Specific heat capacity results

Example 9.1 A process involves the use of benzene as a liquid under pressure. The temperature can be varied over a range. Compare the fire and explosion hazards of operating with a liquid process inventory of 1000 kmol at 100 and 150°C based on the theoretical combustion energy resulting from catastrophic failure of the equipment. The normal boiling point of benzene is 80°C, the latent heat of vaporization is 31,000 kJ kmol the specific heat capacity is 150 kJkmoh °C , and the heat of combustion is 3.2 x 10 kJkmok. ... 

For a thermometer to react rapidly to changes in the surrounding temperature, the magnitude of the time constant should be small. This involves a high surface area to liquid mass ratio, a high heat transfer coefficient and a low specific heat capacity for the bulb liquid. With a large time constant, the instrument will respond slowly and may result in a dynamic measurement error. 

R = 8.3145 kJ-K 1-kmol 1 and T is the reactor temperature (K). T is also the supply temperature of A whose yet unknown inventory mA is in the form of a superheated liquid. The total amount of B to be produced is 1000 kmol. T and mA are to be selected with the additional consideration of safety. The normal boiling point of A is 70°C, its latent heat of vaporization is 25,000 kJ-kmol-1, the liquid specific heat capacity is 140 kJ-kmol K 1, and its heat of combustion is 2.5 x 106 k.bkrnol. The residence time of the reactor is 1 min, and the safety is measured in terms of fire and explosion hazards on the basis of the theoretical combustion energy resulting form catastrophic failure of the equipment. 

The temperature profile of a planetary atmosphere depends both on the composition and some simple thermodynamics. The temperature decreases with altitude at a rate called the lapse rate. As a parcel of air rises, the pressure falls as we have seen, which means that the volume will increase as a result of an adiabatic expansion. The change in enthalpy H coupled with the definition of the specific heat capacity... 

The SI unit for heat capacity is J-K k Molar heat capacities (Cm) are expressed as the ratio of heat supplied per unit amount of substance resulting in a change in temperature and have SI units of J-K -moC (at either constant volume or pressure). Specific heat capacities (Cy or Cp) are expressed as the ratio of heat supplied per unit mass resulting in a change in temperature (at constant volume or pressure, respectively) and have SI units of J-K -kg . Debye s theory of specific heat capacities applies quantum theory in the evaluation of certain heat capacities. 

If the mean specific heat capacity does not change appreciably during reaction, rearranging eqn. (34) and integrating leads to the result... 

ATOMIC HEAT. The product of the gram-atomic weight of an element and its specific heat The result is the atomic heat capacity per gram-atom. For many solid elements, the atomic heal capacity is very nearly the same, especially at higher temperatures and is approximately equal to 3R, where R is the gas constant (Law of Dulong and Petit). 

MOLAR HEAT. The product of the gram-molecular weight of a compound and its specific heat. The result is the heat capacity per gratrt-inolecular weight... 

In order to obtain accurate results, this function should be accounted for when the temperature of a reaction mass tends to vary over a wider range. However, in the condensed phase the variation of heat capacity with temperature is small. Moreover, in case of doubt and for safety purposes, the specific heat capacity should be approximated by lower values. Thus, the effect of temperature can be ignored and generally the heat capacity determined at a (lower) process temperature is used for the calculation of the adiabatic temperature rise. 

A reaction should be stopped by flooding with a cold solvent. The amount of solvent needs to be sufficient to cool the reaction mass to a thermally stable level. To test this theory, flooding was tested in a Calvet calorimeter (Figure 10.4). The experiment showed that the dilution is endothermal with a heat release of—ffikjkg"1 of mixture (reaction mass and solvent). The reaction mass (2230 kg) has a specific heat capacity of 1.7kJ kg 1 K 1 and a temperature of 100 °C. The dilution is with 1000 kg of a solvent at 30 °C, with a specific heat capacity of 2.6kJ kg"1 K"1. The resulting mixing temperature (Tm) can be calculated from a heat balance ... 

In the original work, Keller [15] used a detection limit of 20Wkg 1 and a specific heat capacity of 1.8kjkg 1 K" obtaining the same result. The explanation is left to the reader as an exercise. 

Fig. 1. Partial specific heat capacity of sperm whale metmyoglobin in aqueous solutions with different pH values in the temperature range in which heat denaturation takes place. The observed heat capacity peak corresponds to the heat absorption upon protein denaturation that also results in a significant heat capacity increase A°CP [for details see Privalov et al. (1986)].

While the procedure for this experiment is provided with a fair amount of detail, students can have input into the design of the calorimeter and, although a list of materials is provided, different materials can be made available and they can choose the ones they think would be most effective. The inquiry aspect of this experiment lies primarily in the detailed analysis of their results required to suggest an appropriate interstitial material and the need to assess sources of error. If, for example, students have a large error in the determination of the specific heat capacity of copper, they must decide what could contribute to the error and then try to redesign their calorimeter or their technique in order to limit the error. 

On the basis of the equipartition of the energy content of a molecule over the degrees of freedom, the maximum value of the molar heat would correspond to 3R per atom. In reality, part of the degrees of freedom are always frozen in, which results in a lower value of the molar heat capacity. The increase of the specific heat capacity with temperature depends on an increase of the vibrational degrees of freedom. 

The result for the thermal expansion coefficient, a, which is equal to (dV/dT)/V, is shown in Fig. 13.36 for the cooling and heating process. In the cooling process a decreases gradually from tq to ag. Hysteresis in the volume causes in the subsequent heating process an anomalous effect in the thermal expansion coefficient, depicted by undershoot and overshoot, as also shown in Fig. 13.36. A similar effect occurs in enthalpy H and accordingly in cp, the specific heat capacity, equal to dH/dT. This effect is frequently observed in DSC (Differential Scanning Calorimetry) experiments. 

When these reactants (both originally at the same temperature) are mixed, the temperature of the mixed solution is observed to increase. Thus the chemical reaction must be releasing energy as heat. This increases the random motions of the solution components, which in turn increases the temperature. The quantity of energy released can be determined from the temperature increase, the mass of the solution, and the specific heat capacity of the solution. For an approximate result we will assume that the calorimeter does not absorb or leak any heat and that the solution can be treated as if it were pure water with a density of 1.0 g/mL. 

Suppose a person weighing 50 kg (mostly water, with specific heat capacity 4.18 J K g ) eats a candy bar containing 14.3 g glucose. If all the glucose reacted with oxygen and the heat produced were used entirely to increase the person s body temperature, what temperature increase would result (In fact, most of the heat produced is lost to the surroundings before such a temperature increase occurs.)... 

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