Physics 3 (PHYF144)
Chap 1: Temperature
-1–
1.1 Temperature and the Zeroth Law of Thermodynamics
Temperature T is a measure of how hot or cold an object is. The SI unit of temperature is
Kelvin (K). Alternative units: degree Celsius ( C) and degree Fahrenheit ( F).
Situation:
Coffee
(Initially at higher T)
Thermometer
(Initially at lower T)
As the thermometer is brought into thermal contact with the coffee, the
thermometer becomes hotter and the coffee cools off a little because of heat
transfer between these two bodies.
After the thermometer settles down, the system is in thermal equilibrium.
Two bodies are said to be in thermal equilibrium if both bodies have the same temperature.
Thermal contact: Two objects are said to be in thermal contact if heat is allowed to pass from
one to the other. This exchange of heat is because of the difference in temperature of the two
objects.
Heat is a form of energy in transit, and NEVER the amount of energy contained within a
particular system. The SI unit of heat is Joule (J);
Other unit: Calorie (with capital C) = 1000 calories = 1 kcal;
1 cal = 4.186 J
The zeroth law of thermodynamics states that if objects A and B are separately in thermal
equilibrium with object C, then objects A and B are in thermal equilibrium to each other even
in the absence of any physical contact between them.
Thermal insulating wall
A
Thermal
conducting walls
A
B
Therefore,
C
Practical example of object C: a thermometer.
If A is not in thermal equilibrium with B, then TA
A
TA
C
B
B
TB
TB .
The zeroth law of thermodynamics is the basis of how a thermometer operates. At thermal
equilibrium, the temperature of the thermometer is equal to the temperature of the environment
(surroundings).
Trimester 1, 2010/2011
Physics 3 (PHYF144)
Chap 1: Temperature
-2–
1.2 Thermometer* and Temperature Scales
Thermometer is a device to measure temperature of a system.
Its operation is based on how a physical property of matter changes with temperature; i.e. the
thermometric quantity.
Thermometric quantity
Volume of a liquid
Electrical resistance of a conductor
Glowing color of an object
Pressure of a gas at constant volume
Thermometer
Mercury thermometer
Resistance thermometer
Optical pyrometer
Constant volume gas thermometer
The most common thermometer in everyday use is the mercury thermometer, which
consists of a mass of mercury liquid in a glass capillary tube. The volume of mercury, thus the
length of the mercury column, increases when heated. In this case the thermometric quantity is
the change in volume of a liquid. Any temperature change is proportional to the change in
length of the liquid. Based on this physical quantity, a temperature scale can be established.
Calibration:
Before a thermometer can be used, it must be calibrated first by associating the
measurable aspect of the its physical property with few known temperatures. The ice and steam
points of water are the calibration points of a thermometer.
The freezing temperature of water is called the ice point and defined to have a
temperature of 0 C = 32 F. ( C: degree Celsius; F: degree Fahrenheit)
The boiling temperature of water is called the steam point and defined to have a
temperature of 100 C = 212 F.
Once the liquid levels in the thermometer have been established at these points, the column is
divided into 100 equal segments for Celsius temperature scale (or into 180 equal segments for
Fahrenheit temperature scale), each denoting a change in temperature of one Celsius degree (or
one Fahrenheit degree).
The conversion between the Celsius and Fahrenheit temperature scales:
0 C = 32 F
100 C = 212 F
Temperature interval: 100 C = 180 F or
5C =9F
So,
or
TF
9
Tc
5
TC
5
(TF
9
32
32)
Thermometers, such as mercury thermometer and resistance thermometer, calibrated in
this way do agree at 0 C and 100 C, but they may not agree exactly at intermediate
temperatures because they have different thermometric properties. In additions, thermometer
has its limited temperature range. A mercury thermometer, for instance, is not useful below the
freezing point of mercury, which is 39 C.
Ideally, we need a universal thermometer whose readings are independent of the substance
used. The gas thermometer approaches this requirement.
Trimester 1, 2010/2011
Physics 3 (PHYF144)
Chap 1: Temperature
-3–
The Constant-Volume Gas Thermometer* and the Absolute Temperature Scale
Scale
Calibration:
Place the flask in an ice-water
bath, and raise or lower the
mercury column B until the gas is
at its original volume say 0 on the
scale.
p gas,0 C
pa
2
h
3
0
1
gh0 C
B
Repeat with a boiling bath, and
raise height of column B until to
get the same volume of gas.
Mercury
Gas
Flexible hose
p gas,100 C
pa
gh100 C
T to be measured
P (Pa)
To measure the temperature of a
substance, the flask is placed in thermal
contact with the substance. Then, we
have the gas pressure ps , and the
temperature of the substance Ts is
interpolated from the graph.
p
A BT
Ps
Ts
0 C
100 C
T ( C)
Using different volumes of dilute gas, we find that all lines extrapolate back to the same
temperature T = –273.15 C, where the pressure inside the thermometer is zero.
