Heat and Kinetic Theory

1
Heat and Kinetic Theory
2
In a Cold Weather
Raleigh, NC, USA 2002
3
In a Hot Weather
Cairo, EGYPT 2007
4
Heat and Hotness
The sensation of hotness is familiar to all of us.
When one hot body and a cold body are placed in
an enclosure, the hotter body will cool and the
colder body will heat until the degree of hotness
of the two bodies is the same.
This is called thermal equilibrium.
5
Heat Transfer
Clearly something has been transferred from one
body to the other to equalize their hotness.
That which has been transferred from the hot
body to the cold body is called heat. Basically
there are three different types of heat transfer
conduction, convection and radiation.
Heat may be transformed into work, and therefore
it is a form of energy.
6
Heated water can turn into steam, which can push
a piston and therefore drive a vehicle.
7
(No Transcript)
8
Kinetic Theory of Matter

• Matter is made of atoms and molecules, which
  are in continuous chaotic
• motion.
• In a gas, the atoms (or molecules) are not
  bound together. They move in
• random directions and collide frequently
  with one another and with the
• walls of the container.

9
Kinetic Theory of Matter
In addition to moving linearly, gas molecules
vibrate and rotate, again in random directions.
10
Kinetic Theory of Matter
In a solid, where the atoms are bound together
the random motion is more restricted. The atoms
are free to vibrate and do so, again randomly,
about some average position to which they are
locked.
The situation with regard to liquids is between
these two extremes. Here the molecules can
vibrate, but they also have some freedom to move
and to rotate.
11
Kinetic Theory of Matter
Because of their motion, the moving particles in
a material possess kinetic energy. This energy
of motion inside materials is called internal
energy, and the motion itself is called thermal
motion. What we have so far qualitatively called
the hotness of a body is a measure of the
internal energy.
In hotter bodies, the random motion of atoms and
molecules is faster than in colder
bodies. Therefore, the hotter an object, the
greater is its internal energy. The physical
sensation of hotness is the effect of this random
atomic and molecular motion on the sensory
mechanism. Temperature is a quantitative measure
of hotness.
12
Kinetic Theory of Matter
It is possible to derive the equations that
describe the behavior of matter as a function of
temperature. Gases are the simplest to
analyze. Gases are made of small particles
(atoms or molecules) which are in continuous
random motion. Each particle travels in a
straight line until it collides with others or
with the walls of the container. After a
collision, the direction and speed of the
particle is changed randomly. In this way
kinetic energy is exchanged among the particles.
13
Kinetic Theory of Matter
The colliding particles also exchange energy with
the wall of the container. If initially the
walls of the container are hotter than the gas,
the particles colliding with the wall on the
average pick up energy from the vibrating
molecules in the wall. As a result, the gas is
heated until it is as hot as the walls. After
that, there is no longer net exchange of energy
between the walls and the gas. This is an
equilibrium situation in which, on the average,
as much energy is delivered to the wall by the
gas particles as is picked up from it.
14
Kinetic Theory of Matter
The speed and corresponding kinetic energy of the
individual particles in a gas vary over a wide
range. The observed speed distribution of gas
molecules in thermal equilibrium is shown in the
figure. This is called the Maxwell-Boltzmann
distribution.
15
Kinetic Theory of Matter
Maxwell-Boltzmann distribution
16
Kinetic Theory of Matter
There is a total number N of molecules in a
container.
After the collision, the change in momentum of
the molecule is
The momentum change will cause a an average force
F1 exerted by the wall.
Here ?t is the average time duration for the
action of the force F1.
For the molecule to collide twice with the same
wall, it must travel a distance 2d in the x
direction. Therefore, the time interval, which is
the average time duration, between two collisions
with the same wall is
17
Kinetic Theory of Matter
The average force exerted on the molecule for
each collision is
According to Newtons third law, the average
force exerted by the molecule on the wall is
equal in magnitude and opposite in direction to
the force shown above.
Each molecule of the gas exerts a force F1 on the
wall. The total force F exerted by all the
molecules on the wall is the sum of these forces.
Here N is the total number of molecules in the
container.
18
Kinetic Theory of Matter
19
Kinetic Theory of Matter
Since the square of the molecule velocity is the
sum of square of three components.
