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Reporter: Hsieh, Tsung-Lin
QuestionA wire with weights attached to each end
is placed across a block of ice. The wire may pass through the ice
without cutting it. Investigate the phenomenon.
Outline
Experimental setupTypical resultsHypothesisPressure effect
WeightThermal conductivityCurvature
Other effectSummary
Experimental Setup
Weights
Camera
Ice
Typical ResultThe wire position is
obtained by MATLAB program.
Duration: 1 hr
Pressure EffectIce under the wire tends to melt.
Heat
Temperature
Pressure
GasSolid
LiquidAtmospheric pressure
Wire pressure
Ice
Schematic Phase Diagram
Temperature
Pressure
GasSolid
LiquidAtmospheric pressure
Wire pressure
Absorbing heat
Cutting
Ice+Water
Schematic Phase Diagram
Hot
Cold
Temperature
Pressure
GasSolid
LiquidAtmospheric pressure
Releasing heat
Ice
Schematic Phase Diagram
Hot
Cold
Pressure effectWeightThermal conductivityCurvature
Hot
Cold
Speed at CenterSpeed of the center of the wire after it sinks
into the ice.
distance
Weight
3kg: 0.114kg: 0.185kg: 0.266kg: 0.307kg: 0.398kg: 0.49
(cm/min)
Stainless steel wire 0.4mm
Weight vs. Speed at Center
Stainless steel wire 0.4mm
Temperature
Pressure
gs
l
Mathematical Estimation• Heat conducting rate:
• From Clausius-Clapeyron equation,
• Center speed upper limit
• Pressure effect plays an important role.
l
d
A0
0lnT
TTLP
)( AvLdt
dmLT
d
Ak
dt
dQ
min/10 1cmv
Hot
Cold
Material vs. Speed at Center
Thermal Conductivity
(W/m-K)Aluminum : 235 Steel : 16.3Good thermal
conductor cuts faster.
speed: 0.30 cm/min
speed: 0.34 cm/min
Water Flow Video
Pressure and Curvature
θ θ
θ θ
T T
rd
T
dr
T
A
F
*2
sin2
r
d
IceCross-section of the Wire
curvature1
r
Cutting SpeedAfter the whole wire sinks into the ice:
Pressure effect dominates
center
Left side
External heat input is more significant
External Heat EffectWater melts due to
external heat input It can solidify again
because the temperature inside the ice is below 00C (-150C~ -0.60C).
External heat
SummaryThe wire passes through the ice
Pressure effectExternal heat effect
The ice regelates (without being cut)Pressure releasesTemperature inside the ice is below 00C
Thank you for your attention.
Ambient TemperatureThe “speed at
center” is almost constant.
Repeatable in different temperature (230C~280C).
Ambient heat can be neglected.
Weight
6kg: 0.124kg: 0.063kg: 0.05
(cm/min)
Temperature inside the Ice
Time interval: 5 min
Time interval: 5 min
Curvature vs. SpeedAt the Beginning of Cutting:
Pressure effect dominates
centerLeft side
Patterns formed on regelated ice
Speed v.s. Curvature –at time 1In the middle of the ice,
speed is positively related to the curvature.
The speed is faster at both side because of external heat.
Fig. Speed of the whole wire
Fig. Acceleration
Speed v.s. Curvature –at time 2In the middle of the ice,
speed is positively related to the curvature.
The speed is faster at both side because of external heat.
Fig. Speed of the whole wire
Fig. Acceleration
