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Chapter 5
Temperature and Heat
2
Temperature
Temperature is loosely defined as a measure of the hotness or coldness of a substance. This is a very subjective definition. We will provide a better definition, shortly.
There are three common temperature scales: Kelvin, Celsius, and Fahrenheit.
3
Temperature, cont’d
The temperature scales can be compared by examining the freezing and boiling points of water. These are determined by the atomic structure
of water. We must do the comparisons at the same
pressure since these phase transitions depend on pressure. Especially the boiling point.
4
Temperature, cont’d
This figure illustrates the relative values of the three temperature scales.
5
Temperature, cont’d
We define absolute zero as the coldest temperature. It is better defined as the temperature at which
all the random motion of matter is halted. The lowest value on the Kelvin scale is
absolute zero. So, 0oK corresponds to absolute zero.
This is -273°C
6
Temperature, cont’d
The freezing point of water is defined to be 0°C. This corresponds to 32°F and 273 K.
The boiling point of water is defined to be 100°C. This corresponds to 212°F and 373 K.
Note that the Kelvin scale is the only scale that is never negative.
7
Temperature, cont’d
To convert from Celsius to Fahrenheit:
To convert from Fahrenheit to Celsius:
[ ] [ ]95F C 32° = ° +
[ ] [ ]( )59C F 32° = ° −
8
Temperature, cont’d
Here is a more definitive definition of temperature: The Kelvin temperature of matter is
proportional to the average kinetic energy of the constituent particles.
This helps explain many phenomena that we will examine. It explains why the pressure of a gas
increases as the gas’ temperature increases.
Kelvin temperature average of atomsKE∝
9
Temperature, cont’d
As the temperature increases, the average KE of the particles increases. The average speed of the particles increases.
At higher temperatures, when the atoms collide with the container walls they impart more momentum — they strike with a larger force.
10
Thermal expansion
We know that the average KE of atoms increases with high temperature. We saw what this means for gases.
The pressure increases as the temperature rises.
What about solids? The solid’s atoms are not free to move like in a
gas. But they can vibrate.
11
Thermal expansion, cont’d
Consider a rod that has a length l. Now heat the rod.
The atoms begin to vibrate more since their KE increases.
Since they are bound to a fixed position, they simply vibrate with a larger amplitude.
12
Thermal expansion, cont’d
The result is that the rod gets longer. The final length of the rod depends on:
The length of the rod l; The change in temperature, ∆T; and The substance.
13
Thermal expansion, cont’d
We can write this mathematically as ∆l is the change in the rod’s length, α is the coefficient of linear expansion and has
units of 1/°C, l is the rod’s initial length (before the
temperature change), and ∆Τ is the change in temperature.
l l Tα∆ = ∆
14
Example
The center span of a steel bridge is 1,600 meters long on a winter day when the temperature is -10°C. How much longer is the span on a summer day when the temperature is 35°C?
15
ANSWER: The problem gives us: The change in temperature is: The change in length is
Example
6
1
2
12 10 / C 10 C
35 C T T
α −= × ° = − ° = °
( )2 1 35 C 10 C 45 CT T T∆ = − = ° − − ° = °
( )( )( )612 10 / C 1600 m 45 C 0.864 m.
l l Tα −
∆ = ∆
= × ° °
=
16
DISCUSSION: This is a change of almost three feet.
Engineers compensate for this by providing expansion joints, as shown.
Example
17
Thermal expansion, cont’d
A bimetallic strip is commonly used in devices that need to monitor temperature. Two dissimilar metals are
bonded together. They have different
coefficients of thermal expansion.
One metal expands more with a given temperature change than the other.
The strip bends.
18
Thermal expansion, cont’d
An analog thermostat is a common example of a bimetallic strip.
Pop up toasters use this principle. Older electric hot pots.
19
Thermal expansion, cont’d
Liquids also undergo thermal expansion with a temperature increase. We typically deal with the volume expansion.
