THERMAL EXPANSION
TEMPERATURE and THERMAL EXPANSIONThermal Expansion It is a
phenomena whereby dimensions of a substance change as temperature
changes. Generally, dimensions increase as temperature increases (
with few exceptions).
Note: Water, in the temperature range from 0C to 4C, decreases
in volume with increasing temperature. In this range, its
coefficient of volume expansion is negative. Above 4C, water
expands. At this temperature, density is maximum.
Thermal ExpansionAmount of expansion depends onchange in
temperatureoriginal lengthNature of the substance (coefficient of
thermal expansion)
Types of Expansion:Linear Expansion : Change in Length , L = L0
TArea Expansion : Change in Area, A = A0 TVolume Expansion : Change
in Volume , V = V0 T
Temp: TTemp: T+TL0LWhen temperature risesmolecules have more
kinetic energy (they are moving faster)consequently, things tend to
expandhas more internal energy thanThe amount of internal energy
depends on the temperature
Concept QuestionAs you heat a block of aluminum from 0 C to 100
C its density 1. Increases 2. Decreases 3. Stays the sameT = 0 CM,
V0r0 = M / V0T = 100 CM, V100r100 = M / V100 < r0Concept
QuestionAn aluminum plate has a circular hole cut in it. A copper
ball (solid sphere) has exactly the same diameter as the hole when
both are at room temperature, and hence can just barely be pushed
through it. If both the plate and the ball are now heated up to a
few hundred degrees Celsius, how will the ball and the hole fit (a
(aluminum) > a (copper) ) ? 1. The ball wont fit through the
hole any more 2. The ball will fit more easily through the hole 3.
Same as at room temperatureThe aluminum plate and copper ball both
have different coefficients of thermal expansion. Aluminum has a
higher coefficient than copper which means the aluminum plate hole
will expand to be larger than the copper ball's expansion and allow
more space for the ball to pass through.Why does the hole get
bigger when the plate expands ???Object at temp TSame object at
higher T:Plate and hole both get largerImagine a plate made from 9
smaller pieces. Each piece expands. If you remove one piece, it
will leave an expanded hole
Thermal Stress Stress that is developed if there is change in
temperature but change in dimension is prevented.
Stress= F/ARecall:Y = stress/strainStress = Y (strain)Strain =
L/L0L = L0 T ; L /L0 = T
Stress = - Y TForce,F = -Y A T Equations:
Linear ExpansionFinal length L = L0 +L = L0 + L0 T L= L0 (1+ T
)Area Expansion Final Area A = A0 +A= A0 + A0 T A= A0 (1+ T )
Volume ExpansionFinal Volume V= V0 +V= V0 + V0 T V= V0 (1+ T
)where; = 2 ; = 3 - coefficient of linear expansion coefficient of
area expansion coefficient of volume expansionSample
problems:1.Steel rails are laid when the temperature is 15C. if the
maximum temperature expected is 45C and the length of each rail is
10m, find the gap between successive rails. Use steel =11x10 -6
/C.
2. A rod of radius 1.0 cm is suspended from the ceiling at a
temperature of 50C. It is to be cooled to a temperature of -10C.
Find a) force needed to prevent contraction b) stress developed at
this condition. Consider Y = 11x1010 N/m2 and =10x10 -6 /C.
Sample problems:3. An 80 gal steel drum is filled with gasoline
when the temperature is 20C. Find the volume of gasoline that will
overflow when temperature becomes 70C. Use steel =11x10 -6 /C and
gasoline = 9.6 x10 -4/ C .
4. A certain metallic rod is found to have lengthened by 0.25%
if the temperature is increased by 1000 C . What is the coefficient
of linear expansion of the rodSample problems:5. A thin brass sheet
at 20C has the same surface area as a thin steel sheet at 0C. At
what common temperature if any will the two sheets have the same
area? Use brass = 19 x10 -6 / C and steel = 10.5 x 10 -6 / C.
6. A 50 m steel tape correctly measures distance at 10C. A
distance measured by the tape at 40C is 105.56 m. What is the
actual distance? Use steel = 11 x 10 -6 / C.
