TEMPERATURE AND HEAT
TEMPERATURE AND PHASES OF MATTER
The words temperature and heat are used together so often that they may appear to mean the same thing. Although they are closely related, they are definitely not the same thing. Temperature is a property of an object related to the average kinetic energy of atoms and molecules in that object; heat is a form of energy and not a property of an object. One of the effects heat can have when it enters an object is to increase its temperature, some other effects are to melt solids or boil liquids. Temperature is a quantitative measure of hot and cold. The words hot and cold are usually relative terms. For example, water is cold to the human hands is warm compared to ice.
Atoms, Molecules, and the Phases of Matter
An atom is the smallest unit of an element. A molecule which is a combination of atoms, is the smallest unit of a compound; i.e. H2O, CO2. ( When talking about smallest unit of substances, we refer to molecules, considering an atom to be a molecule with only one constituent.) The most common phases of matter are solid, liquid, and gas.
Molecules in solids are bound to one another as if connected by springs. Solids has rigidity and retains its shape because the average positions of the molecules are fixed.
Molecules in liquids are freer to move, acting like sticky ball bearings, Strong forces keep the molecules in a liquid from getting too far apart, but they can slide over one another with ease. Liquids flow and cannot retain its shape unless it is in a container.
Molecules in gases are much farther apart than in either solid or liquid. The forces between molecules in a gas are weak, that the molecules of a gas act almost independently of one another and will escape if not in a closed container. The molecules are constantly in random motion. The velocities of the molecules are distributed over a wide range, with the average speed depending on the temperature of the object. The average kinetic energy of the molecules is directly related to temperature : the higher the temperature, the greater the average speed.
Temperature Scales and Thermometers
Thermometer is any device that measures temperature. A large variety of such devices exists, but he most common are mercury thermometers and bimetallic strips
1. Fahrenheit scale – common in the U. S. developed by Gabriel Fahrenheit ( 1686 – 1736 ) a
manufacturer of meteorological instruments in the Netherlands.
2. Celsius scale – most common worldwide, popularized by the Swedish astronomer Anders Celsius in 1742.
3. Kelvin scale – important scale for scientific and technical work. The scale was proposed in 1848 by
William Thomson, Lord Kelvin (1824 –1907). The Kelvin scale is an absolute temperature scale.
The average kinetic energy of the molecules in a gas is directly proportional to the absolute temperature
tF = 9/5 (tC) + 32 ° = 1.8 (tC) + 32 ° ® to convert Celsius temp. to Fahrenheit temp.
tC = 5/9 ( tF – 32 ° ) ** to convert Fahrenheit temp. to Celsius temp.
TK = tC + 273.15 ** to convert Celsius temp. to Kelvin temp.
TR = tF + 459.67 ** to convert Fahrenheit temp. to Rankine temperature
Thermal Expansion
Most materials expand when heated and contracts when cooled. This property is due to the increase in the average kinetic energy of molecules with increasing temperature . The amount that an object expands depends on its size, the material of which it is made, and the size of temperature change. The quantitative expression for the amount of linear expansion in an object is defined by /\L = La /\t , where /\L is the change in length of the object , /\t is the change in temperature and a is the coefficient of linear expansion. The change in length is too small to be observed by the naked eye. That might seem inconsistent with the familiar operation of the clinical thermometer, in which the length of the column of mercury changes very noticeably. Clinical thermometers have reservoir of mercury in the bulb at the bottom. The mercury in the reservoir expands inside a glass container that expands more slowly than mercury. The mercury flows out of the reservoir into a small diameter tube, making the expansion very noticeable.
Water behaves normally at most temperature, but if it is cooled to about 4 ° C it will expand with further cooling until it reaches 0 ° C. Water freezing in pipes or engine cooling systems can damage them.
