Heat capacity of the system

In the summer, the COP of an air-to-air heat pump decreases as the outdoor temperature rises, reducing the cooling capacity. Normally the thermal needs of the building are met since it is common practice to size a heat pump so that it will deliver adequate cooling capacity in all but the most extreme summer conditions. The winter heating capacity of the system is then determined by this tradeoff, and if the heating capacity is inadequate, supplemental electric or fossil fuel heat is required. 

The quantity C appearing in this equation is known as the heat capacity of the system. It represents the amount of heat required to raise the temperature of the system 1°C and has the units J/°C. 

A reaction mixture is heated in a vessel fitted with an agitator and a steam coil of area 10 m2 fed with steam at 393 K. The heat capacity of the system is equal to that of 500 kg of water. The overall coefficient of heat transfer from the vessel of area 5 m2 is 10 W/m2 K. It takes 1800 s to heat the contents from ambient temperature of 293 to 333 K. How long will it take to heat the system to 363 K and what is the maximum temperature which can be reached ... 

In most processes, a reversible absorption of heat is accompanied by a change in temperature, and a calculation of the corresponding entropy change requires an evaluation of the integral of q/T. The term q is related to the heat capacity of the system which is usually expressed as a function of temperature. In a constant volume process, for example, the entropy change is... 

The linearity of van t Hoff plots, such as Figure 3.14, depends on the degree to which the isobaric heat capacity of the system (Cp) remains constant between the... 

Cp is the (total) molar heat capacity of the system at constant pressure, usually approximated, as though for an ideal solution, by1... 

Equation 12.3-16 is valid whether heat is transferred to or from the system, and whether the reaction is exothermic or endothermic. Note that each term on the left side of equation 12.3-16 may be an input or an output. Furthermore, CP is the molar heat capacity of the system, and is given by equation 12.3-13 as such, it may depend on both T and composition (through /A). The right side of equation 12.3-16 may also be expressed on a specific-mass basis (12.3-11). This does not affect the consistency of the units of the terms in the energy balance, which are usually J s-1. 

The enthalpy released or absorbed in a process can be described by Equation 6 for constant volume conditions and an isobaric process. While determining the safety subindex Irm the heat release of the main reaction is calculated for the total reaction mass (i.e. both the reactants and diluents are included) to take account the heat capacity of the system which absorbs part of the energy released ... 

Thus, the derivative of the energy with respect to the temperature of a closed system at constant volume is equal to the heat capacity of the system at constant volume. 

When a system is heated, its temperature generally increases. This increase in temperature is dependent on the heat capacity of the system under constant volume or constant pressure. Therefore, the heat capacity is defined as the ratio of heat added to a system to its corresponding temperature change. If the system is under constant volume, the molar heat capacity is Cv, whereas the molar capacity is Cp for a system under constant pressure. Then,... 

Given the speed of these combustion reactions, establishing a detailed mechanism presents experimental challenges. Nonetheless, a few basic principles have emerged. In those reactions where a salt is a by-product, the heat released from the reaction melts the salt and provides a liquid medium in which the product and reactants can combine. This has been inferred from the results of syntheses that were deliberately loaded with additional product salt, which increased the heat capacity of the system. This additional heat capacity resulted in a lower peak reaction temperature. If enough salt was added, the peak reaction temperature was insufficient for reaching a self-sustaining reaction. 

This same calculation can be made for the self-propagating high-temperature reaction if the functional form of the variable-temperature heat capacity is known. From this calculation we see how adding additional product salt reduces the temperature that the reaction can reach by increasing the heat capacity of the system. 

Evaluations of the interaction of P, with the hydrocarbonaceous ligates in terms of Eqs. (74)—(81), however, do not represent complete descriptions of the binding process, because the condition(s) under which the thermal energy of the system is increased has not been specified. If the heat capacity of the system is increased under experimental conditions where the pressure P does not change significantly, then Eq. (80) can be simplified and the specific heat capacity can be redefined as follows ... 

Our discussion so far has been limited to determining A//n or AE n by directly carrying out step II (or its inverse). However, it is often not necessary to carry out this step in actuality. If we know or can determine the heat capacity of the system, the temperature change (Tj — /j) resulting from step I provides all the additional information we need ... 

It may appear from this that any exothermic reaction system, no matter how dilute, should have an ignition temperature. This is not necessarily the case since the rate of temperature rise will depend on the heat capacity of the system and in very dilute systems an appreciable fraction of the reaction may be over before the ignition limit can bo reached. 

The heat capacity of the system is obtained from Equation 8.3-13 as... 

Furthermore, the temperature of the system changes from T to if this modification were produced alone it would absorb a quantity of heat C T — T), where C is the total heat capacity of the system for the conditions in which it is placed. 

Equations should be selected or a new more general equation developed which have a molecular-statistical basis and describe the relationships between the amount of adsorption, the heat of adsorption, the heat capacity of the system, the pressure, and the temperature. Various constants in these equations must have a clear physical meaning. These equations must describe the exact shape of the isotherms (Figure 2) and must reduce to the Henry equation at low coverage. 

Direct measurements of the heat capacities of the system zeolite NaCaA-n-heptane have been made in the temperature range 25°-240°C with the drop calorimeter described above. 

Figure 3. Heat capacity of the system n-heptane zeolite NaCaA...

In the summation the specific heats of the substances which are produced with evolution of heat are reckoned positive. The temperature coefficient of the heat of reaction is therefore equal to the change in the heat capacity of the system, consequent on the reaction. The heat of reaction increases with temperature when the substances formed in the reaction have a smaller heat capacity than the substances which disappear in the reverse case it decreases with temperature. For endothermic reactions in which Q is negative, an increase in Q means a diminution in the numerical value of the heat of reaction, and conversely. 

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