Molar heat capacity defined

The relative apparent molar heat capacity [Pg.365]

Another observable property of gases is the heat capacity. The molar heat capacity of monatomic gases was measured and found to be equal to (3/2)R, the value predicted for a perfect (point particle) gas. But, actual atoms had a well defined physical size. Since finite spheres would be expected to rotate, where was the heat capacity due to rotation Maxwell worried about this failure of the kinetic theory. Another type of eyes was required to see this result in its proper context. 

This, of course, is the difference between the heat capacity of the solution and the sum of those of the unmixed liquid elements. Using Eq. (38) and defining relative partial molar heat capacities of the components as... 

Closely related to specific heat is the molar heat capacity (Cm), defined as the amount of heat necessary to raise the temperature of 1 mol of a substance by 1°C. 

The heat capacities that have been discussed previously refer to closed, single-phase systems. In such cases the variables that define the state of the system are either the temperature and pressure or the temperature and volume, and we are concerned with the heat capacities at constant pressure or constant volume. In this section and Section 9.3 we are concerned with a more general concept of heat capacity, particularly the molar heat capacity of a phase that is in equilibrium with other phases and the heat capacity of a thermodynamic system as a whole. Equation (2.5), C = dQ/dT, is the basic equation for the definition of the heat capacity which, when combined with Equation (9.1) or (9.2), gives the relations by which the more general heat capacities can be calculated. Actually dQ/dT is a ratio of differentials and has no value until a path is defined. The general problem becomes the determination of the variables to be used in each case and of the restrictions that must be placed on these variables so that only the temperature is independent. 

The determination of the molar heat capacity of a phase saturated with respect to other phases in a multicomponent system requires the application of sufficient conditions to define the heat capacity. Although expressions are developed here for the molar heat capacity of a saturated phase in general, the expressions can be evaluated only if the phase is pure. The molar enthalpy of a phase is a function of the temperature, pressure, and (C — 1) mole fractions, where C represents the number of components. Thus,... 

The specific heat at constant pressure, cp, and the molar heat capacity at constant pressure, CP m, are defined by... 

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,... 

Thermochemical measurements are based on the relationships between heat and temperature. The measurement that relates to the two is heat capacity, defined as the amount of heat that is required to raise the temperature of a substance 1°C. (The amount of substance is sometimes expressed in moles or in grams.) The heat capacity of a mole of a substance is known as the molar heat capacity, while the heat capacity for gram values of a substance are known as specific heat capacities. The specific heat of a substance is the amount of heat required to raise 1 gram of the substance 1°C. The formula that is used to calculate specific heat is Equation 17.4 ... 

Equation (4.4), giving the temperature dependence of the molar heat capacity C p, allows integration of the first term on the right of Eq. (5.15). For this purpose, we define a mean heat capacity for the integral by an equation analogous to Eq. (4.6) ... 

The specific heat capacity is the heat that must be added per kg of a substance to raise the temperature by one Kelvin or one degree Celsius. The molar heat capacity is the specific heat multiplied by the molar mass (the molar mass of a structural unit in the case of polymers). Specific and molar heat capacity may be defined at constant volume or at constant pressure. The heat added causes a change in the internal energy (It) and in the enthalpy (heat content, H) of the substance. The following notations can be formulated ... 

The molar heat capacity (Cp) of a pure compound at constant pressure is defined... 

The molar heat capacity of a substance is defined as the energy required to raise the temperature of 1 mole of that substance by 1 K. Thus we might conclude that the molar heat capacity of an ideal gas is yR. However, we will have to qualify this conclusion when we consider the implications of the PV work that can occur when a gas is heated. 

Heat capacity Cp is defined as the energy required to change the temperature of a unit mass (specific heat) or mole (molar heat capacity) of the material by one degree. Typical units are J/(kg K). 

In Chapter 1 you learned that the specific heat of water is 4.18 J/g °C. The molar heat capacity is defined as the specific heat or heat capacity per mole of material. Calculate the molar heat capacity for water. What value(s) limited the number of significant figures in your answer ... 

The molar heat capacities at constant volume and constant pressure are defined by the relations... 

The definition of the specific molar heat capacity of the reference state, Cp, and the determination of the correction factor, CF(Zm, 6), are discussed next. The specific molar heat capacity of the reference state, Cp, is defined by... 

The molar heat capacity related to a process occurring at constant volume. This is denoted by Cy and is defined by... 

To evaluate the integral one needs to have the standard enthalpy change as a function of temperature. This information can be computed from the partial molar heat capacities. The partial molar heat capacity for component j is defined by... 

Heat capacity - Defined in general as dQ/dT, where dQ is the amount of heat that must be added to a system to increase its temperature by a small amount dT. The heat capacity at constant pressure is = (dHIdT), that at constant volume is Cy = (dE/dT)y, where H is enthalpy, E is internal energy, p is pressure, Tis volume, and T is temperature. An upper case C normally indicates the molar heat capacity, while a lower case c is used for the specific (per unit mass) heat capacity. [1]... 

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