THERMAL PHYSICS I

1. The ancient view was that heat is a colourless, weightless, fluid which occupies no volume
has no smell, etc. This imagined substance - called phlogiston - was supposedly stored in
objects and transferred between objects. It took a long time to reject this notion. Why is it
wrong? Because (as we will see) heat can be created and destroyed, whereas liquids keep
their volume and cannot be created or destroyed.
2. We are all familiar with an intuitive notion of temperature. We know that hotter things
have higher temperature. But let us try to define temperature more rigorously. In the
diagram below, the three bodies A,B,C are in contact with each other. After sufficient
time passes, one thing will be common to all three - a quantity that we call temperature.
high T h e a t low T
A B
C
3. Now let us understand heat. Heat is energy, but it is a very special kind of energy: it is
that energy which flows from a system at high temprature to a system at low temperature.
Stated in a slightly different way: heat is the flow of internal energy due to a temperature
difference. (Note that we do not have to know about atoms, molecules, and the internal
composition of a body to be able to define heat - all that will come later).
4. The term "thermal equilibrium" is extremely important to our understanding of heat. If
some objects (say, a glass of water placed in the open atmosphere) are put in thermal
contact but there is no heat exchange, then we say that the objects are in thermal
equilibrium. So, if the glass of water is hot or cold initially, after sufficient time passes it
will be in thermal equilibrium and will neither receive nor lose heat to the atmosphere.
5. We have an intuitive understanding of temperature, but how do we measure it? Answer:
by looking at some physical property that changes when the temperature changes. So, for
example, when the temperature rises most things expand, the electrical resistance changes,
some things change colour, etc. These are called "thermometric properties".
6. Let's take a practical example: the constant volume gas
thermometer. Here the reference level is kept fixed by
raising or lowering the tube on the right side (the tube
below is made of rubber or some flexible material). So
the gas volume is fixed. The gas pressure is g h,
and so the pressure is known from measuring h.
ρ × ×
To find the temperature of a substance, the gas flask
is placed in thermal contact with the substance. When
the temperature is high, the pressure is large. From the
graph of pressure vers
0 0
us temperature, you can easily
read off the temperature. Note that we are using two
fixed points, which we call 0 and 100 . This is
called the Centigrade scale, and the two fixed points
C C
correspond to the freezing and boiling of water.
7. There is a temperature below which it is not possible
to go. In other words, if you cool and cool there
comes a point after which you cannot cool any more!
How do we know this? Take different gases and plot
how their pressure changes as you cool them down.
You can see from the graph that all the lines, when
drawn backwards, meet exactly at one point. This
point is the abs
0 0
olute zero of temperature and lies at
about -273.15 . This is also called 0 K, or zero
degrees Kelvin.
C
8. Temperature Scales. If you had been born 300 years
ago, and if you had discovered a reliable way to tell
different levels of "hotness", then maybe today there
would be a temperature scale
0 0
0
named after you! The
relation between Centigrade, Fahrenheit, and Kelvin
scales is illustrated to your right. You can see that
absolute zero corresponds to -460 , - 273.15 ,
and 0 . The
K C
K Kelvin scale is the most suited for
scientific purposes, and you should be careful to use
this in all heat related calculations.
Conversion between degrees Celsius and degrees Fahrenheit: ( / ) 32
Conversion between degrees Fahrenheit and degrees Celsius: ( / )( 32 )
Conversion between Celsius a
F C
C F
T F CT F
T C F T F
= +
= −
􀁄 􀁄 􀁄
􀁄 􀁄 􀁄
nd Kelvin temperatures: T=TC +273.15
9. How hot is hot, and how cold is cold? Whenever a
scientist says something is large or small, it is always
relative to something. The hottest thing ever was the
universe when it just came
8
into existence (more about
this in the last lecture). After this comes the hydrogen
bomb (10 K). The surface of the sun is not so hot, only
5500K. Copper melts around 1000K, water turns to
-7
steam at 373K. If you cool further, then all the gases
start to solidify. The lowest temperature that has ever
been achieved is 10 , which is one tenth of one
millionth of one degree! W
K
hy not still lower? We shall
later why this is not possible.
10. When you rub your hands, they get hot. Mechanical work has been converted into heat.
The first person to investigate this scientifically was Joule. In the experiment below, he
allowed a weight to drop. This turned a paddle that stirred up the water and caused the
temperature to rise. The water got hotter if the weight was released from a greater height.
Joule established the units for the mechanical equivalent of heat. The units we use today
are: 1 calorie (1 cal) raises the temperature of 1 g of water by 1 °C
1 cal = 4.186 Joule, 1 kilocalorie (1 kcal) = 1000 cal
Remember also that joule is the unit of work: when a force of one newton acts through a
distance of one metre, the work done is one joule.
PHYSICS –PHY101 VU
© Copyright Virtual University of Pakistan
118
at T
0 L
L
ΔL
0 at T
Coefficient of volume expansion β (1/°C )
Quartz Glass Al Hg Air
Steel
10−6 10−5 10−4 10−3
11. Let's now consider one important effect of heat - most things expand when heated. Of
course, our world is 3-dimensional but if there is a thin long rod then the most visible
effect of heating it is that the rod increases in length. By how much?
