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Transcript
Chapter 14 – Temperature and Heat
Introduction
Contents:
1. Temperature and thermal equilibrium
2. Thermometer and temperature scale
3. Heat conduction
4. Heat convection and radiation
5. Thermal Expansion
Objectives
1. Explain the concept of temperature and heat
2. Define and explain thermal equilibrium and the
Zeroth Law of Thermodynamics
3. Explain physical changes of thermometric quantities
such as change of volume, length, gas pressure, electrical resistance and radiated
wavelength of hot body.
4. State the absolute temperature and the values of pressure and temperature for the
triple point of water.
5. Write and use the relationship between temperature and thermometric quantities
for ideal gas temperature scale T=
T=
x  x0
100 0C.
x100  x 0
x
273.16K and the celcius temperature scale
x0
6. Explain mechanism of heat transfer through solids and distinguish the conduction
of heat through metal and non-metal solids.
7. Define thermal conductivity and application of the equation
Q kA(T2  T1 )
for one dimensional heat transfer.

t
x
8. Investigate quantitatively heat conduction through combination of rods of
different materials, insulated and non-insulated rods, good and bad conductor.
9. explain the mechanism of natural and forced heat convection.
10. Explain the mechanism of heat transfer through radiation and use the equation of
the Stefan-Boltzmann law
11. Define and use the principle of linear, area and volume thermal expansion and
state the relationship between them.
12. Understand thermal expansion of water at 4 0C
Conceptual Map of Chapter 14
Thermal Equilibrium
Zeroth Law of
Thermodynamics
Temperature
Heat transfer
Heat
Thermometry
Thermal Expansion
Conduction
Convection
Linear
Thermometer
Temperature
Scale
Area
Volume
Radiation
INTRODUCTION
As we discuss thermal properties of a body or system, we
always relate it to temperature, a fundamental physical
quantity. How does the hot air differ from cold air? We use
thermometers to record the temperature. We also like to relate the
temperature and heat. In this chapter we would like to examine the
nature of heat and the ways in which we measure temperature.
14.1 – Temperature and thermal equilibrium
Temperature is defined as a relative measure of hotness or coldness. Scientifically, it is
a scalar quantity that is same for the two systems in thermal equilibrium.
When a hot body is in thermal contact with a cold body, gradually both bodies will
experience the same temperature. Both objects are in thermal equilibrium as two or
more systems having same temperature. It is based on the Zeroth Law of
Thermodynamics which states that if object A is in thermal equilibrium with object B,
and object B is in thermal equilibrium with object C, then object C is also in
thermal equilibrium with object A.
14.2 Thermometer and temperature scale
Temperature scale is used to determine the temperature of a body quantitatively. There
are three types of temperature scale – Celsius, Fahrenheit and Kelvin with unit of 0C, 0F
and K respectively. Fortunately, many physical properties of materials change
sufficiently with temperature to be used as the bases for thermometers. The ice point and
the steam point of water are two convenient fixed points are the temperatures at which
pure water freezes and boils under the pressure of 1 atm (standard pressure). The boiling
and freezing points is defined as equilibrium temperature for water and steam at standard
pressure.
On the Celsius scale, ice point is labeled as 0 0C and steam point as 1000C, whereas
on the Fahrenheit scale, both are labeled at 32 0F and 212 0F respectively. On the
Celsius scale, there are 100 equal intervals; on the Fahrenheit scale, there are 180
intervals. Therefore, Celsius degree is larger than a Fahrenheit degree.
Kelvin scale is introduced after it is found that the minimum temperature under this
temperature, the concept of temperature is meaningless. This temperature is
designated as the absolute zero. On the Kelvin scale, it is written as 0K, ice point as
273.15 K and steam point as 373.15K. Kelvin scale is also called as absolute
temperature scale or ideal gas law temperature scale.
The relationship of these temperature scales can be written as:
5
TC  (TF  320 )
9
9
TF  TC  320
5
TK  TC  273.15
TC is for Celsius; TF is for Fahrenheit and TK is for Kelvin.
Sample question:
If the room temperature is measured at 270C, what is temperature on the kelvin and
Fahrenheit scale?
Solution:
TK = TC +273.15
= 27 +273.15
 300K
9
TC +320
5
9
= 270 +320
5
= 80.6 0F
Note: For distinction, a particular temperature measurement, such as 200C, is written
with 0C whereas a temperature interval, such as T = 800C – 600C = 20 C0
(pronounced 20 Celsius degrees).
TF =
14.3 Thermometer
Thermometer is an instrument to measure temperature. The
operation principle is based on physical properties that
change with temperature. These properties are called
thermometric quantities. Commonly, thermometric
quantities can change linearly with temperature and be
measurable.
For instance, the thermometer that is commonly used is
mercury thermometer. The thermal expansion of mercury is
a thermometric property and the volume is used as
thermometric quantity. Due to the fixed crossed sectional
area, thermometer can have the length of the capillary of
mercury as thermometric quantity.
The following chart shows the type of thermometer with its thermometric quantity.
Type
Mercury in capillary tube
constant volume gas
Constant pressure gas
Thermocouple
Electrical resistance
Pyrometer
Thermometric quantity
length (l)
pressure (p)
volume (v)
electro motive force (emf)
resistance (ohm)
colour
A good thermometer should have following properties:
 Accuracy – big change of material thermometric quantity with respect to the
small change of temperature.
 Precision –a precise reading can be taken with respect to the real temperature
 Reliability – the same temperature can be recorded after repetitive
measurement.
 Sensitivity – thermal equilibrium can be achieved with the system and
temperature can be measured instantly.
Besides, a practical thermometer should be portable, continuously readable, fixed phase
of material that is used within the wide range of measurement and the working material
should change realistically and linearly with respect to temperature.
14.4 Relationship of temperature and thermometric quantities.
Let X be the thermometric quantity, which is p, V, R,  or l. If thermometer with
quantity X is measured at ice and steam points, Xi and Xs, the temperature T at Celsius
scale can be written as:
 X  Xi  0
T
100 C

