Heat capacity of a system

From Eqs. (45) and (46) it is apparent that the calculation of the energy and heat capacity of a system depends on the evaluation of the partition function a a function of temperature. In the more general case of molecules with an internal structure, the energy distributions of the various degrees of freedom must bo determined. This problem is outlined briefly in the following section. 

By definition, the heat capacity of a system is the amount of energy required to raise its temperature by 1 K. The unit is J KT1. To allow calculations and comparisons, the specific heat capacity is more commonly used ... 

When the heat capacity of a system is known as a function of the temperature, the heat absorbed by the system for a given temperature change can be calculated by integration of Equation (2.5). The integral is a line integral and the path for integration must be known. 

The heat capacity of a system is defined as the amount of heat, q, required to raise the temperature of the system by AT. Thus,... 

Since the stability condition for a chemical reaction is (dA/de) < 0, the heat capacity at constant composition is always less than the heat capacity of a system that remains in equilibrium as it receives heat. Certain fluid molecules, such as supercooled liquid glycerin, can vibrate but not rotate freely, which is called libration. As the temperature increases, more molecules rotate, and the variable s becomes the extent of libration-rotation transformation. If the transformation equilibrium is reached rather slowly, the heat capacity (Cp e) will be lower than the heat capacity measured in slow heating. 

The reduction in the heat capacity of a system which is consequent on most spontaneous chemical reactions led Th. W. Richards to the hypothesis that the atomic volumes of the elements are diminished when they enter into combination. The action of the chemical forces may, therefore, be compared to a mechanical compression. ... 

The partial differential notation is used because is a function of the volume (or pressure) as well as the temperature the subscript V as applied to the partial derivative in equation (9.9) indicates that in this case the volume is maintained constant. The heat capacity of a system at constant volume is therefore equal to the rate of increase of the energy content with temperature at constant volume. 

For a specified change in state of a system that has a definite temperature change dT associated with it, the heat withdrawn from the surroundings may have different values, since it depends upon the path of the change in state. Therefore it is not surprising that a system has more than one value of heat capacity. In fact, the heat capacity of a system may have any value from minus infinity to plus infinity. Only two values, Cp and C , have major importance, however. Since they are not equal, it is important to find the relation between them. 

The heat capacity of a system for a given process is defined as the quantity of heat required to produce a unit temperature increment in that process. ... 

In tank formation, the tank full of electrolyte has great heat capacity, so substantial amount of heat has to be generated for the temperature in the tank to rise (Fig. 12.1). This is not the case with container formation, however. There is a small volume of electrolyte in the battery and hence the latter s heat capacity is small. The heat capacity of a system is the measure of the heat energy required to increase the temperature of the system by 1 °C. The heat capacity of 1 g of mass is called specific heat. The electrolyte has the highest specific heat as compared to the specific heats of the other battery components. During soaking, the temperature in the battery increases rapidly... 

The heat capacity of a system tells us how much heat energy must be transferred to a system to achieve a given temperature change. 

Furthermore, even within the assumption of pairwise additivity, there are thermodynamic quantities which, although very important, are not expressible in terms of the pair distribution functions. For example, the heat capacity of a system can hardly be investigated within the framework of ordinary MDF s its investigation is rendered somewhat more feasible within the framework of the GMDF s. 

Heat is necessary to rise the temperature of a given substance which depends on the temperature range. The heat capacity of a system is defined as the heat required to rise the temperature of the system through Celsius (or one kelvin) and is denoted by C. It varies with temperature and is more accurately defined in the differential form. If the temperature of the system rises by dT when a small amount of heat dq is supplied, then heat capacity,... 

The heat capacity at a constant composition is always less than heat capacity of a system that remains in equilibrium with respect to as it receives heat. ... 

Notice that the higher the heat capacity of a system, the smaller the change in temperature for a given amount of absorbed heat. We define the heat capacity (C) of a system as the quantity of heat required to change its temperature by 1 °C. As we can see by solving Equation 6.5 for heat capacity, the units of heat capacity are those of heat (typically J) divided by those of temperature (typically °C). 

The heat capacity of a system C is defined as the ratio between added heat SQ and the temperature increment dT of the system... 

The heat capacity of a system at constant volume is denoted C and the heat capacity at constant pressure is denoted Cp. The heat capacity C is an extensive quantity, C being dependent on the size of the system. The unit for the heat... 

The definition of the heat capacity of a system C distinguishes between heat capacity at constant volume C, and heat capacity at constant pressure Cp. For solid substances and hquids C, and Cp are almost identical for gases Cp is significantly greater than The difference in Cp and C, for gases is due to the following ... 

The quantity of heat required to change the temperature of a system by one degree is called the heat capacity of the system. Heat capacity is represented by the symbol C. To obtain the heat capacity of a system (for example, a reaction vessel or 10 grams of water), we deliver a known quantity of heat, q, and measure the temperature change produced, AT. The heat capacity, C, is then calculated as... 

Once we know the heat capacity of a system, we can use it to convert an observed temperature change into a quantity of heat (or vice versa) by solving equation (7.3) for q or AT. For example. 

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