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phase : kx ± ωt
kx − ωt ⇒
kx + ωt ⇒
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Wave traveling in + x direction
Wave traveling in - x direction
k=
2π
λ
ω=
2π
T
'
y ( x,t) = [ 2y m sin kx] cosωt
antinodes
node
Question – Answer time
Chapter 11.7-: Angular Momentum
Chapter 12: Equilibrium
Chapter 13: Gravity
Chapter 14: Fluids
Chapter 15: Simple Harmonic
Oscillations
Chapter
18:
Temperature,
Heat,
and
Thermodynamics
Definitions
“System”- particular object or set of objects
“Environment” - everything else in the universe What is “State” (or condition) of system?
- macroscopic description - in terms of detectable quantities:
volume,
pressure, mass, temperature
(“State Variables”)
Study of thermal energy --> temperature
Temperature
&
Thermometers
Linear scale : need 2 points to define Fahrenheit [° F]
Celsius [° C]
body temp and ~1/3 of body temp ~100 ° F
~33 ° F
“freezing point” and “boiling point” of water
0°C
100 ° C
Kelvin [K]
Absolute zero and triple point of water
0K 273.16 K Conversion factors

T
=
T
−
273.15
K→ ° C C
K
° C → ° F
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TF = 95 TC + 32 
(1 ΔK = 1 Δ C)
18‐4:
Measuring
Temperature
Need two points
and linear scale
T=absolute zero
Water triple
point.
Phase Diagram of Water
18‐4:
Measuring
Temperature
Triple Point of Water: Defined as T3=273.16 K
The Constant-Volume Gas Thermometer
A gas filled bulb is connected to a Hg
manometer. The pressure volume can
be maintained constant by raising or
lowering the the Hg level in reservoir R.
T of liquid defined at T=Cp
p = p0 + ρ g(−h)
(C=constant)
 p
 p
T = T3   = (273.16K )  
 p3 
 p3 
18‐4:
Measuring
Temperature
The Constant-Volume Gas Thermometer
A gas filled bulb is connected to a Hg manometer.
The pressure volume can be maintained constant by
raising or lowering the the Hg level in reservoir R.
T of liquid defined at T=Cp
p = p0 + ρ g(−h)
 p
 p
T = T3   = (273.16K )  
 p3 
 p3 
Still have a problem because answer depends upon p.

p
T = (273.16K )  lim p→0 
p3 

Keep V fixed: Figure shows
Measurement for boiling water
Fahrenheit originally established a scale in
which the temperature of an ice-water-salt
mixture was set at 0 degrees.
18‐4:
Temperature
Scales
Checkpoint
1:
The
figure
here
shows
three
linear
temperature
scales
with
the
freezing
and
boiling
points
of
water
indicated.
(a) Rank the degrees on these scales by size, greatest first.
18‐4:
Temperature
Scales
Checkpoint
1:
The
figure
here
shows
three
linear
temperature
scales
with
the
freezing
and
boiling
points
of
water
indicated.
(b) Rank the following temperatures, highest first: 50oX, 50o W and 500 Y
Thermal
expansion
Most substances expand when heated and contract when cooled ZrW2O8 is a ceramic with negative thermal expansion over a wide temperature range, 0-1050 K
The change in length, ΔL ( = L - L0 ), of almost all solids is ~ directly proportional to the change in temperature, ΔT ( = T - T0 )
α = coefficient of thermal expansion ΔL = αL 0 ΔT
L = L 0 (1 + αΔT )
What causes thermal expansion?
Thermal
expansion
of
the
Brooklyn
Bridge
Problem 1: Brooklyn Bridge Expansion
The steel bed of the main suspension bridge is
490 m long at + 20°C. If the extremes in
temperature are - 20°C to + 40°C, how much will
it contract and expand? [ α steel = 12 ×10−6 (°C) –1 ]
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The solution is to use expansion joints
α steel = 12 ×10−6 (°C) –1
ΔL = α steel L0ΔT
= 12 ×10−6 (°C) –1 (490m)(60°C)
= 35 cm
Example:
Bimetal
Strip
Common device to measure and control
temperature
F = kx = kL0 (1 + αΔT )