Chapter 4 final

A Wrong Idea
Often the concepts of heat and temperature are
thought to be the same, but they are not.
Perhaps the reason the two are usually and
incorrectly thought to be the same is because as
human beings on Earth everyday experience leads
us to notice that when you heat something up, say
like putting a pot of water on the stove, then the
temperature of that something goes up. More heat,
more temperature - they must be the same, right?
Turns out, though, this is not true.
Nov 29, 2011 Dr. Hassan Salem Ashour 1

Initial Definitions
Temperature is a number that is related to the
average kinetic energy of the molecules of a
substance. If temperature is measured in Kelvin
degrees, then this number is directly proportional to
the average kinetic energy of the molecules.
Total energy is made up of not only of the kinetic
energies of the molecules of the substance, but total
energy is also made up of the potential energies of the
molecules.
Heat is energy in transit, this energy when absorbed it
is convert to internal energy of the body which
absorbed heat

More About Temperature
So, temperature is not energy. It is, though, a number
that relates to one type of energy possessed by the
molecules of a substance. Temperature directly relates
to the kinetic energy of the molecules. The molecules
have another type of energy besides kinetic, however;
they have potential energy, also. Temperature readings
do not tell you anything directly about this potential
energy.

Temperature can be measured in a variety of units. If
you measure it in degrees Kelvin, then the
temperature value is directly proportional to the
average kinetic energy of the molecules in the
substance. Notice we did not say that temperature is
the kinetic energy. We said it is a number, if in
degrees Kelvin, is proportional to the average kinetic
energies of the molecules; that is, if you double the
Kelvin temperature of a substance, you double the
average kinetic energy of its molecules.

For example, if the substance is ice, it can melt into water. This
change does not cause a raise in temperature. The moment
before melting the average kinetic energy of the ice molecules
is the same as the average kinetic energy of the water
molecules a moment after melting. Although heat is absorbed
by this change of state, the absorbed energy is not used to
speed up the molecules. The energy is used to change the
bonding between the molecules. Changing the manner in which
the molecules bond to one another constitutes a change in
potential energy. Heat comes in and there is an increase in the
potential energy of the molecules. Their kinetic energy remains
unchanged.

So, when heat comes into a substance,
energy comes into a substance. That energy
can be used to increase the kinetic energy of
the molecules, which would cause an
increase in temperature. Or that heat could be
used to increase the potential energy of the
molecules causing a change in state that is
not accompanied by an increase in
temperature.

TEMPERATURE AND HEAT
Heat: is energy in transit. So, the heat as a form of energy can flow into
the body or out of the body depending whether this body in thermal
equilibrium with its surroundings or not.
Temperature: of a system can be defined as the property that determines
whether or not the body is in thermal equilibrium with its surroundings.
Internal Energy: is the energy a substance has because of its temperature
•Translational kinetic energy of atoms.
•Rotational and vibrational kinetic energy of molecules.
•Kinetic energy due to internal movements of atoms within molecules.
•Potential energy due to (attractive) forces between molecules.

The branch of heat relating to the measurement of temperature of a body
is called Thermometry
Thermometry

Construction
The Physical properties of a substance plays an important role in the
Construction of a thermometer.
For example: The platinum resistance thermometer is based on the principle
of the change in resistance with temperature change.
Calibration
Meting point of ice, boiling point of water, melting point of silver and melting
point of gold are taken as fixed points
Centigrade scale: is built by dividing the interval between the melting point of
ice and boiling point water to 100 equal parts and each represents 1C
Fahrenheit Scale: is built by dividing the interval by 180 equal parts.
Sensitivity
The thermometers will be sensitive if
1. it can detect small changes in temperature,
2. It does show the temperature of the body in a short time,
3. It does NOT take large quantity of heat for its own from the body
under measurement

Types of Thermometers
1. Liquid Thermometers: based on the volume change of liquids due to the
Change in temperature
2. Gas Thermometers: based on the volume change of gases due to the
Change in temperature
3. Resistance Thermometers: based on the resistance change of resistors
due to the Change in temperature
Temperature Scales
1. Centigrade or Celsius,
2. Fahrenheit,
3. Kelvin or Absolute,
4. Rankine

Celsius and Fahrenheit
0C 32F
100C 212F
M
L
N
Consider we have a body its temperature
Level is at M, its temperature C is
0100
0