The average value of v2 for all the molecules in
the container is related to the average values of
vx2, vy2, and vz2 according to the following
equation
Because the motion is completely random, the
average values of vx2, vy2, and vz2 are actually
equal to each other.
20
Kinetic Theory of Matter
Then we have
Gas pressure P in the container is then
The pressure is proportional to the number of
molecules per unit volume and to the average
translational kinetic energy of the molecules.
21
Molecular Interpretation of Temperature
But the equation of state for ideal gas is
Boltzmann constant
Temperature is a direct measure of average
molecular kinetic energy.
OR
The total internal energy of the whole gas system
is
22
Root-Mean-Square Speed
The root-mean-square speed of the gas molecules is
is the gas constant.
is the molar mass of gas molecules.
23
(No Transcript)
24
Specific Heat of an Ideal Gas System
25
Heat
Heat is measured in calories. The calorie is
defined as the heat required to raise the
temperature of 1 g of water from 14.5 C to 15.5
C.
In the life sciences, heat is commonly measured
in kilocalorie units and is abbreviated as
Calorie.
26
McDonalds Nutrition Values
27
Specific Heat
Specific heat is the quantity of heat required to
raise the temperature of 1 g of a substance by 1
degree.
The human body is composed of water, proteins,
fat, and minerals. Its specific heat reflects
this composition.
With 75 water and 25 protein, the specific heat
of the body would be
The specific heat of the average human body is
closer to 0.83 due to its fat and mineral content.
28
Latent Heats
In order to convert a solid to a liquid at the
same temperature or to convert a liquid to a gas,
heat energy must be added to the substance. The
energy is called latent heat.
29
(No Transcript)
30
Transfer of Heat
Conduction
The heat enters one end of the rod and increases
the internal energy of the atoms near the heat
source. In a solid material, the internal energy
is in vibration of bound atoms and in the random
motion of free electrons, which exist in some
materials. The increased vibrational motion is
transferred down the rod through collisions with
neighboring atoms and eventually the other end of
the rod will become hot. Heat transfer via atomic
vibrations is slow. Materials such as metals,
which contains free electrons, are good
conductors of heat. The electrons in metals
transfer heat rapidly down the rod.
31
Transfer of Heat conduction
The amount of heat conducted per second
through a block of material is given by
The constant is the coefficient of
thermal conductivity.
32
Transfer of Heat
Convection
In solids, heat transfer occurs by conduction in
fluids (gases and liquids), heat transfer
proceeds primarily by convection.
When a liquid or a gas is heated, the molecules
near the heat source gain energy and tend to move
away from the heat source. Therefore, the fluid
near the heat source becomes less dense. Fluid
from the denser region flows into the rarefied
region, causing convection currents. These
currents carry energy away from the heat source.
33
(No Transcript)
34
Transfer of Heat
Radiation
Charged particles in a material are in constant
random motion and, therefore, emit
electromagnetic radiation. In this way, internal
energy is converted into radiation, called
thermal radiation. When a body is relatively
cool, the radiation from it is in the
long-wavelength region to which the eye does not
respond. At high temperatures, some of the
electromagnetic radiation is in the visible
region, and the body is observed to glow. When
electromagnetic radiation impinges on an object,
the charged particles (electrons) in the object
are set into motion and gain kinetic energy.
Electromagnetic radiation is, therefore,
transformed into internal energy.
e emissivity Stefan-Boltzmann constant
35
Diffusion
Diffusion is the main mechanism for the delivery
of oxygen and nutrients into cells and for the
elimination of waste products from cells. On a
large scale, diffusive motion is relatively slow,
but on the small scale of tissue cells, diffusive
motion is fast enough to provide for the life
function of cells.
Diffusion is the direct consequence of the random
thermal motion of molecules. The molecule has a
thermal velocity v and travels on the average a
distance L (mean free path) before colliding with
another molecule.
After a certain number of collisions the molecule
will be found a distance S from the starting
point.
36
Diffusion
The time required for molecules to diffuse a
distance S is
In a liquid such as water, molecules are close
together. The mean free path of a diffusing
molecule is short, about cm. At room
temperature, the velocity of a light molecule may
be about cm/sec.