Coefficients of Linear Expansion (a ) at 20 ° C
Material
|
a / ° C
|
Material
|
a/ ° C
|
Material
|
a/ ° C
|
Solids
|
Glass (ordinary)
|
9 x 10 – 6
|
Ethyl alcohol
|
370 x 10 – 6
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Aluminum
|
25 x 10 – 6
|
Glass ( pyrex )
|
3 x 10 – 6
|
Gasoline
|
320 x 10 – 6
|
Brass
|
19 x 10 – 6
|
Quartz
|
0.4 x 10 – 6
|
Glycerin
|
170 x 10 – 6
|
Gold
|
14 x 10 – 6
|
Concrete, brick
|
12 x 10 – 6
|
Mercury
|
60 x 10– 6
|
Iron or Steel
|
12 x 10 – 6
|
Marble ( average)
|
2.5 x 10 – 6
|
Water
|
70 x 10– 6
|
Lead
|
29 x 10 – 6
|
Liquids
|
Gases
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Silver
|
18 x 10– 6
|
Ether
|
550 x 10 – 6
|
Air & most others
|
1100 x 10 – 6
|
Density
Density is defined as the mass per unit volume occupied by an object or substance.
p = m / v , p => (Greek letter, rho) density , m => mass , v => volume
Densities of the most common substances ( 1 g/cm3 = 1000 kg/m3 )
Substances
|
p
|
Substances
|
p
|
Substances
|
p
|
Aluminum
|
2.70
|
Bone
|
1.70
|
Gases
| |
Brass
|
8.44
|
Ice ( 0° C )
|
0.917
|
Air
|
1.29 x 10 –3
|
Copper (ave.)
|
8.8
|
Carbon dioxide
|
1.98 x 10 –3
| ||
Gold
|
19.3
|
Liquids
|
Carbon monoxide
|
1.25 x 10 –3
| |
Iron or Steel
|
7.8
|
Water ( 4° C )
|
1.000
|
Hydrogen
|
0.090 x 10 –3
|
Lead
|
11.3
|
Blood, plasma
|
1.03
|
Helium
|
0.18 x 10 –3
|
Silver
|
10.1
|
Blood, whole
|
1.05
|
Methane
|
0.72 x 10 –3
|
Uranium
|
18.7
|
Seawater
|
1.025
|
Nitrogen
|
1.25 x 10 –3
|
Concrete
|
2.3
|
Mercury
|
13.6
|
Nitrous oxide
|
1.98 x 10 –3
|
Cork
|
0.24
|
Ethyl alcohol
|
0.79
|
Oxygen
|
1.43 x 10 –3
|
Glass
|
2.6
|
Gasoline
|
0.68
|
Water (steam,100°C)
|
0.60 x 10 –3
|
Granite
|
2.7
|
Glycerin
|
1.26
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Wood
|
0.3 – 0.9
|
Olive oil
|
0.92
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Heat : One Cause of Temperature Change
Heat is defined as energy which is transferred between a substance and its surroundings or between one part of a substance and another as a result of temperature difference. In nature, heat always flows from a hot body to a cold body until a common temperature is reached. One obvious effect of heat is to change temperature. Heat gain can increase temperature and heat loss can decrease temperature. Heat transfer also causes phase changes, such as melting , boiling, freezing, and condensation.
Q = s m /\ t .
where : Q => quantity/ amount of heat, m => mass , s => specific heat , /\ t => change of temp.
Specific heat is the heat required to change the temperature of a unit mass of a substance by one degree.
Heat of fusion ( solidification ) is the quantity of heat that must be supplied to a substance at its melting point to convert it completely to liquid ( solid ) at the same temperature.
Heat of vaporization ( condensation ) is the quantity of heat per unit mass that must be supplied to a substance at its boiling point to convert it completely to a gas ( liquid ) at the same temperature.
Vaporization – a change of phase from liquid to gas.
Condensation – a change of phase from gas to liquid.
Fusion ( melting ) – change of phase from solid to liquid.
Solidification – a change of phase from liquid to solid.
Sublimation - a change of phase from solid to gas without passing the liquid phase.
Boiling – vaporization of liquid in bubbles accompanied by agitation of liquid as the bubble rise, expand and burst.