C
NL
ML
C F And its temperature on the Fahrenheit scale is
32212
32



F
NL
ML
Equate these equations
   
32
5
9
,
32
9
5
32
180
100
100180
32
10032212
32







CFor
FCFC
CFCF

Note that: TC = 5/9 TF
TC = TKand
Example 4.1
Find the temperature at which the Fahrenheit and the Celsius
scales coincide?
Solution:
This will happen when
C FT T
, so we can put in the conversion equation that:
5
( 32) 9 5 160 4 160 40
9
C C C C C C FT T T T T so T T           

Zeroth Law of Thermodynamics
If bodies A and B are separately in thermal equilibrium
with a third body, C, then A and B will be in thermal equilibrium
with each other if placed in thermal contact.

Ideal Gas and Heat Capacity
The properties of a gas of a mass m confined to a container of volume V
at pressure P and Temperature T determined experimentally.
In general, the equation that interrelates these quantities is called the
“equation of state”
The equation of state is quite complicated but if the gas is maintained
at very low pressure the equation of state is found to be very simple!
Such a low density Gas is called an Ideal Gas,
So the ideal gas is any gas at low pressure which means the
intermolecular distances is large, low density, and thus the interaction
among the particles is assumed to be almost negligible so that the
particles constitute an ideal gas.

The experiment showed that the relation between the pressure
inversely proportional to volume at constant temperature.
PV=constant at Constant Temperature sometimes called Boyle’s law
P
PV

TC
V
P=constant
.Const
T
V
 Which is called Charles’s law
,const
T
PV

If we double the number of moles the volume will double of we want to
keep the temperature the pressure the same
gas1
gas2
gas3
To the same temp
-273.15C

So, we can write,
nRTPV 
Where, R is the universal gas constant, and n is the
number of moles
11
314.8 
 KJmoleR
Standard conditions for a gas are defines to be
CTandatmP 
0,1 

litreV
litrem
m
mN
mN
V
mN
J
mN
J
V
mNPaatmP
atm
KKJmolemole
P
nRT
V
KTK
418.22
10001
022418.0022418.0
,022418.0
10013.1
15.273314.81
10013.110013.11
,
1
15.273314.81
,15.273
3
3
2
225
255
11



















Example: What is the volume of one mole of an ideal gas at standard conditions

Units of Heat:
Calorie: is the amount of heat necessary to raise the
temperature of 1 gram of water from 14.5 C to 15.5C
Btu: (British thermal Unit) is the heat required to raise the
1lb of water from 63F to 64F
calJBtu
Jcal
25210551
186.41



Heat capacity and Specific Heat
The amount of heat energy required to raise the temperature of a
given substance by some amount varies from one substance to
other.
The amount of heat required to raise 1kg of water 1C is 4189J, but
for copper is 387J.

Heat capacity
Defined as the amount of heat required to raise a unit mass a unit temperature
So, the heat required to make a temp change in a mass m
TmcQ 
( )f iQ m c T m c T T    
If both substances are mixed and left until their temperature so we can
apply the conservation remain constant (final temperature 𝑇𝑓), of energy
as,
( )
( )
w w f w
x
x x f
m c T T
c
m T T




The average kinetic energy per molecule in
an ideal gas is given by
123
23
1038.1
/1003.6'
,
2
3
,
2
3




JKk
moleatomnumbersavogadroN
whereTkKorT
N
R
K
B
A
B
A
The internal energy is the sum of the kinetic
energies, that is
nRTU
2
3


Thermal Expansion
Suppose a body of a length L at a temperature T0, if this body is heated
To T1, the body dimension will change due to temperature change.
Expansion of solids can be divided to classes
1. isotropic, the body dimensions will change equally in all directions
2. Anisotropic, the body dimension will NOT change equally in
all directions
 Coefficient of Linear Expansion
The expansion of solids can be in length, area, or volume. The expansion
In length is called linear expansion.
  ,, 0llTl  and on the nature of the material
Tl
l
Tll



1
0
0  Alpha is the coefficient of
linear expansion

Experimentally, the linear coefficient of expansion can be found
0l
l
T
0l
l
ΔT

The Area and volume expansions are
TA
A



1

TV
V



1

If the solid characteristics is isotropic then we can say,
 3,2  and
Where 𝐴 is the surface area
Where 𝑉 is the volume

Example: An aluminum tube is 3.00 meter long at 20C. What is its length at
1. 100 C, 2. 0C. If you know that the Aluminum coefficient of linear expansion
is
  16
102

