Temperature

  1. Descriptive Phenomena.
    Temperature and heat are related; a difference of temperature causes heat to flow from the hotter body to the colder body and when the two bodies are at the same temperature there is no heat flows; they are in a state of thermal equilibrium.
    1. Temperature:
      1. Definition of temperature: temperature measures the intensity of heat, rather than the amount of heat, that is, the hotter the body the higher its temperature, and vice versa. Or, more practically temperature is what a thermometer measures. This is a descriptive definition and not an explanation of what temperature is.
      2. The measurement of temperature. Thermometry is the science of the measurement of temperature and it makes use of the thermometric properties of matter.
        1. Thermometric properties are those properties of matter that change with temperature; for example, the volume change of gases, liquids, and solids with temperature is a thermometric property. Color and electrical resistance are two other thermometric properties.
        2. A thermometer is a device that makes use of the thermometric properties to measure temperature. The term "thermometer" was first coined in 1624.
          (1) The first thermometer was the air thermometer, which made use of the expansion of air to measure temperature. A device, later called the thermoscope, using this expansion of air, was used by Arabic and Medieval physicians to determine whether the patient had a fever or not. It did not measure temperature but only indicated that the body's temperature was not normal. Galileo is reported to have invented sometime between 1592 and 1603 (about 1597) the air thermometer; but there is no description of it in his extant works. He apparently turned this medical instrument into a temperature-measuring device by attaching a numerical scale to it to measure the expansion or contraction of the air with temperature change. Galileo's air thermometer consisted of glass bulb filled with air, or some gas, attached to the upper end of a vertical tube, which is filled with water, and whose lower end is placed in a dish or open container of water. As the temperature changes, the air in the bulb expands or contracts in volume, so that the level of water in the tube rises or falls. Unfortunately, this level of the water in the tube also changed by the change of the air pressure, without changing the temperature. Galileo did not recognize this defect. But one of Galileo's contemporary, the Dutchman Cornelius Drebbell (1572-1634), recognized this defect and proposed that the liquid at the lower end of the tube also be enclosed a bulb. Galileo's air thermometer did not depend upon the expansion of the liquid to measure temperature, although the level of the liquid did vary with temperature of the liquid. This expansion and contraction of the liquid was so small in comparison to the variation in the volume of the air or gas that it was usually ignored.

          (2) The first liquid in glass thermometer was proposed by French chemist John (Jean) Rey (1627-1704) in 1632; he proposed that the water in the thermometer be used to measure temperature by the expansion and contraction of the water instead of the air. But technical difficulties prevented the construction of such a device. Twenty-five years later the water was replaced by alcohol and two years later in 1659 by mercury. The first accurate mercury-in-glass thermometer was constructed about 1715 by Gabriel Daniel Fahrenheit (1686-1736), a maker of meteorological instruments, who was born at Danzig (now Gdansk, Poland) and emigrated to Amsterdam, Holland.

        3. Temperature scales: In order to measure temperature quantitatively, some sort of numerical scale must be defined. The first suggestions for a temperature scale using two fixed points were made about 1665. But until the adoption of Fahrenheit's scale 1724, there was no standard scale for the measurement of temperature; of course, the early thermometers had division marks on the glass tube, but they were arbitrary divisions and unique to the instrument, so that no comparative readings could be taken.
          (1) The Fahrenheit scale. Fahrenheit was trying to devise a scale that would preclude the use of negative values for temperature. To this end, he assigned the value of the lower fixed point of zero degrees for the lowest temperature that could be obtained in his day, the temperature of a freezing mixture of water and salt. As to the other fixed point he assigned the temperature of the human body. Then he divided the distance between the two fixed points into 12 major pairs; each split in turn into 8 divisions. Thus the temperature he assigned to high fixed point and the temperature of the human body was 96 degrees. Later Fahrenheit adjusted his scale to make the temperature of boiling pure water exactly 212 degrees. This set the freezing point of pure water at 32 degrees. Thus the body temperature is 98.6 degrees. The Netherlands and Great Britain immediately adopted the new scale in 1724 as soon as Fahrenheit announced it and it was later adopted by Canada and United States. The unit of measurement, the Fahrenheit degree, F°, is defined as 1/180 of the temperature interval between the freezing point and the boiling point of pure water at one atmosphere of pressure. That is,
          1 F° = (212°F - 32°F)/180.