Consider water as a “special” example. A volume of water increases with an increase
in temperature above 4°C. Between 0° and 4°C, water contracts with an
increase in temperature. Water is most dense at 4°C.
20
Thermal expansion, cont’d
Gases also expand with an increase in temperature.
For a given pressure, the volume of a gas is proportional to its temperature: This means that if you heat a balloon, the
volume will increase. It is (almost) constant pressure since the
balloon is capable of expanding.
V T∝
21
Thermal expansion, cont’d
Instead of a balloon, consider a gas in a metal container of fixed volume, e.g., a can of beans.
The pressure and temperature are related through: Heating the can increases the pressure.
Get the can hot enough, it will explode.
p T∝
22
Thermal expansion, cont’d
What if we let the pressure, volume and temperature change?
These three quantities are related through the ideal gas law:
This is the general statement from which the
previous cases are special examples.
pV T∝
Pressure Volume Temperature Tutorial
http://www.mhhe.com/physsci/physical/giambattista/thermo/thermodynamics.html
23
First law of thermodynamics
So far, we have discussed only one way to increase an object’s temperature: expose it to something that has a higher
temperature. There is another possibility:
Do work on it.
24
First law of thermodynamics, cont’d
Consider a piston pushing on a gas in a cylinder. Forcing the piston down requires a force. Applying this force through a distance means
you are doing work. The work is done
against the gas. You compress the
gas. The gas gets hot.
25
First law of thermodynamics, cont’d
A diesel engine uses this concept. The diesel/air mixture is compressed in the
cylinder. At maximum compression the mixture ignites. The pressure increase from
the explosion and pushes the piston down.
This causes the crankshaft to turn.
26
First law of thermodynamics, cont’d
Compressing a gas increases its temperature.
We noted previously that temperature is related to the average kinetic energy of the gas atoms/molecules.
So compressing the gas increases its internal energy.
27
First law of thermodynamics, cont’d
Internal energy is the sum of the kinetic and potential energies of all the atoms and molecules in a substance. Internal energy is represented by the symbol U.
For gases, we only deal with the kinetic energy part of the internal energy. The particles interact only during collisions, which
is infrequent.
28
First law of thermodynamics, cont’d
Heat is a form of energy that is transferred between two substances because they have different temperatures. An object does not have heat. An object transfers heat when its temperature
is raised by contact with a hotter object or lowered by contact with a cooler object.
Heat is represented by the symbol Q.
29
First law of thermodynamics, cont’d
The First Law of Thermodynamics states that the change in internal energy of a substance equals the work done on it plus the heat transferred to it:
NOTE: Q or heat can be positive or negative! +Q means you add heat; -Q means you take
away or remove heat.
workU Q∆ = +
30
First law of thermodynamics, cont’d
Recall that work can be positive or negative. When a gas is compressed, positive work is
done on the gas. The change in internal energy is positive — the
gas’ internal energy increases. When a gas expands, negative work is done
on the gas. The change in internal energy is negative — the
gas’ internal energy decreases.
31
First law of thermodynamics, cont’d
Internal energy is important during phase transitions. When you boil water, you increase the water’s
temperature and its internal energy. As the water undergoes the phase change to
water vapor, its internal energy increases but its temperature remains at 100°C. The energy added to the water to evaporate it is
applied to break the bonds holding the molecules together — not to the molecular kinetic energy.
32
Heat transfer
There are three types of heat transfer: Conduction: the transfer of heat between
atoms and molecules in direct contact. Convection: the transfer of heat by buoyant
mixing in a fluid. Radiation: the transfer of heat by way of
electromagnetic waves.
33
Heat transfer — conduction
Heat is conducted across the boundary between two substances. For a pan on a stove, the conduction occurs
because the flame is in contact with the bottom of the pan.
Conduction also occurs within the pan. The bottom gets
hot and makes the top hot.
