specific heat, c,
which is heat capacity of a material per unit
mass. Specific heat is measured in J/(K?kg).
Heat capacity of a water balloon is large due to
both high specific heat and large mass of the
water inside the ball.
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Specific heat, c, is heat capacity of a material
per unit mass. Specific heat is measured in
J/(K?kg).
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The equilibrium temperature.
Situation two objects with different
temperatures, T1 and T2, are brought in a thermal
contact and reach thermal equilibrium at a
temperature T after a while.
Heat DQ1 is transferred to Object 1 heat DQ2 is
transferred to Object 2. By energy conservation
By definition of heat capacity and specific heat
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Heat transfer

• Conduction.
• Convection
• Radiation

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SettingA rectangular slab of thickness Dx and
with an area A.The front side of the slab is at
a temperature T the back side has a somewhat
different temperature, TDT.We are trying to
calculate the heat-flow rate, the amount of heat
flowing through the slab per unit time,H DQ/Dt.
We expect H to be proportional to

the area of the slab, the temperature
difference, DT, between the back and the front
and inversely proportional
to the
thickness of the slab, Dx. H should also somehow
depend of properties of the material the slab is
made of