Changes in Temperature

3 CHANGES IN TEMPERATURE 8.3a Sensible Heat and Heat Capacities 

The term sensible heat signifies heat that must be transferred to raise or lower the temperature of a substance or mixture of substances. The quantity of heat required to produce a temperature change in a system can be determined from the appropriate form of the first law of thermodynamics  

The specific internal energy of a substance depends strongly on temperature. If the temperature is raised or lowered in such a way that the system volume remains constant, the specific internal energy might vary as shown in the following plot  

A temperature change AT from Tj leads to a change AO in specific internal energy. As AT - 0, the ratio AW/AT approaches a limiting value (i.e., the slope of the curve at Ti), which is by definition the heat capacity at constant volume of the substance, denoted by Cv 

Since the plot of 0 versus T is not generally a straight line, C (the slope of the curve) is a function of temperature. 

A change in concentration or volume may alter the position of an equiUbrium (i.e., the relative amounts of reactants and products), but it does not change the value of the equilibrium constant. Only a change in temperature can alter the value of the equilibrium constant To understand why, consider the following reaction  

If we treat heat as though it were a reactant, we can use Le Chatelier s principle to predict what will happen if we add or remove heat. Increasing the temperature (adding heat) will shift the reaction in the forward direction because heat appears on the reactant side. Lowering the temperature (removing heat) will shift the reaction in the reverse directioa Consequently, the equilibrium constant, given by 

Another example of this phenomenon is the equilibrirrm between the following ions  

As we learned at the end of Chapter 11, rapid ascent to a high altitude can cause altitude sickness. The symptoms of altitude sickness, including dizziness, headache, and nausea, are caused by hypoxia, an insufficient oxygen supply to hody tissues. In severe cases, without prompt treatment, a victim may slip into a coma and die. And yet a person staying at a high altitude for weeks or months can recover gradually from altitude sickness, adjust to the low oxygen content in the atmosphere, and live and function normally. 

The combination of oxygen with the hemoglohin (Hb) molecule, which carries oxygen through the blood, is a complex reaction, but for our purposes it can be represented by the following simplified equation  

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One assumes the existence of a fluid that obeys Boyle s law (equation (A2.1.4) ) and that, on adiabatic expansion into a vacuum, shows no change in temperature, i.e. for which/yF=/(0) and = 0. (All... 

Most response functions of poiymers obey a time-temperature or frequency-temperature superjDosition [43, 44], A change in temperature is equivaient to a shift of tire iogaritiimic frequency axis ... 

Finally the influence of the temperature and addition of ethanol on the enantioselectivity of the Diels-Alder reaction was studied. Table 3.3 summarises the results for different aqueous media. Apparently, changes in temperature as well as the presence of varying amounts of ethanol have only a modest influence on the selectivity of the Cu(tryptophan)-catalysed Diels-Alder reaction in aqueous solution. However, reaction times tend to increase significantly at lower temperatures. Also increasing the alcohol content induces an increase of the reaction times. 

Figure 13.2. The change in temperature in Europe over the past 1000 years.

Conversion of Specific Gravity at 25°/25°C to Density at any Temperature from 0° to 40°C. Liquids change volume with change in temperature, but the amount of this change, /3 (coefficient of cubical expansion), varies widely with different liquids, and to some extent for the same liquid at different temperatures. 

Joule-Thompson Coefficient for Real Gases. This expresses the change in temperature with respect to change in pressure at constant enthalpy ... 

This table lists values of /3, the cubical coefficient of thermal expansion, taken from Essentials of Quantitative Analysis, by Benedetti-Pichler, and from various other sources. The value of /3 represents the relative increases in volume for a change in temperature of 1°C at temperatures in the vicinity of 25°C, and is equal to 3 a, where a is the linear coefficient of thermal expansion. Data are given for the types of glass from which volumetic apparatus is most commonly made, and also for some other materials which have been or may be used in the fabrication of apparatus employed in analytical work. 

The new international temperature scale, known as ITS-90, was adopted in September 1989. However, neither the definition of thermodynamic temperature nor the definition of the kelvin or the Celsius temperature scales has changed it is the way in which we are to realize these definitions that has changed. The changes concern the recommended thermometers to be used in different regions of the temperature scale and the list of secondary standard fixed points. The changes in temperature determined using ITS-90 from the previous IPTS-68 are always less than 0.4 K, and almost always less than 0.2 K, over the range 0-1300 K. 

Concentration is not the only property that may be used to construct a titration curve. Other parameters, such as temperature or the absorbance of light, may be used if they show a significant change in value at the equivalence point. Many titration reactions, for example, are exothermic. As the titrant and analyte react, the temperature of the system steadily increases. Once the titration is complete, further additions of titrant do not produce as exothermic a response, and the change in temperature levels off. A typical titration curve of temperature versus volume of titrant is shown in Figure 9.3. The titration curve contains two linear segments, the intersection of which marks the equivalence point. 

Finding the End Point by Monitoring Temperature The reaction between an acid and a base is exothermic. Heat generated by the reaction increases the temperature of the titration mixture. The progress of the titration, therefore, can be followed by monitoring the change in temperature. 