34
Heat transfer — conduction
Thermal insulators are materials through which energy is transferred slowly.
Wood is a good thermal insulator because it contains large amounts of trapped air that slow down the transfer of energy.
Thermal conductors are materials through which energy is transferred quickly.
Metals are good thermal conductors because they contain electrons that are free to move throughout the material.
35
Heat transfer — conduction
A hard-wood floor feels colder than a carpeted floor because the wood conducts heat more quickly from your foot than the carpet.
You can judge a good conductor if it feels colder than another substance at the same temperature.
36
Heat transfer — convection
Convection is also responsible for certain weather patterns.
During the day, the ground warms more quickly than the water. The cooler air moves in to replace
the warmer air that rises. During the night, the water retains
its heat longer than the ground. The cooler air above the ground
moves to replace the warmer air that rises above the water.
37
Heat transfer — radiation
Radiation is the transfer of heat via electromagnetic waves.
You feel the “heat” of a light bulb because of: The bulb radiates some
of its energy as visible light and some as infra-red heat.
The bulb warms the air through conduction.
The warm air rises through convection.
38
Specific heat capacity
Transferring heat to/from a substance changes its internal energy.
The substance’s change in temperature for a given change in internal energy depends on the type of substance. It requires much more energy to raise the
temperature of water than the temperature of air.
39
Specific heat capacity, cont’d
The amount of heat transferred to a substance is proportional to the substance’s change in temperature:
The amount of heat transferred to accomplish a certain temperature change depends on the mass of substance:
More mass means more particles to absorb the added energy.
Q T∝ ∆
Q m∝
40
Specific heat capacity, cont’d
The amount of heat transferred to accomplish a certain temperature depends on the type of material:
We use the specific heat capacity, C, to represent the amount of energy required to raise 1 kg of a substance by a temperature of 1°C.
Q C∝
Q mC T= ∆
41
Specific heat capacity, cont’d
Here is a table of some specific heat capacities.
Notice that water has the highest heat capacity.
42
Specific heat capacity, cont’d
Recall that heat is a transfer of energy. So we use joules as a unit for heat. Historically, the unit of a calorie was used for
heat. It was a revolutionary idea that heat and
energy are equivalent. The conversion between joules and calories:
1 cal 4.184 J=
43
Example
Let’s compute how much energy it takes to make a cup of coffee. Eight ounces of water has a mass of about 0.22 kilograms. How much heat must be transferred to the water to raise its temperature from 10°C to the boiling point, 100°C?
44
ANSWER: The problem gives us: The temperature change is The heat transferred is
Example
0.22 kg 4,180 J/kg·ºC 10º C 100º C
i
f
m C T T
= = = =
100º C 10º C 90º Cf iT T T∆ = − = − =
( )( )( )0.22 4,180 90 82, 764 J
Q mC T= ∆ = =
45
DISCUSSION: This is approximately the same energy required to accelerate a pickup to a speed of nearly 30 mph.
Example
46
Example
A 5-kilogram concrete block falls to the ground from a height of 30 meters. If all of its original potential energy goes to heat the block when it hits the ground, what is its change in temperature?
47
ANSWER: The problem gives us: The potential energy of the block is:
Example
5 kg 670 J/kg·ºC 30 m
m C h
= = =
( )( )( )25 kg 9.8 m/s 30 m 1470 J.
PE mgh= =
=
48
ANSWER: This energy equals the heat transferred to the block: The temperature change is found from
Example
1470 J.Q PE= =
. Q
Q mC T T mC
= ∆ ⇒ ∆ =
49
ANSWER: The resulting temperature change is
Example
( )( ) 1470 J 1470 J
J5 kg 670 J/kg·ºC 3350 ºC
0.44ºC.
T∆ = =
=
50
DISCUSSION: You typically do no notice the temperature changes associated with everyday actions.