          (2) The Celsius scale. The rest of the world was not satisfied with Fahrenheit's temperature scale; it seemed too arbitrary. In the early 1740's the Swedish astronomer, Anders Celsius (1701-1744), devised a temperature scale in which the temperature interval between the freezing point and the boiling point of pure water is divided into 100 steps. After some indecision, Celsius placed the freezing point of pure water at 0 and the boiling point at 100. Hence the unit of measurement is called the Centigrade degree, C°, from the Latin for one/one hundredth of the grade, and is defined as 1/100 of the temperature interval between the freezing point and the boiling point of pure water at one atmosphere of pressure.
          That is,
          1 C° = (100°C - 0°C)/100.
          The scale was originally called the centigrade scale from the name of its unit of measurement, but now the scientists favor the use of its inventor's name to name the scale, hence its name is now the Celsius temperature scale. The Celsius was not the only temperature scale proposed in the first half of the eighteenth century. A French physicist, Antoine Ferchauit de Reaumur, proposed a scale that placed the freezing point of pure water at zero and the boiling point of water at 80. While this scale was widely favored at first, it gradually faded into scientific oblivion. Celsius proposed his scale in 1743 and it has been adopted widely outside the English speaking world (although Canada and Great Britain have now officially converted to the Celsius scale).

          (3) Conversion between scales.

          (a) To convert the temperature measurement on the Celsius scale to that on the Fahrenheit scale, two steps must be done:
          (1) the unit must be converted and
          (2) an adjustment must be made for the number assigned to freezing point of water.
          The Fahrenheit degree is 1/180 of the temperature interval between the freezing point and the boiling point of pure water. And the centigrade degree is 1/100 of the temperature interval between the freezing point and the boiling point of pure water; hence the ratio of Fahrenheit unit to the centigrade unit is
          180/100 or 9/5 of the centigrade degree. Now the freezing point of pure water is 32° on the Fahrenheit scale and 0° on the Celsius scale. So after the unit conversion from centigrade units to Fahrenheit units, this adjustment must be made; 32°F must be added. That is,
          F = (9/5)C + 32. (1)
          Thus, for example, to convert room temperature 20°C from Celsius to Fahrenheit scale multiply 20°C by 9/5, which is 36°F and add 32°F to get 68°F.

          (b) Now to convert a temperature from the Fahrenheit to Celsius scale, two steps also must be done:
          (1) the adjustment for the assigned to the freezing point of water must be made and
          (2) the units must be converted.
          Since the freezing point of water on Fahrenheit scale is 32°F and 0°C on the Celsius scale, 32°F must be subtracted from the Fahrenheit temperature. And since the ratio of centigrade unit to Fahrenheit unit is 100/180 or 5/9 of the Fahrenheit degree, the result of the first step must be multiplied by 5/9 to convert it centigrade units. That is,
          C = (5/9)(F - 32). (2)
          Thus, for example, to convert room temperature of 68°F to the Celsius scale, subtract 32°F from 68°F to get 36°F and then multiply this by 5/9 to get 20°C.

          The only temperature that reads the same on both scales is -40°; that is,
          -40°C = -40°F.

      3. General Definition of Temperature. A thermometric property, such as length, volume, pressure, electrical resistance, etc., may be used in the definition of temperature. Let
        A0 be some thermometric property at 0°C,
        A100 be the same thermometric property at 100°C, and let
        At be the same thermometric property at some unknown temperature t.

        On the Celsius scale the size of the unit interval, the centigrade degree, is
        (A100 - A0)/100, or
        1C° = (1/100)(A100 - A0), (3)
        where quantity (A100 - A0) is the size of change of the thermometric property between 0°C and 100°C; or, in other words, there is one hundred degrees in the change of the thermometric property between 100°C and 0°C, that is,
        100°C = A100 - A0.