The SCE has the advantage that the concentration of Ck, and, therefore, the potential of the electrode, remains constant even if the KCl solution partially evaporates. On the other hand, a significant disadvantage of the SCE is that the solubility of KCl is sensitive to a change in temperature. At higher temperatures the concentration of Ck increases, and the electrode s potential decreases. Eor example, the potential of... 

A pH electrode is normally standardized using two buffers one near a pH of 7 and one that is more acidic or basic depending on the sample s expected pH. The pH electrode is immersed in the first buffer, and the standardize or calibrate control is adjusted until the meter reads the correct pH. The electrode is placed in the second buffer, and the slope or temperature control is adjusted to the-buffer s pH. Some pH meters are equipped with a temperature compensation feature, allowing the pH meter to correct the measured pH for any change in temperature. In this case a thermistor is placed in the sample and connected to the pH meter. The temperature control is set to the solution s temperature, and the pH meter is calibrated using the calibrate and slope controls. If a change in the sample s temperature is indicated by the thermistor, the pH meter adjusts the slope of the calibration based on an assumed Nerstian response of 2.303RT/F. 

The rate of a reaction is temperature-dependent. To avoid a determinate error resulting from a systematic change in temperature or to minimize indeterminate errors due to fluctuations in temperature, the reaction cell must have a thermostat to maintain a constant temperature. 

There is no discontinuity in volume, among other variables, at the Curie point, but there is a change in temperature coefficient of V, as evidenced by a change in slope. To understand why this is called a second-order transition, we begin by recalling the definitions of some basic physical properties of matter ... 

From the point of view of technology, it is convenient to classify polymers as thermosetting and thermoplastic. The former set by chemical crosslinks introduced during fabrication and hence do not change appreciably in their deformability with changes in temperature. Thermoplastics, on the other hand, soften and/or melt on heating and can therefore be altered in shape by heating... 

Using typical activation energies out of Tables 6.2-6.4, estimate the percent change in the rate of polymerization with a 1°C change in temperature at 50°C for thermally initiated and photinitiated polymerization. 

Note that this method of standardizing D values makes no allowance for the possibility that a molecule may change size, shape, or solvation with changes in temperature. In the next section we shall survey the behavior of polymeric materials in an ultracentrifuge. We shall see that diffusion coefficients can be... 

Materials that typify thermoresponsive behavior are polyethylene—poly (ethylene glycol) copolymers that are used to functionalize the surfaces of polyethylene films (smart surfaces) (20). When the copolymer is immersed in water, the poly(ethylene glycol) functionaUties at the surfaces have solvation behavior similar to poly(ethylene glycol) itself. The abiUty to design a smart surface in these cases is based on the observed behavior of inverse temperature-dependent solubiUty of poly(alkene oxide)s in water. The behavior is used to produce surface-modified polymers that reversibly change their hydrophilicity and solvation with changes in temperatures. Similar behaviors have been observed as a function of changes in pH (21—24). 

Other examples of materials that respond smartly to changes in temperature are the poly(ethylene glycol)s-modifted cottons, polyesters, and... 

Lubricants. Petroleum lubricants continue to be the mainstay for automotive, industrial, and process lubricants. Synthetic oils are used extensively in industry and for jet engines they, of course, are made from hydrocarbons. Since the viscosity index (a measure of the viscosity behavior of a lubricant with change in temperature) of lube oil fractions from different cmdes may vary from +140 to as low as —300, additional refining steps are needed. To improve the viscosity index (VI), lube oil fractions are subjected to solvent extraction, solvent dewaxing, solvent deasphalting, and hydrogenation. Furthermore, automotive lube oils typically contain about 12—14% additives. These additives maybe oxidation inhibitors to prevent formation of gum and varnish, corrosion inhibitors, or detergent dispersants, and viscosity index improvers. The United States consumption of lubricants is shown in Table 7. 

Aluminum. All primary aluminum as of 1995 is produced by molten salt electrolysis, which requires a feed of high purity alumina to the reduction cell. The Bayer process is a chemical purification of the bauxite ore by selective leaching of aluminum according to equation 35. Other oxide constituents of the ore, namely siUca, iron oxide, and titanium oxide remain in the residue, known as red mud. No solution purification is required and pure aluminum hydroxide is obtained by precipitation after reversing reaction 35 through a change in temperature or hydroxide concentration the precipitate is calcined to yield pure alumina. 

The solubihty of a number of sodium orthophosphates is depicted in Figure 7. Some of the sodium phosphates dissolve or precipitate incongmendy, affording a different Na20/P20 ratio in the solution phase from that of the soHd phase. Sodium phosphates that precipitate are also a function of the temperature. As the temperature increases, the sodium phosphates that may precipitate from solution tend to be anhydrous or lower hydrates than those equiUbrium sodium phosphate phases at lower temperature. Whereas most of the phases in Figure 7 represent congmentiy soluble sodium phosphates, soHd phases appear or disappear upon changes in temperature. 

Effect of Temperature. In addition to being often dependent on parameters such as shear stress, shear rate, and time, viscosity is highly sensitive to changes in temperature. Most materials decrease in viscosity as temperature increases. The dependence is logarithmic and can be substantial, up to 10% change/°C. This has important implications for processing and handling of materials and for viscosity measurement. 

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