01 Thermal Expansion of Matter
01 Thermal Expansion of Matter
01 Thermal Expansion of Matter
Thermometry
a science which deals with the study, design, construction,
calibration and testing of a thermometer.
Thermometer a device used in measuring the temperature of a body or a
system.
Temperature (t or T) a manifestation of heat. It is the degree of hotness or
coldness of a body or a system and tells the direction of the flow of heat.
System anything that is enclosed and maybe subjected to study purposes.
Hotter
Colder
tB
tA
Temperature Scales
1. Metric (CGS and MKS)
a. Centigrade or Celsius (oC)
b. Kelvin (K)
2. English
a. Fahrenheit (oF)
b. Rankine (oR)
Fixed points used to compare temperature scales.
- temperature at which a substance undergo a change in phase
Boiling/Condensation Point(BP/CP) point at which liquid and gas co-exist at
normal pressure and at thermal equilibrium.
Freezing/Melting Point(FP/MP) point at which solid and liquid co-exist at
normal pressure and at thermal equilibrium.
Absolute Zero is a state of matter where its pressure is equal to zero and
attains its minimum possible total energy.
1
Note:
1. oC, oF, K, and oR are temperature readings directly from the
thermometer.
2. Co, Fo, , and Ro are units for any difference or change in the
temperature.
3. 1 Co = 1 K and 1 Fo = 1 Ro (observe temperature scales below)
o
o
Ex. Temperature readings: t o 20 C , t f 50 C
t t f t o 50 o C 20 o C 30C o
Temperature Scales
o
BP/CP
100
212
373.2
672
Temperature, t
tc
tf
tk
tR
FP/MP
32
273.2
492
Conversion by Interpolation
t f 32
tc 0
t 273.2
t 492
k
R
100 0 212 32 373.2 273.2 672 492
t c (t f 32)
5
,
9
9
32
5
t f tc
Thermal Expansion
- a phenomenon whereby the dimensions of a body change when its
temperature changes. Generally, when a substance are heated
(temperature is increased), they expand but when they are cooled
(temperature is decreased), they contract.
-
Expansion of Solids:
Linear Expansion
change in length due a change in temperature.
Consider a body of initial length Lo at initial temperature t o
to
tf
Lo
Lo
Change in length,
L Lo t
So
L Lot
but
L L Lo
Let
L Lo Lot
L Lo Lot
So final length
L Lo (1 t )
The relationship governing the linear expansion of a long thin rod can be
reasoned out as follows:
Area Expansion
3
Lo
t
Wo
Initial area
Final area
Ao Lo Wo
Change in area
A Ao t
So
A Ao t
A L W
A Ao (1 t )
Volume Expansion
In the same way, due to change in temperature;
Change in volume
V Vo t
V Vo 1 t
dt
Lo
Initial volume
Vo = Lo3
V L3
Final volume
Due to a change of temperature dt, the volume will change by dV
dV d ( L3 ) 3L2 dL
dV = 3Lo3 dt = 3Vo dt
V = 3Vo t = Vo t
Then
3 =
2 =
Sample Problems
1. A copper bar is 80 cm long at 15 o C . What is the increase in length when
heated to 35 o C ? The linear expansion coefficient for copper is
1.7 x10 5 o C 1 .
Ans. L 2.7 x10 4 m
L
0.039%
Lo