Temperature Changes Heat Capacity

TABLE 3.4 Specific Heat Capacities of Some Common Substances 

Similarly, only two U.S. states have never recorded a temperature above 100 °F. One of them is obvious Alaska. It is too far north to get that hot. The other one, however, may come as a surprise. It is Hawaii. The water that surrounds America s only island state moderates the temperature, preventing Hawaii from ever getting too hot. 

If you want to heat a metal plate to as high a temperature as possible for a given energy input, you should rriake the plate out of  

Have you ever loaded a cooler with ice and then added room-temperature drinks If you have, you know that the ice quickly melts. In contrast, if you load your cooler with chilled drinks, the ice lasts for hours. Why the difference The answer is related to the high heat capacity of the water within the drinks. As we just learned, water must absorb a lot of heat to raise its temperature, and it must also release a lot of heat to lower its temperature. When the warm drinks are placed into the ice, they release heat, which then melts the ice. The chilled drinks, on the other hand, are already cold, so they do not release much heat. It is always better to load your cooler with chilled drinks—that way, the ice will last the rest of the day. 

CAN YOU ANSWER THIS Suppose you are cold-weather camping and decide to heat some objects to bring into your sleeping bag for added warmth. You place a large water jug and a rock of equal mass close to the fire. Over time, both the rock and the water jug warm to about 38 °C (100 °F). If you could bring only one into your sleeping bag, which one should you bring to keep you the warmest Why  

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As explained in See. 3.1.5, the heat eapaeity of a closed system is defined as the ratio of an infinitesimal quantity of heat transferred across the boundary under specified conditions and the resulting infinitesimal temperature change heat capacity = dq/dT. The heat capacities of isoehorie (eonstant volume) and isobarie (eonstant pressure) processes are of particular interest. 

The number of terms required in equation (2.19) depends upon the substance and the temperature interval. For small temperature differences, heat capacity changes with temperature are small and Cp can be represented reasonably well by the constant term a. For larger temperature changes a and b are used in equation (2.19), and over very large temperature ranges, higher power terms are included. Tables of the coefficients for equation (2.19) for a number of substances are summarized in the literature,2 with an abbreviated list3 summarized in Table 2.1. 

It is thus seen that heat capacity at constant volume is the rate of change of internal energy with temperature, while heat capacity at constant pressure is the rate of change of enthalpy with temperature. Like internal energy, enthalpy and heat capacity are also extensive properties. The heat capacity values of substances are usually expressed per unit mass or mole. For instance, the specific heat which is the heat capacity per gram of the substance or the molar heat, which is the heat capacity per mole of the substance, are generally considered. The heat capacity of a substance increases with increase in temperature. This variation is usually represented by an empirical relationship such as... 

The cost of recovery will be reduced if the streams are located conveniently close. The amount of energy that can be recovered will depend on the temperature, flow, heat capacity, and temperature change possible, in each stream. A reasonable temperature driving force must be maintained to keep the exchanger area to a practical size. The most efficient exchanger will be the one in which the shell and tube flows are truly countercurrent. Multiple tube pass exchangers are usually used for practical reasons. With multiple tube passes the flow will be part counter-current and part co-current and temperature crosses can occur, which will reduce the efficiency of heat recovery (see Chapter 12). 

Heat exchanger network resilience analysis can become nonlinear and nonconvex in the cases of phase change and temperature-dependent heat capacities, varying stream split fractions, or uncertain flow rates or heat transfer coefficients. This section presents resilience tests developed by Saboo et al. (1987a,b) for (1) minimum unit HENs with piecewise constant heat capacities (but no stream splits or flow rate uncertainties), (2) minimum unit HENs with stream splits (but constant heat capacities and no flow rate uncertainties), and (3) minimum unit HENs with flow rate and temperature uncertainties (but constant heat capacities and no stream splits). 

Most chemical processing plants include pure or multicomponent streams which change phase or which have strongly temperature-dependent heat capacities. Under these conditions the minimum approach temperature in a network can occur anywhere inside an exchanger. Therefore integral or differential equations are generally required to locate A Tm. 

Develop techniques to test the resilience of class 2 HENs with stream splits and/or bypasses, temperature and/or flow rate uncertainties, and temperature-dependent heat capacities and phase change. It may be possible to extend the active constraint strategy to class 2 problems. This would allow resilience testing of class 2 problems with stream splits and/or bypasses and temperature and/or flow rate uncertainties. However, the uncertainty range would still have to be divided into pinch regions (as in Saboo, 1984). 

Extend the multiperiod synthesis-analysis-resynthesis algorithm to handle temperature-dependent heat capacities and phase change and uncertain heat transfer coefficients. 

Effects of change in temperature on heat capacity and heats of vaporization are negligible. Heat losses from the column are negligible. Effects of pressure drop over the column may be neglected. 

ProTherm (16) is a large collection of thermodynamic data on protein stability, which has information on 1) protein sequence and stmcture (2) mutation details (wild-type and mutant amino acid hydrophobic to polar, charged to hydrophobic, aliphatic to aromatic, etc.), 3) thermodynamic data obtained from thermal and chemical denaturation experiments (free energy change, transition temperature, enthalpy change, heat capacity change, etc.), 4) experimental methods and conditions (pH, temperature, buffer and ions, measurement and method, etc.), 5) functionality (enzyme activity, binding constants, etc.), and 6) literature. 

However, it is also possible that there is no change in entropy (and, hence, enthalpy) during the transition instead there is a discontinuity in the second derivative of the free energy with respect to temperature (the heat capacity— Equation (3)). Such transitions are termed second order ... 

This equation is quite useful, particularly if the temperature range AT is not very large. Over short ranges of temperature the heat capacity of most substances does not change very much. 

Differential scanning calorimetry DSC Energy difference Enthalpies and temperature of phase changes, heat capacity, desolvations, reactions, decompositions... 

The standard enthalpy change for reaction 2 is also independent of temperature. The heat capacity of the reacting liquid is 0.8 cal/(cm -°C). 

Figure 2.46 illustrates the completed analysis. A number of other polymers are described in the ATHAS Data Bank, described in the next section. Most data are available for polyethylene. The heat capacity of the crystalline polyethylene is characterized by a T dependence to 10 K. This is followed by a change to a linear temperature dependence up to about 200 K. This second temperature dependence of the heat capacity fits a one-dimensional Debye function. Then, one notices a slowing of the increase of the crystalline heat capacity with temperature at about 200 to 250 K, to show a renewed increase above 300 K, to reach values equal to and higher than the heat capacity of melted polyethylene (close to the melting temperature). The heat capacity of the glassy polyethylene shows large deviations from the heat capacity of the crystal below 50 K (see Fig. 2.45). At these temperatures the absolute value of the heat capacity is, however, so small that it does not show up in Fig. 2.46. After...

Enthalpy en- thal-pe n [en- + Gk thalpein to heat] (ca. 1924) (heat content) n. Thermodynamically, the enthalpy of a system is the sum of the internal energy and the pressure-volume product multiplied by the pressure H = E + pv where H is the enthalpy or heat content, E the internal energy of the system, p the pressure, and v is the volume. We are usually concerned about changes in enthalpy rather than absolute values. Enthalpies of polymers are usually stated per unit mass, e.g., kj/kg, and are ordinarily referred to room temperature, 20-25°C, at which temperature enthalpy is arbitrarily set to zero. The rate of change of enthalpy with temperature is heat capacity. 

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