Xs  Xi 
which X is the value of thermometric quantity at temperature T. Therefore, temperature
T can be written in Fahrenheit scale as:
 X  Xi  0
0
T
180

32
F.

Xs  Xi 
General equation for any temperature scale is as follows:
 X  Xi 
T
N  Ts

Xs  Xi 
Problem:
The length of mercury for mercury thermometer is used to measure the temperature of
unknown liquid is 0.5 cm at 0 0C and 13.0 cm at 100 0C. Determine the temperature of
the liquid if the length of mercury is 6.0 cm.
Solution:
Option 1
If the length of mercury capillary tube is linearly changed with temperature T, the general
equation is:
T=kl+c
with k and c are constant. At the lower scale (0 0C) and upper scale (100 0C), the
equations become:
Ti = k li + c
Ts = k ls + c
If both equations is solved simultaneously, therefore,
Ts  Ti 100 0 C
k=
= 8.0 0C/cm

 s   i 12.5cm
c = Ti – k  i = Ti - k  s = - 4.0 0C
Therefore
T = (8.0 0C/cm)  - 4.0 0C
For  =6.0 cm,
T = (8.0 0C/cm)(6.0) - 4.0 0C = 44.0 0C
Option 11
Use the general equation
 6.0  0.5 
T
100  44.00 C

13.0  0.5 
14.5 The constant-volume gas thermometer
Thermometric quantity for X is pressure, p of a gas with fixed mass and constant
volume. A simple type of the thermometer is shown below.
A constant-volume gas thermometer measures the
pressure of the gas contained in the flask immersed in
the bath. The volume of gas in the flask is kept
constant by raising or lowering reservoir B such that
the mercury level in column A remains constant.
The bulb contains the gas is immersed in the bath with higher temperature. The gas
temperature increases, the gas expands and raises mercury level in tube B. The pressure
of the gas in the bulb can be written as:
p = p0 + gh
p0 is atmospheric pressure,  is mercury density, g is gravity and h is height difference of
mercury level.
If the bulb is place in the environment at different temperature T, the pressure p is also
changed. The change of p against T from various gases is shown in the following chart.
Note that, for all gases, the pressure extrapolates to zero at the unique temperature of –
273.15 0C.
The linear relationship between pressure p and temperature T can be written
generally as:
T = kp
with k as a constant.
The fixed point for the measurement is the
triple point of water where the steam, water
and ice exist in equilibrium. The triple point
for water is at 0.01 0C or 273.16K. Therefore
the equation can be written as:
273.16K
k
pt
pt is the pressure at the triple point of water.
Thus the relation of T and p can be written as,
 273.16K 
p
p
t