These temperature changes are usually too small to be noticed. But not always…
Example
51
Example
A car weighs 3,800 lbs and is speeding on I-75 at 90 miles per hour. The brake rotors are made of 20 kg of iron and steel composite. The car comes to the crest of a hill and traffic is stopped ahead. The driver slams on the brakes and stops the car just in time. What is the temperature change in the rotors?
52
ANSWER: The problem gives us: The kinetic energy of the car is:
Example
3, 800 16, 910 1725 kg 460 J/kg·ºC 90 mph =40.23m/s
20 kg
car
iron
rotors
W lbs N m C
v m
= = = = = =
( )( )221 1 1725 kg 40.23 m/s 2 2 1, 395, 915.63 J.
KE mv= =
=
53
ANSWER: This energy equals the heat transferred to the rotors: The temperature change is found from
Example
1, 395, 915.63 J.Q KE= =
. Q
Q mC T T mC
= ∆ ⇒ ∆ =
54
ANSWER: The resulting temperature change is
Example
( )( ) 1, 395, 915.63 J 1, 395, 915.63 J
J20 kg 460 J/kg·ºC 9200 ºC
151.73ºC.
T∆ = =
= About 305oF
55
Example
A satellite in low Earth orbit loses power and eventually reenters the Earth’s atmosphere. As it moves downward through the increasingly dense air, the friction force of air resistance converts the satellite’s kinetic energy into internal energy. If the satellite is mostly aluminum and all of its kinetic energy is converted into internal energy, what would be its temperature increase. (Take its speed to initially be 7,900 m/s.)
56
ANSWER: The problem gives us: The kinetic energy of the satellite is: The heat transferred to the satellite is:
Example
7, 900 m/s 890 J/kg·ºC
v C = =
21 2KE mv=
Q mC T= ∆
57
ANSWER: These two energies are equal since all of its KE is transformed into internal energy: The temperature change is
Example
21 2 mv mC T= ∆
( ) ( )
22 7, 900 m/s 2 2 890 J/kg·ºC 35, 061.8ºC.
v T
C ∆ = =
=
58
DISCUSSION: Note that the internal energy would not increase this much — the aluminum would melt. The temperature is about 63,143oF Even if 90% of the energy was lost to the air, the remaining 10% would be enough to melt the satellite — at least fry the electronics.
Example
59
Phase transitions
A phase transition or change of state occurs when a substance changes from one phase of matter to another.
60
Phase transitions, cont’d
The temperature of a substance undergoing a phase change is constant. It is the internal energy that changes.
61
Phase transitions, cont’d
To melt or freeze 1 kg of ice (2.2 lb) requires that 334,000 J of energy be transferred. This amount of energy is called the latent
heat of fusion of water. To boil or condense 1 kg of water requires
that 2,260,000 J of energy be transferred. This amount of energy is called the latent
heat of vaporization or condensation of water.
62
Phase transitions, cont’d
This explains why we use ice to keep drinks cold. It requires a large amount of energy to melt
ice. The energy to melt the ice is removed from
your drink. As long as there is ice in the drink, the
temperature remains near 0°C.
63
Example Example 5.5 Ice at 0ºC is used to cool water from room temperature (20ºC) to 0ºC. How much water can be cooled by using 1 kilogram of ice?
64
ANSWER: The problem gives us: The amount of water is:
Example Example 5.5
334, 000 J 4,180 J/kg·ºC
20 ºC
Q C T
= − =
∆ = −
( )( ) 334, 000 J
4,180 J/kg·ºC 20º 4 kg
Q m
C T C −
= = ∆ −
=
65
DISCUSSION: So ice at 0ºC can cool about four times its own mass of water from 20ºC to 0ºC. Note that we assumed no energy is lost to the environment — the cup, the air, the table, …
Example Example 5.5
66
Humidity
At temperatures below their boiling point, liquids gradually go into the gas phase through a process called evaporation. Some liquid molecules escape the liquid’s
surface because of their large KE. During this same time, some vapor molecules
are absorbed by the liquid’s surface since they have low KE.