This temperature is called absolute zero.
TK
TC
273.15
p (Pa)
p CT (T in kelvins)
p
C constant
T
T ( C)
273.15 C
0 C
100 C
T (K)
0K
(lower limit)
Trimester 1, 2010/2011
273.15 K
(no upper limit )
Physics 3 (PHYF144)
Note:
Chap 1: Temperature
Temperature difference, T:
Temperature, T
1 C
-4–
1 C = 1 K = 1.8 (=180/100) F
1 K; 1 C = 274.15 K
[ TC = TK]
[TC
TK ]
Example: 30 C = (273.15+30) K; 30 C = 30 K
Example 1: Converting Temperature
The body temperature of a child in fever is 104 F. What is this temperature in degrees Celsius
and in kelvin?
5
TC
(TF 32)
9
TK TC 273.15
5
(104 32)
40 273.15
9
313 K
40  C
Exercise: At what temperature is the Fahrenheit scale reading equal to the Celsius scale
reading?
Answer: 40 F = 40 C
Example 2: The ratio of pressures of a gas at melting point of lead and its pressure at the triple
point of water, when the gas is kept at constant volume, is found to be 2.1982. What is the
Kelvin temperature of the melting point of lead? [The triple point of water is a unique
combination of temperature and pressure at which solid water (ice), liquid water, and water
vapor can all coexist. The temperature at triple point of water is 0.01 C = 273.16 K ]
From above graph of pressure versus temperature in kelvin, p
T
p1
T1
p2
T2
T2
p2
T1
p1
C
constant .
(2.1982)(273.16 K ) 600.46 K
Exercise: A pressure of 10 mm Hg is measured at the tripled-point of water using a constantvolume gas thermometer, what will the pressure be (in mm Hg) at 50 C?
Answer: 11.8
1.3 Thermal Expansion of Solids and Liquids
Generally, objects expand when heated. If temperature of a metal rod is raised by T, then the
length increases by amount L:
L
or
L
L0
Initial length at To
L0 T
Lo (T To )
Average coefficient of linear expansion (K-1 or C
Applications: bimetal strips in thermostats and relays.
For volume expansion, all 3 dimensions expand:
V
For area expansion,
Trimester 1, 2010/2011
A
Vo T
2 Ao T
3 Vo T
where
3
-1
)
Physics 3 (PHYF144)
Chap 1: Temperature
-5–
The unusual behavior of water*:
Water contracts (to higher density) as it cools down to 4 C but
then expands (to lower density) as it further cools to 0 C.
Hence ice floats.
0 C
4 C
If water behaved like most substances, contracting
continuously on cooling and freezing, lakes would freeze solid
and destroy all plant and animal life that cannot withstand the
freezing.
T
Example 3: In a hot day, a truck loaded with 37000 L of diesel. Suddenly, the rain fell and
temperature dropped by 23.0 K. Given the average coefficient of volume expansion diesel =
9.50 10-4 /C . Find V.
V
Vo T
(9.50 10
808 L
4
C  1 )(37000L)( 23.0 C o )
Exercise 1: A bridge is made with segments of concrete 50 m long. If the linear expansion
coefficient is 12 10-6 C 1, how much spacing (in cm) is needed to allow for expansion during
an extreme temperature change of 150 F ?
Answer: 5.0
1.4 Macroscopic Description of an Ideal Gas
F
For an ideal gas (approximated by a dilute real gas):
pV
nRT
Nk BT
R = 8.31 J/mol-K = universal gas constant
R
kB
= Boltzmann’s constant
NA
n = # of moles (=
Gas
# of molecules, N
)
Avogadro's number, N A
V = volume, m3
p = pressure, Pa
Note: 1.0 atm = 1.013 105Pa
T = temperature, K
(1 Pa = 1 Nm-2)
Example 4: Squeezing a tank of gas
p1 = 120 kPa
V1 = 35 10-3 m3
p2 = 240 kPa
T1 = 300 K
V2 = 20 10-3 m3
T2 = ?
(Initial state)
Trimester 1, 2010/2011
(Final state)
Physics 3 (PHYF144)
Chap 1: Temperature
-6–
Since there is no gas escapes during the compression, n remains constant.
Therefore,
pV nRT
p 2V2
T2
T1
pV
p1V1
nR constant
T
(240 kPa)(20 10 3 m 3 )
300 K
p1V1 p 2V2
(120 kPa)(35 10 3 m 3 )
T1
T2
343 K
Exercise: One mole of an ideal gas has a temperature of 25 C. What is the final temperature
(in C), if the volume is held constant and the pressure is doubled?
Answer: 323 C
Trimester 1, 2010/2011