T= 
If the bulb containing certain type of gas (oxygen, hydrogen, nitrogen or air) is place in
the boiling water, the graph of T against p is shown as follows.
T(K)
O2
air
N2
H2
p
From the above graph, even different type of gas is used, the same reading of temperature
at steam point is recorded with the condition that the pressure is negligible. The graph
also confirms that when the pressure is lowered, the real gases properties disappear and
act like ideal gas. The details of ideal gas property will be explained in gas kinetic
theory.
The measured temperature at zero pressure does not depend on type and the amount of
gas is used. Thus, the temperature at ideal gas scale can be defined as,
14.8 Latent heat and phase change
The material commonly exists in phase of solid, liquid or vapor. In the solid phase, the
molecules have strong bond that they cannot move freely and only vibrate at equilibrium.
The molecules in liquid move freely but still have strong bond that they could not escape
easily from the liquid surface. The gas molecules move more freely than the liquid.
As the material experiences the phase change, for instance from solid to liquid or from
liquid to gas, the temperature remain constant even heat is added to the molecules. While
the molecules has the phase change, the heat never increases the mean kinetic energy of
molecules, but it is used to overcome the bond among the molecules. The heat involved
in the phase change of molecules is known as latent heat. Thus, the amount of heat Q
affects the mass of m of the material can be written as,
Q=mL
The latent heat for a solid-liquid phase change is called the latent heat of fusion (Lf) and
that for a liquid-gas phase change is called the latent heat of vaporization (Lv). These
often referred to as simply the heat of fusion and the heat of vaporization.
During melting and vaporization, heat is needed by water. On the other hand, the heat is
released from water during freezing and condensation.
The pressure should remain constant during the phase change. It can effect the boiling
and ice point. For instance, if the pressure is above 1 atm, the water will boil above 100
0
C and more heat is needed to increase the temperature.
Problem:
How much heat is required for 50 g ice at 0 0C to vaporize completely to be steam at
1000C?
Solution:
There are three stages to be considered.
1. The phase change, melting of ice at 0 0C
2. The temperature increase from 0 0C to 1000C
3. The phase change, vaporization of water at 100 0C
Thus, the amount of heat is required,
Q = m Lf + mc T + m Lv
= 0.05( 333 + 4200(100) +2264)
=21, 130 kJ.
14. 9 Heat (thermal energy transfer)
Conduction of heat occurs when the temperature of a body is not uniform. For instance, a
rod is heat at one end of the rod. The heat flows from the hot end to the cold end. In the
microscopic level, the heat transfer can be described as the transfer of kinetic energy of
molecules of high kinetic energy to the low kinetic energy molecules. In the gas phase,
the transfer of heat is through the collision of molecules. In solid phase, the molecules
only vibrate at equilibrium point. The molecules has more vibration at hot region, thus
has more kinetic energy. The kinetic energy is transferred to the adjacent molecules
which result the transfer of heat through solid.
Most metals are good conductors whereas non-metals are weak heat conductors or good
heat insulators. The reason is metals have more free electrons that act as the agents of
heat transfer. On the other hand, non-metals have few free electrons. Gases are good heat
insulators because the distance between atoms or molecules is extremely large.
Let us consider heat conduction through a rod which has cross sectional area A and
length x as shown below.
Let say the cold end has temperature of T1 and the hot end has temperature of T2. The
heat flows from T2 to T1. The transfer rate of heat through the rod is proportional to the
cross-sectional area and the temperature difference, T and inversely proportional to the
length of the rod. We can deduce the rate of heat conduction as,
Q AT

t
x
Q
AT
 k
t
x
T
where k is known as thermal conductivity coefficient.
is called temperature gradient.
x
or
The negative sign show the heat is transferred downward the temperature gradient.
The ability of the material to conduct heat depends on thermal conductivity, k. The bigger
k, the better the ability of matter to conduct heat. Material with small k value becomes a
good insulator.
The temperature distribution along the heat conductor depends on whether the conductor
is well insulated or not. If sides of conductor are not insulated, part of the heat will escape
to surrounding. It can be well described similar to the line of magnetic or electrical field.
The pattern is shown as below.
There the decrease of temperature is not uniformly distributed.
If the conductor is well insulated every sides so that no heat escapes to surrounding, all
heat will be transferred to the cold end of the rod. The pattern of heat conduction is
shown below..
The situation is common assumption to solve problems related to heat conduction
calculation. The conduction pattern are uniformly distributed. The situation shows the
heat flow achieving good distribution of heat.
The values of specific heat for several materials are shown in the following chart,
Material
Specific heat
Solid:
876
 aluminium
390
 kuprum
460
 iron
837
 glass
1758
 wood
Liquid
4200
 water
138
 mercury
1716
 benzene
Gas
1047
 air
5192
 helium
2010
 water vapor
The specific heat of water is 4200 J kg-1 K-1. It means the heat amount of 4200 J is
needed to increase the temperature of 1 kg of water to 1K. For certain material, the
specific heat is constant and independent of the mass. Therefore, the specific heat is one
of physical characteristic to distinguish the type of material.
The specific heat can be obtained through several methods. The common one
experimentally done on liquid or solid is the mixing method. Other methods like
electrical and continuous flow methods can also determine the specific heat of material.
All methods basically are based on the principle of thermal energy conservation.
Sample problem
A metal with mass of 0.3 kg at the temperature of 95 0C is immersed in 0.05 kg of copper
calorimeter that contains 0.25 kg water at 25 0C. If the final temperature of the mixture is
38 0C, calculate the specific heat of the metal.
Solution
Let assume that no heat escape to surrounding. From the conservation of heat,
(Heat from metal) = (heat obtained by calorimeter) + (Heat obtained by water)
(m c T)M
=
(m c T)C
+
(m c T)W
(0.3) c (95-38) =
(0.05)(390)(38 – 25)
+
(0.25)(4200)(38 – 25)
c = 813 J kg-1 K-1