The time required for molecules to diffuse a
distance of 10-3 cm, which is the typical size
of a tissue cell, is
The time required for molecules to diffuse a
distance of 1 cm is
37
Diffusion
38
Transport of Molecules by Diffusion
The diffusion coefficient of salt (NaCl) in water
can be estimated by
The diffusion velocity of molecules diffusing a
distance from a position of density to
a position of lower density is
The flux, the number of molecules arriving per
second per unit area, J is given by
where D is called the diffusion coefficient.
39
Diffusion through membranes
In the simplest model, the biological membrane
can be regarded as porous, with the size and the
density of the pores governing the diffusion
through the membrane.
The net flux of molecules J flowing through a
membrane is given in terms of the permeability of
the membrane P
Diffusion is a slow process over distances larger
than a few millimeters. Therefore, large living
organisms must use circulating systems to
transport oxygen nutrients and waste products to
and from the cells. The evolution of the
respiratory system in animals is a direct
consequence of the inadequacy of diffusive
transportation over long distances.
40
Oxygen acquisition
Animals require energy to function. The energy is
provided by food, which is oxidized by the body.
On the average, 0.207 liter of oxygen at 760 torr
are required for every Cal of energy released by
the oxidation of food in the body. At rest, an
average 70-kg adult requires about 70 Cal of
energy per hour, which implies a consumption of
14.5 liter of oxygen per hour.
The simplest way to obtain the required oxygen is
by diffusion through the skin. This method,
however, cannot supply the needs of large
animals. It has been determined that in a person
only about 2 of oxygen consumed at rest is
obtained by diffusion through the skin. The rest
of the oxygen I is obtained through the lungs.
The maximum linear size of the animal that can
get its oxygen entirely by skin diffusion can be
estimated to be about 0.5 cm. Therefore, only
small animals, such as insects, can rely entirely
on the diffusion transfer to provide them with
oxygen.
Exercise 9-7
41
9-7. (a) Diffusion rate of oxygen through skin
14.5 /h0.02/70104 cm2 1.7110-5
/h-cm2 (b) With the stated assumptions the
volume of a 70kg person is 70103 cm3
Therefore oxygen needed is 14.5
/70103 2.0710-4 / cm3hr Maximum
radius of animal is obtained from
2.0710-4 volume of animal 1.7110-5 area
of animal 2.0710-4 4/3 xpr3
1.7110-5 4pr2 r 0.248 cm
diameter 0.5 cm
42
The Respiratory System
When the diaphragm descends, the volume of the
lungs increases, causing a reduction in gas
pressure inside the lungs. As a result, air
enters the lungs through the trachea. The trachea
branches into smaller and smaller tubes, which
finally terminate at tiny cavities called
alveoli. It is here that gas is exchanged by
diffusion between the blood and the air in the
lungs.
43
The lungs of an adult contain about 300 million
alveoli with diameters ranging between 0.1 and
0.3 mm. The total alveolar area of the lungs is
about 100 m2, which is about 50 times larger
than the total surface area of the skin. The
barrier between the alveolar air and the blood in
the capillaries is very thin, only about 4 x
10-5 cm. Therefore, the gas exchange of oxygen
into the blood and CO_2 out of the blood is very
fast.
44
Surfactants and Breathing
The radii of the alveoli range from about 0.05 to
0.15 mm. The inner wall of the alveoli is coated
with a thin layer of water that protects the
tissue. The surface tension of this water layer
tends to minimize the surface thereby shrinking
the alveolar cavity. When the diaphragm descends,
the incoming air has to enter the alveoli and
expand them to their full size. Because the
alveoli are embedded in a moist medium, expanding
the alveoli is analogous to creating a bubble
inside a liquid. To create a gas bubble if radius
R in a liquid with surface tension T, the
pressure of the gas injected into the liquid must
be greater than the pressure of the surrounding
liquid by
Breathing is made possible by surfactants that
cover the alveolar water layer and greatly reduce
its surface tension. These surfactant molecules
are a complex mixture of lipids and proteins
produced by special cells in the alveoli and they
can reduce surface tension by as much as a factor
of 70 (to about 1dyn/cm).
45
END