How much liquid evaporates depends upon how many vapor molecules are in the air.
67
Humidity, cont’d
Humidity is the mass of water vapor in the air per unit volume. It is the density of the water vapor in the air. It has the same unit as mass density (kg/m3).
Low humidity is around 0.001 kg/m3 (cold day in a dry climate).
High humidity is about 0.03 kg/m3 (hot, humid day). Normal air density is around 1.29 kg/m3.
68
Humidity, cont’d
At any given temperature, there is a maximum possible humidity called the saturation density. At the saturation density, the water vapor
readily transitions to the liquid phase. Water condenses in the air and on any available
surfaces. This is what happens during the formation of fog and
dew.
69
Humidity, cont’d
The saturation density is larger at higher temperatures because the vapor molecules have greater KE and are less likely to adhere to each other when they collide.
It is less likely they will form droplets.
70
Humidity, cont’d
Here is the same information presented in the previous table (the left figure).
71
Humidity, cont’d
So the humidity alone does not determine how readily water condenses.
The saturation density is also relevant. These two are related through the relative
humidity.
72
Humidity, cont’d
Relative humidity is expressed as a percentage of the humidity to the saturation density:
The temperature at which the condensation appears for a constant humidity is called the dew point.
humidity relative humidity 100%
saturation density = ×
73
Humidity, cont’d
The dew point is therefore the temperature at which a given humidity equals the saturation density.
74
Example Example 5.6 What is the relative humidity when the humidity
if 0.009 kg/m3 and the temperature is 20ºC?
75
ANSWER: The relative humidity is:
Example Example 5.6
3
3
0.009 kg/m relative humidity 100%
0.0173 kg/m 52%
= ×
=
76
Heat engines and the 2nd law of thermodynamics A heat engine is a device that transforms
heat into mechanical energy or work. It absorbs heat from a hot source (such as
burning fuel), Converts some of this energy into usable
mechanical energy or work, and Outputs the remaining energy as heat to some
lower-temperature reservoir.
77
Heat engines and the 2nd law of thermodynamics, cont’d Gasoline, diesel and jet engines are all heat
engines. Each converts the heat released from burning
a fuel into mechanical energy. Gasoline and diesel engines release the rest of
the heat to the air (exhaust pipe, radiator, etc).
Although the details of heat engines are complicated, we can represent them with a simple diagram.
78
Heat engines and the 2nd law of thermodynamics, cont’d The heat engines remove energy Qh from a
heat source at temperature Th.
Some of this is output as work.
The rest of the energy Ql is released to a heat sink at temperature Tl.
79
Heat engines and the 2nd law of thermodynamics, cont’d The Second Law of Thermodynamics
states that no device can be built that will repeatedly extract heat from a source and deliver mechanical work or energy without ejecting some heat to a lower-temperature reservoir. This basically means that you cannot create a
device of perfect efficiency. You must have some wasted energy that is
released as heat.
80
Heat engines and the 2nd law of thermodynamics, cont’d The efficiency of any device can be written
as:
If the efficiency is 25% then only ¼ of the input
energy is available in a usable form.
output energy efficiency 100%
input energy = ×
81
Heat engines and the 2nd law of thermodynamics, cont’d For heat engines, we can write the efficiency
as:
Qh is the energy input to the heat engine.
work efficiency 100%
hQ = ×
82
Heat engines and the 2nd law of thermodynamics, cont’d There is a theoretical upper limit on the
maximum efficiency of a heat engine. This maximum energy is called the Carnot
efficiency: The temperatures must be expressed in
Kelvin.
Carnot efficiency 100%h l h
T T T −
= ×
83
Example
A typical nuclear power plant uses steam at a temperature of 1,500ºF (1,088.6 oK). The steam leaves the turbine at a temperature of about 212ºF (373 oK). What is the theoretical maximum efficiency of the power plant?