Problems :
1. How much heat must be removed from 3500 g of water to reduce the temperature from 90°C to 25°C?
2. How much heat is to be added to 2500 g of lead to increase the temperature from 32°C to 58°C ?
Table of Specific heat of various substances at 20° C
Substance
|
s ( cal/g.°C , kcal/kg.°C)
|
Substance
|
s ( cal/g.°C , kcal/kg.°C
|
Aluminum
|
0.217
|
Ethyl alcohol
|
0.58
|
Brass
|
0.090
|
Glycerin
|
0.60
|
Copper
|
o.o92
|
Mercury
|
0.033
|
Gold
|
0.031
|
Water ( 15 ° C )
|
1.000
|
Iron or Steel
|
0.11
|
Gases at Constant Pressure
| |
Lead
|
0.030
|
Air
|
0.25
|
Silver
|
0.056
|
Carbon dioxide
|
0.199
|
Glass
|
0.20
|
Helium
|
1.240
|
Ice ( – 5 ° C )
|
0.50
|
Nitrogen
|
0.248
|
Porcelain
|
0.26
|
Oxygen
|
0.218
|
Wood
|
0.40
|
Water ( 100 °C steam)
|
0.482
|
Human body ( ave.)
|
0.83
|
Protein
|
0.40
|
Change of Phase and Latent heat
Most change of phase of a substance from one phase to another require large amounts of energy compared to the energy needed for temperature changes. Energy must be put into a substance to cause it to melt or boil. Energy must be put into a substance to cause it to freeze or condense ( gas to liquid ). The energy can be heat transfer or can be due to work done on or by the system. Energy used to cause a phase change does not cause a temperature change. It is a change of phase at constant temperature. ( Ex. ice at 0° C to water at 0° C or water at 100° C to steam at 100° C ). The amount of energy required to change phase is defined by :
Q = mhf or Q = mhv
hf is heat of fusion and hv is the heat of vaporization which are the amounts of heat required per unit mass to cause a phase change express in calorie per gram ( cal / g ).
The energy associated with a change of phase is called latent heat.
Latent Heat of various Substances
Substance
|
Melting Point (°C)
|
Heat of Fusion, h f
( cal / g , Kcal / kg)
|
Boiling Point (°C)
|
Heat of Vaporization, h v ( cal/g, Kcal/kg )
|
Oxygen
|
– 218.8
|
3.3
|
– 183
|
51
|
Ethyl Alcohol
|
– 114
|
25
|
78
|
204
|
Ammonia
|
– 75
|
108
|
– 33
|
327
|
Mercury
|
– 39
|
2.8
|
357
|
70
|
Water
|
0
|
80
|
100
|
540
|
Lead
|
327
|
5.9
|
1750
|
208
|
Aluminum
|
660
|
90
|
2450
|
2720
|
Silver
|
960
|
21
|
2193
|
558
|
Copper
|
1083
|
32
|
2300
|
1211
|
Uranium
|
1133
|
20
|
3900
|
454
|
Tungsten
|
3410
|
44
|
5900
|
1150
|
Problems : 1. An aluminum tray contains 1800 g of water at 0 ° C. Determine the quantity of heat needed to change phase from water to ice at 0° C. How many minutes does it take for the water to become ice if heat is removed at the rate of 30 cal / sec. ?
2. A burn produced by live steam at 100 ° C is more severe than one produced by the same amount of water at 100 ° C. To verify this, ( a ) Calculate the heat that must be removed from 5 g of water at 100 ° C to lower its temperature to 34 ° C ( skin temperature ); (b) calculate the heat that must be removed from 5 g of steam at 100 ° C to condense it and then lower its temperature to 34 ° C , and compare this with the answer in part ( a ).
3. A 120 g ice cube initially at – 20 ° C is placed in a container with 600 g of water initially at 30 ° C. Neglecting the heat loses to the container, what is the final temperature of the water – ice mixture ?
Evaporation and Relative Humidity
Water and other substances can evaporate at temperatures far below their boiling points. Ice can sublimate directly into vapor at temperature lower than 0 ° C. Humidity has a definite effect on the net evaporation rate of water; the higher the humidity, the lower the net evaporation rate. At any given temperature, air has a certain capacity to hold water vapor. This capacity increases with temperature.
Relative humidity is defined as the ratio of the actual vapor density to the saturation vapor density. Saturation vapor density is the maximum amount that air can hold at a given temperature. The quantitative expression for relative humidity is
% Relative Humidity = Vapor density x 100
saturation vapor density
A relative humidity of 100 % means the air is totally saturated and can hold no more water vapor anymore. The relative humidity is dependent on temperature. There are two reasons that the relative humidity affects the net evaporation rate. (1) If evaporation increases relative humidity to 100 %, then water vapor simply condenses out of the air at the same rate as evaporation puts it in. (2) Water molecules in the air may strike the water ( or ice ) and stick. The greater the humidity, the more likely this is to occur.