        Now by definition, the temperature t is the number of degrees of temperature, the number of the unit intervals, between temperature t°C and 0°C. Hence,
        (t°C - 0°C)/(100°C - 0°C) = (At - A0)/(A100 - A0), or
        (t°C/100°C) = (At - A0)/(A100 - A0), or
        t°C = 100°C(At - A0)/(A100 - A0), (4)
        where the quantity At - A0 is the change in the thermometric property between the temperatures t°C and 0°C.
        If the thermometric property A is taken to be length L, then
        t°C = 100°C(Lt - L0)/(L100 - L0). (5)
        If the thermometric property A is taken to be the volume of a gas, V,
        at a constant pressure, then
        t°C = 100°C(Vt - V0)/(V100 - V0). (6)
        If the thermometric property A is taken to be the pressure of a gas, p,
        at a constant volume, then
        t°C = 100°C(pt - p0)/(p100 - p0). (7)

        In 1887 the International Committee on Weights and Measures adopted, as the standard, the constant volume gas thermometer, using hydrogen gas (helium is now preferred). All other thermometers must be calibrated in the terms of this standard, using equation (7) by comparison of their readings with those of the standard gas thermometer.

        If the thermometric property A is taken to be the electrical resistance R in ohms, then
        t°C = 100°C(Rt - R0)/(R100 - R0). (8)

      4. Linear Expansion of Solids. Nearly all solid substances expand with increasing temperature. Consider a steel rod;
        if at the temperature T0 the steel rod has a length L0,
        then at temperature T0 + ΔT
        its length will have an increase length, L0 + ΔL.
        The change in length L does not depend only on the change of temperature ΔT, but also on the initial length of the rod L0. For example, if a rod 1 meter long increases its length 1 mm for a given temperature change, a rod of the same substance 2 meter long will increase its length 2 mm for the same temperature change. That is, the change in length is not absolute but relative; it is the relative change in length per unit temperature change that is the intrinsic natural property of a solid substance and is expressed by the coefficient of linear expansion, which has been defined as follows:
        α = (1/L0)(ΔL/ΔT). (9)
        The unit of α is "per degree", or degree-1, (C°)-1.
        If equation (9) is solved for ΔL, we find that the linear thermal expansion ΔL in the temperature change ΔT is
        ΔL = L0αΔT. (10)
        This shows that if a body has length L0 at temperature T0,
        then its length L at the temperature
        T = T0 + ΔT is given by
        L = L0 + ΔL,
        or, substituting for ΔL by equation (10), we get
        L = L0 + L0αΔT = L0(1 + αΔT). (11)

      5. Volume Expansion of Solids. When a rod is heated, not only does its length increase, but its diameter also increases (and its cross-sectional area) with increasing temperature; consequently, the volume of the rod also increases. To describe quantitatively this thermal property, the coefficient of volume expansion β has been defined as follows,
        β = (1/V0)(ΔV/ΔT). (12)
        The unit of β is "per degree", degree-1, (C°)-1, the same as the unit of α. This definition holds only if the material is isotropic (that is, expands uniformly in all directions) and the α for the material is very much less than one, that is, α << 1, so that β = 3α. If equation (12) is solved for ΔV, we find that the volume thermal expansion ΔV in the temperature change ΔT is
        ΔV = V0βΔT. (13)
        This shows that if a body has volume V0 at temperature T0,
        then its volume V at the temperature
        T = T0 + ΔT is given by
        V = V0 + ΔV,
        or, substituting for ΔV by equation (13) we get
        V = V0 + V0βΔT = V0(1 + βΔT). (14)