5 5 ( 32) (1500 32) 815.6
9 9 273 1088.6
o o o
o o
C F F
K C
= − = − =
= + =
84
ANSWER: The problem gives us: The Carnot efficiency is then
Example
1088.6 K
373 K
o h
o l
T
T
=
=
Carnot efficiency 100%
1088.6 373 100%
1088.6 65.7%
h l
h
T T T −
= ×
− = ×
=
85
DISCUSSION: This is the ideal efficiency. Normal efficiencies are around 35 – 40%.
Example
86
Heat engines and the 2nd law of thermodynamics, cont’d A heat mover is a device that acts like a heat
engine in reverse. It uses an external energy source to move
heat to flow from a cooler substance to a warmer substance. Examples are refrigerators, air conditioners, heat
pumps, etc.
87
Heat engines and the 2nd law of thermodynamics, cont’d Here is a diagram representing a heat mover. Notice that it is similar to a heat pump,
except: Work is input
rather than output. The energy flows
from low to high temperature.
88
Heat engines and the 2nd law of thermodynamics, cont’d Here is a diagram representing a refrigerator.
As the refrigerant vaporizes, it absorbs heat from the environment.
As the refrigerant condenses, it releases heat to the environment.
This all happens because of the external energy source that drives the pump.
89
SUMMARY
90
SUMMARY
91
SUMMARY
Chapter 5
Temperature
Temperature, cont’d
Temperature, cont’d
Temperature, cont’d
Temperature, cont’d
Temperature, cont’d
Temperature, cont’d
Temperature, cont’d
Thermal expansion
Thermal expansion, cont’d
Thermal expansion, cont’d
Thermal expansion, cont’d
Example�
Example�
Example�
Thermal expansion, cont’d
Thermal expansion, cont’d
Thermal expansion, cont’d
Thermal expansion, cont’d
Thermal expansion, cont’d
Thermal expansion, cont’d
First law of thermodynamics
First law of thermodynamics, cont’d
First law of thermodynamics, cont’d
First law of thermodynamics, cont’d
First law of thermodynamics, cont’d
First law of thermodynamics, cont’d
First law of thermodynamics, cont’d
First law of thermodynamics, cont’d
First law of thermodynamics, cont’d
Heat transfer
Heat transfer — conduction
Heat transfer — conduction
Heat transfer — conduction
Heat transfer — convection
Heat transfer — radiation
Specific heat capacity
Specific heat capacity, cont’d
Specific heat capacity, cont’d
Specific heat capacity, cont’d
Specific heat capacity, cont’d
Example�
Example�
Example�
Example�
Example�
Example�
Example�
Example�
Example�
Example�
Example�
Example�
Example�
Example�
Example�
Example�
Phase transitions
Phase transitions, cont’d
Phase transitions, cont’d
Phase transitions, cont’d
Example�Example 5.5
Example�Example 5.5
Example�Example 5.5
Humidity
Humidity, cont’d
Humidity, cont’d
Humidity, cont’d
Humidity, cont’d
Humidity, cont’d
Humidity, cont’d
Humidity, cont’d
Example�Example 5.6
Example�Example 5.6
Heat engines and the 2nd law of thermodynamics
Heat engines and the 2nd law of thermodynamics, cont’d
Heat engines and the 2nd law of thermodynamics, cont’d
Heat engines and the 2nd law of thermodynamics, cont’d
Heat engines and the 2nd law of thermodynamics, cont’d
Heat engines and the 2nd law of thermodynamics, cont’d
Heat engines and the 2nd law of thermodynamics, cont’d
Example�
Example�
Example�
Heat engines and the 2nd law of thermodynamics, cont’d
Heat engines and the 2nd law of thermodynamics, cont’d
Heat engines and the 2nd law of thermodynamics, cont’d
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