Methods of Heat Transfer
1. Conduction
2. Convection
3. Radiation
** Conduction – transfer of heat through stationary matter by physical contact. (Ex. bare feet & cold floor).
** Convection – transfer of heat by the movement of mass. ( Ex. Home with forced– air furnace )
** Radiation – heat transfer that occurs when visible light, infrared radiation, or another form of
electromagnetic radiation is emitted or absorbed. ( Ex. Sunlight warming the Earth )
Heat and the Human Body
Problem :
Heat transferred into or out of the body and thermal energy generated by the body can cause temperature changes. Normal body temperatures fall into narrow range. If body temperature becomes too high or too low, significant irreversible damage, even death, can occur. One serious problem with the body’s temperature regulating mechanism is that cell metabolism increases with the increase in temperature. Increase metabolism generates more heat and this can cause temperature to increase further. If the body temperature rises about 42°C, the body’s cooling mechanism can not keep up, and external intervention such as an alcohol rub is necessary. An analogous problem exists when body temperature becomes too low; cell metabolism decreases, and insufficient body heat is produced to prevent body temperature from dropping further.
Heat flows from a hot body to a cold body. Thus heat is transferred out of the body when surrounding temperatures are low and into the body when surrounding temperatures are high. Only the evaporation of perspiration keeps body temperature from rising uncontrollably when surrounding temperatures are high.
EFFICIENCY ( % ) of the body and of mechanical devices
Body
| |
Cycling
|
20 %
|
Swimming, surface
|
2 %
|
Swimming, submerged
|
4 %
|
Shoveling
|
3 %
|
Steam Engine
|
17 %
|
Gasoline Engine
|
38 %
|
Nuclear Power Plant
|
35 %
|
Coal Power Plant
|
42 %
|
The evaporation of perspiration relies on convection to carry away the energy used to make the perspiration change
phase. In addition to the evaporation of perspiration from the skin there is a significant evaporation of water from the lungs.
Energy and Oxygen Consumption Rate
Activity
|
Power : Rate of Energy Consumption
|
Oxygen Consumption
( Liters O2 / min )
| |
Kcal / min
|
( w )
| ||
Sleeping
|
1.2
|
83
|
0.24
|
Sitting at rest
|
1.7
|
120
|
0.34
|
Standing, relaxed
|
1.8
|
125
|
0.36
|
Sitting in class
|
3.0
|
210
|
0.60
|
Walking slowly ( 4.8 km/ hr )
|
3.8
|
265
|
0.76
|
Cycling ( 13 – 18 km/ hr )
|
5.7
|
400
|
1.14
|
Shivering
|
6.1
|
425
|
1.21
|
Playing tennis
|
6.3
|
440
|
1.26
|
Swimming breaststroke
|
6.8
|
475
|
1.36
|
Ice Skating ( 14.5 km/ hr )
|
7.8
|
545
|
1.56
|
Climbing stairs ( 116/ min )
|
9.8
|
685
|
1.96
|
Cycling ( 21 km/ hr )
|
10.0
|
700
|
2.00
|
Playing basketball
|
11.4
|
800
|
2.28
|
Cycling, Professional racer
|
26.5
|
1855
|
5.30
|
Problem :
1. How many grams of water must be evaporated per minute by a cyclist maintaining 15 km/ hr in order to get rid of body heat produced on a day when temperature is 34° C (normal skin temperature).
Solution :
Since air temperature is equal to the skin temperature, there is no heat transfer by conduction and radiation. Then all the body heat must be transferred out by evaporation of perspiration from the skin and water form the lungs. From the table, the power consumption while cycling at 15 km/hr is 400 w and the efficiency is 20 %.
Eff = Po / Pi => Po = Eff ( Pi ) = 0.20 ( 400 ) = 80 w
Pi = Po + Pheat => Pheat = Pi – Po = 400 – 80 = 320 w
Pheat = Q / t => Q = ( Pheat ) t = 320 ( 60 )/ ( 4.186 ) = 4,587 cal = 4.587 kcal /min
The heat of vaporization of water at body temperature is 580 cal / gram.
Energy required to cause change of phase :
Q = m hv => m = Q/ hv = 4,587 cal / 580 cal/g = 7.9 grams.
Note that 7.9 grams is the amount of water that evaporates every minute.