        The Coefficients of Expansion.
        Substances α, × 10-6 (C°)-1 β, × 10-6 (C°)-1
        Solids

        iron or steel 11 33
        aluminum 26 77
        brass 18.9 56
        ordinary glass 8.5 26
        Pyrex glass 3.3 10
        fused quartz 0.40 1
        platinum 9.0 27
        concrete 12 36
        lead 29 87
        Liquids

        methyl alcohol
        		1134
        carbon tetrachloride
        		581
        glycerin
        		485
        mercury
        		182
        turpentine
        		900
        gasoline
        		960
        Gases

        air
        		3670
        carbon dioxide
        		3740
        hydrogen
        		3660
        helium
        		3665

      6. The Volume Expansion of Water. Most liquids expand more or less uniformly with increase of temperature (as long as a phase change does not occur). Water, however, does not follow this usual behavior. If water at 0°C is heated, its volume decreases until its temperature reaches 4°C; then above 4C, as it is continues to be heated, the volume of the water behaves normally and expands as the temperature increases. Thus water has the least volume and its greatest density at 4°C of 1000 kg/m3, and its coefficient of volume expansion is zero. This property of water is very important, especially for the survival of aquatic life during cold winters. In a fresh water lake, as the surface water is cooled to 4°C, it becomes denser and sinks to the bottom of the lake, thereby pushing up the warmer water to the surface. A continual mixing takes place and the water deep in the lake remains at about 4°C as the colder (and less dense) water at the surface freezes. This convection process continues until the entire lake is at 4°C; further cooling of the surface water decreases the density of the water, which remains at the surface. When the surface water reaches 0°C it freezes, and reduces the heat loss from the interior of the lake. Thus lakes very seldom freeze entirely. This is why lakes freeze from the surface down, and thus allows the aquatic life to survive in the fresh water lakes.

      7. Mercury Thermometers. Mercury is not the ideal thermometric substance, but because of their compactness and simplicity, mercury thermometers are widely used. They usually consist of a glass bulb connected to a glass capillary (a tube with small inside diameter) closed at its upper end. The glass bulb is filled completely with mercury so that it will expand into the capillary tube as it is heated. Thus the thermal expansion of mercury is used to measure temperature; the temperature change is defined to be proportional to the change in the length of the mercury column in the capillary.
        Consider, as an example, a mercury thermometer that has a quartz bulb of a volume of 0.300 cm3 and a capillary with an inside diameter of 0.0100 cm. How much does the indicating thread of mercury move when the temperature changes from 30.0°C to 40.0°C, ignoring the expansion of the quartz bulb. From the above table, the coefficient of volume expansion for mercury is 182 × 10-6 (C°)-1. Hence, using equation (13),
        ΔV = V0βΔT = (0.300 cm3)[182 × 10-6 (C°)-1](10.0C°) = 5.5 × 10-4 cm3.
        Since the additional volume of the thin cylindrical column of mercury in the indicating capillary tube is equal to the change in the volume of mercury and
        since the volume of the cylinder = (cross-sectional area)(height)
        where the cross-sectional area of this cylindrical volume is πr2 and r = radius of the column = 0.005 cm,
        we can find the height h of the rise of the mercury in the capillary to be
        h = volume/area = (5.5 × 10-4 cm3)/π(0.005 cm)2 = 7.0 cm.

      8. Other Thermometers. Since mercury freezes at 38.8°C, the use of the mercury thermometer for measuring very low temperatures is limited. For measuring very low temperatures other liquids than mercury are used in the glass thermometer; alcohol (freezes at 115°C) or pentane (freezes at 131°C) are used. Since mercury boils at 356.9°C, mercury in ordinary glass can not be used to measure high temperatures. But if the thermometer is made of strong, high-melting point borosilicate glass with the space above the mercury filled with an inert gas such as argon at about 20 atm pressure, to prevent the mercury from boiling, temperatures up to 550°C may be read.

        Since electrical resistance changes with temperature, a thermometer consisting of a wire made of a pure metal, like platinum, can be used to measure temperatures. The platinum resistance thermometer consists essentially of coil of platinum wire mounted in a strain-free glass capsule. The platinum resistance changes by about 0.3% for a temperature change of 1C°. It can be used to measure very high temperatures.