( )
0 0
0 0
0 0
Look at the above diagram. Call the length of the rod at as . When the rod is heated
to , then the length increases to 1 . The difference of the lengths is,
T L
T LL T T
L L L T
α
α
= ⎡⎣ + − ⎤⎦
− = ( − )0 0 , or . Here is just a dimensionless number that tells you
how a particular material expands. It is called the coefficient of linear expansion. If was
zero, then the material woul
T LαLT α
α
Δ = Δ
0
0
d not expand at all. You can also write it as / .
Similarly, define a coefficient of volume expansion call it as / .
12. There is a relation between and , the linear and volum
L L
T
V V
T
α
β β
α β
Δ
=
Δ
Δ
− − ≡
Δ
3 3
3 3 2 3 2 3 3 3
e coefficients. Let's look at the
change in volume due to expansion: ( ) ( )
3 3
V L L L L T
L L T L T L T
α
α α α
′= +Δ = + Δ
= + Δ + Δ + Δ
3 3 3 3
We are only looking for small changes, so the higher terms in can be safely dropped.
Hence 3 . From the defin
L L T V V T
T
V V T
α α
α
≈ + Δ = + Δ
Δ
Δ = Δ ition, this we immediately see that 3 . Just to
get an idea, here is what looks like for various different materials:
β α
β
=
13. We can use the fact that different metals expand at different rates to make thermostats.
For example, you need a thermostat to prevent an electric iron from getting too hot or a
refrigerator from getting too cold. In the diagram below, one metal is bonded to another.
When they expand together, one expands less than the other and the shape is distorted.
This breaks off a circuit, as shown here.
0 0
14. Water behaves strangely - for certain temperatures, it
contracts when heated (instead of expanding)! Look
at the graph: between 0 C and 4 C, it exhibits strange
or anomalous behaviour. The reason is complicated
and has to do with the molecular structure of water.
If water behaved normally, it would be very bad for
fish in the winter because they rely upon the bottom
of the lake or sea to remain liquid even though there
the surface is frozen.
15. We define the "heat capacity" of a body as , where is the increase in
temperature when an amount of heat is added to the body. Heat capacity is always
positive; and have
C Q T
T
Q
Q T
= Δ
Δ
Δ the same sign. The larger the heat capacity, the smaller is the
change in the body's temperature when a fixed amount of heat is added. In general,
Q = mcΔT , where Q= heat added , m=mass ,c=specific heat , and ΔT = change in
temperature. Water has a very large specific heat ,
1.0 /(º ); this means it takes one calorie
to raise the temperature of 1 gm of water by 1 degree
Celsius. In joules
c
c= cal Cg
per kilogram this is the same as 4186.
In the table are the specific heats of various common
materials. You can see that metals have small , which
means that it is relatively easy to
c
raise or lower their
temperatures. The opposite is true of water. Note also
that steam and ice have smaller ' than water. This
shows that knowing the chemical composition is not
c s
enough.
16. A 0.5-kg block of metal with an initial temperature of 30.0 is dropped into a container
holding 1.12 kg of water at 20.0 . If the final temperature of the block-water system is
20.
C
C
􀁄
􀁄
4 , what is the specific heat of the metal?
SOLUTION: Write an expression for the heat flow out of the block ( ).
Do the same for water, ( ). Now use the fact t
block b b b
water w w w
C
Q mcT T
Q mc T T
= −
= −
􀁄
hat all the energy that is
lost by the block is gained by the water: ( ) ( ) 0
From this, ( ) (1.12 )[4186 /( )](20.4 20.0 )
( ) (0.500 )(3
block water b b b w w w
w w w
b
b b
Q Q TmcT T mc T T
c m c T T kg J kg K C C
m T T kg
= ⇒ − − − =
− ⋅ −
= =
−
􀁄 􀁄
0.0 20.4 )
391 /( )
C C
J kg K
−
= ⋅
􀁄 􀁄
17. When lifting a "daigchee" from a stove, you would be wise to use a cloth. Why? Because
metals transfer, or conduct, heat easily whereas cloth does not. Scientifically we define
conductivity using experiments and apparatus similar to the following:
Heat flows from the hotter to the colder plate. Let us use the following symbols:
= thermal conductivity = heat transferred
= cross sectio
k Q
A nal area = duration of heat transfer
= length = temperature difference
Then the heat transferred in time is,
t
L T
t Q k
Δ
= . This formula allows us to measure
if all the other quantities in it are measured.
18. Conduction is one possible way by which heat is transferred from one portion of a
system
A T t
L
k
⎛Δ ⎞
⎜ ⎟
⎝ ⎠
to another. It does not involve physical transport of particles. However, there is
another way by which heat can be transferred - convection. In convection, heat is carried
by a moving fluid. So when you heat a pot of water, molecules at the bottom move up,
and the ones at the top come down - the water has currents inside it that transfer heat.
Another mechanism for transferring heat is through radiation. We have already talked
about this while discussing blackbody radiation and the Stefan-Boltzman Law