2. Determine the increase of temperature in one hour for the cyclist in problem 1 if his mass is 78 kilograms and there is no lost of body heat generated to the surroundings.
The energy required to cause temperature change is Q = s m /\ t => /\ t = Q / sm
From the table, the specific heat of the human body is 0.83 cal / g ° C or 0.83 kcal/ kg ° C ;
hence /\ t = ( 4.587 kcal / min )( 60 min ) / ( 0.83 kcal /kg ° C ) ( 78 kg ) = 4.25 ° C
3. Using the Table of Energy and Oxygen Consumption rate, compute the power generated by waste heat put into a classroom by 38 students of Physics 201. Determine how many kilocalories of energy do the students put into the room during a one hour lecture.
From the table above, for a person sitting in class the power generated in 210 w/ person; hence
Pheat = ( 210 w / person) ( 38 persons ) = 7,980 w = 7.98 kw
On the same table, the energy generated is 3 kcal / min./ person ; hence
Q = ( 3 kcal/min/ person ) ( 38 persons ) ( 60 min. ) = 6,840 kcal or 6,840,000 calories
Diagnostic and Therapeutic uses of Heat and Cold
Diagnostics : A person’s overall temperature can indicate the presence and seriousness of an infection. One of the body’s defense mechanisms against disease is to raise its temperature. When temperature becomes too high, it can be dangerous to the person, likewise if it is too low (hypothermia ), it also requires attention. Body temperature has an effect on the measurement of the gas content of the blood ( e.g. oxygen and carbon dioxide ), so such measurements must be corrected for variations from normal temperature.
Skin temperature is lower than core temperature but higher than normal room temperature. It is therefore possible to measure the infrared radiation from a person. The technique of measuring infrared radiation and thereby mapping temperature is called thermography and the picture obtained is called thermograph.
Thermography gives an indication of blood supply, since one of the methods of heat transfer in the body is by blood flow. A depressed skin temperature indicates a deficiency of blood flow to a given region and could be caused by clotting, stroke, etc. A locally elevated temperature can indicate the presence of a malignant ( cancerous ) tumor. Such tumors grow very rapidly compared to other tissues and thus require an increased blood supply.
Therapeutic uses of Heat
Two reasons for the mechanism of relief by elevated temperature :
( 1 ) relaxation of muscles and ( 2 ) increase blood flow.
There are many methods of treating various ills with heat. The simplest is by conduction using hot towels, heating pads, and the like. Heat transfer by radiation is also feasible; heat lamps emit most of their energy in the form of infrared radiation. Newborn infants are sometimes placed under an infrared heater to replace the heat they would have received from their mothers.
Forms of electromagnetic radiation are also used. Deep heating with microwaves and other forms of radio waves is called microwave or radiothermy. This mode of heat transfer must be carefully controlled to affect only the intended area.
Ultrasound diathermy is another form of “heat” treatment. Ultrasound is sound having a frequency above the human audible range. It can carry energy into the body, depositing it as a thermal energy. If sufficiently intense, it can cause a significant local temperature increase. Because sound is a coordinated vibration of matter, it is not really heat transfer, but the energy carried in by the sound does end up as thermal energy when absorbed.
Therapeutic uses of Cold
The removal of heat from the body can also be of therapeutic value. The method of removing heat is most often conduction, sometimes convection. Lowered temperature acts as a local anesthetic. Children who are teething are fond of sucking on ice cubes to relieve pain. Swelling can sometimes be reduced by the application of ice packs.
Cryosurgery is surgery using the application of cold. Cold is used to freeze small regions of the body. Warts and tumors can be treated in this way. Small parts of the brain can be frozen to treat Parkinson’s disease, although this technique has given way to the use of drugs. A detached retina can be reattached by spot freezing it to the back of the eye. The frozen tissue forms scars, which serves as tiny welds.
Lower temperature can serve as preservative, as in food refrigerators and freezers. Blood, bone marrow, and sperm are among the substances preserved by freezing. This can be thawed and revived, suggesting the possibility of placing people in suspended animation. It is not clear that this will ever be possible, because the survival rate of various tissues depends on the rapidity of the freeze and thaw, and no single process works well for all types of tissues. Techniques are being developed for the freeze preservation of more complicated tissues and organs. Some success has been achieved in preserving corneas, for example.
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