 
CAl
Solution:
 
mml
mTll
48.0
108.4201003102 46
0

 

 
mml
mTll
12.0
102.12003102 46
0

 


Example: The active element of a certain laser is made if a glass rod 30 cm long
by 1.5 cm in diameter. If the temperature of the rode is increased by 65 C, find the
increase in a. in its length, b. In its diameter, and c. in its volume, if alpha is
  16
109

 
C
Solution:
  cmTll 01755.06530109 6
0  

  23
2
6
0 10068.265
2
5.1
10922 cmTAA 






 
  232
0
769.110068.275.0 cmA
AAA
new
new





cm
A
r new
new 7504.0
769.1


Volume expansion
   
36
322
09304.0650143.531093
0143.533075.0
3
1
3
cmV
cmlrV
TVV
TV
V










Heat Conduction
Heat transfer always occurs from regions of higher to regions of
lower temperatures,
L
tyconductivithermalcalledisk
l
T
kAH
AH
l
H
TH
,
,
,
1
,






Copper pipe 2m long, 0.004 m thickness, and surface area of 0.12 square meter
If the water temp is 80 C and the room temp is 15C, at what rate the is heat
conducted through the pipe wall If we assume the outside surface of the pipe
is at 15C.
Solution:
  W
m
K
mKWm
l
T
kAH 000,780
004.0
65
12.0400 211








 
Do you believe this is a true answer!
I think not!
By no means the temp of the outer surface can be 15C, it would be very close to
80C which makes the heat loss rate much less than the above value.

Heat transfer by conviction
Heat may be carried by the motion of fluid, this is called conviction.
The convictive heat transfer for a surface area A is approximately by
TAqH 
Where q is the convictive heat transfer constant

Radiation
We know that heat can be transmitted through vacuum.
This process is called Radiation
Generally, every object at non-absolute-zero temperature radiates radiation at all
Wavelengths (theoretically speaking). But the amount of energy radiated at each
wavelength depends on the body temperature.
A body at temperature 800C will look red, but at temperature 3000C would look White
The wavelength at which the radiation is most intense is given by the
Wien Displacement law
mKconstisBwhere
T
B 3
10898.2., 

Sun surface temp is 6000K. What is wavelength of maximum radiation?
m
K
mK 7
3
1083.4
6000
10898.2 





Wind Chill Factor
Wind chill factor
The effective temperature decrease rapidly as the wind velocity increases.

Hypothermia: Abnormally low body temperature. The condition
needs treatment at body temperatures of 35C (95 F) or below. And
hypothermia becomes life threatening below body temperatures of
32.2 C (90 F).
Stage 1
Body temperature drops by 1–2 °C below normal temperature (down to
35–37 °C ). Mild to strong shivering occurs. The victim is unable to
perform complex tasks with the hands; the hands become numb.
Breathing becomes quick and shallow. Victim may feel sick to their
stomach, and very tired. Often, a person will experience a warm
sensation, as if they have recovered, but they are in fact heading into
Stage 2. Another test to see if the person is entering stage 2 is if they
are unable to touch their thumb with their little finger; this is the first
stage of muscles not working. They might start to have trouble seeing.
Dr. Hassan Salem AshourNov 29, 2011 44

Stage 2
Body temperature drops by 2–4 °C below normal temperature (33–35 °C).
Shivering becomes more violent. Muscle miscoordination becomes
apparent. Movements are slow and labored, accompanied by a stumbling
pace and mild confusion, although the victim may appear alert. Surface
blood vessels contract further as the body focuses its remaining resources
on keeping the vital organs warm. The victim becomes pale. Lips, ears,
fingers and toes may become blue.
Stage 3
Body temperature drops below approximately 32 °C. Shivering usually
stops. Difficulty speaking, sluggish thinking, and amnesia (memory loss)
start to appear; inability to use hands and stumbling is also usually
present. Cellular metabolic processes shut down. Below 30 °C, the
exposed skin becomes blue and puffy, muscle coordination becomes very
poor, walking becomes almost impossible, and the victim exhibits
incoherent/irrational behavior including terminal burrowing or even a
stupor. Pulse and respiration rates decrease significantly, but fast heart
rates can occur. Major organs fail. Clinical death occurs. Because of
decreased cellular activity in stage 3 hypothermia, the body will actually
take longer to undergo brain death.

Chapter 4 final

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Chapter 4 final