## Info

Temperature

Fig. 1.10 Four sequential processes diagrammed in pressure-temperature space is closed by the dashed arrow, a cyclic process is produced. It is not necessary that the paths connecting the thermodynamic states (numbered corners) be straight lines. Nor is a sequence of connected processes necessary; the simplest process connects two states (points).

### 1.6 Thermodynamic Properties

Even pure substances possess a large number of quantitative properties, including electrical, magnetic, optical, mechanical, transport, and thermodynamic. Only the last category is of interest here.

Thermodynamic properties are sometimes called state functions because they depend only on the state or condition of the system. They do not depend on the process or the path by which the particular state was achieved. For example, water vapor at a specified pressure and temperature is the same whether created by evaporating liquid water or by reacting H2 and O2.

1.6.1 Types of properties

Pure substances have only five fundamental or primitive thermodynamic properties, which are those that cannot be derived from other thermodynamic properties. These are, with their common symbols:

T = temperature p = pressure V = volume U = internal energy S = entropy

In addition, the following three derived thermodynamic properties are combinations of the primitive properties.

H = U + pV = enthalpy F = U - TS = Helmholz free energy G = H - TS = Gibbs free energy

The derived properties were conceived because the particular combination of the properties they represent are natural variables describing commonly encountered processes. For example, in isobaric (constant-pressure) processes involving only pV work, the heat exchanged between system and surroundings is equal to the change in the system's enthalpy. In another example, when pressure and temperature are fixed, chemical equilibrium is achieved when the Gibbs free energy is a minimum. The Helmholz free energy is rarely used in engineering thermodynamics, but its importance lies in the link that it provides between microscopic and macroscopic thermodynamics.

The eight basic thermodynamic properties can be classified as intensive or extensive. By intensive is meant the independence of the property on the quantity of substance (or equivalently, on the size of the system). Temperature and pressure are intensive properties. All of the others are extensive: their value is proportional to the quantity of the substance in the system. This feature permits V, S, U, H, F, and G to be made intensive simply by dividing by the quantity of the substance in the system. Quantity can be measured in terms of mass, moles, or number of molecules. Taking the number of moles, n, as the measure of quantity, the intensive counterparts of V, G are v = V/n, g = G/n. The lower-case designations are reserved for intensive properties, which are also called specific properties. The specific volume v is the reciprocal of the density of the substance. Pressure and temperature cannot be extensive; they are uniquely intensive properties.

Other thermodynamic properties are defined as partial derivatives of one of the eight properties listed above. The heat capacities (also called specific heats) at constant volume and at constant pressure,

physically represent the increases in internal energy and enthalpy, respectively, per degree of temperature increase. They are written as partial derivatives because of the restraints indicated by the subscripts on the derivatives. For CV, the increase in temperature is required to occur at a fixed volume. For Cp, on the other hand, the system's pressure is maintained constant during the increase in temperature.

Two other important derivative thermodynamic properties involve the fractional changes in volume as temperature or pressure is increased. The coefficient of thermal expansion a and the coefficient of compressibility P are defined by:

Because the specific volume (or density) of a substance depends on both temperature and pressure, a and P are defined as partial derivatives in order to indicate the property that is to be held constant during the increase of the other property. Both a and P are positive numbers, which accounts for the negative sign in the definition of p.

### 1.6.2 Absolute Vs Relative Properties

Another distinction among the basic thermodynamic properties is whether or not they possess absolute values. That is, is there a state in which a particular property has a value of zero? For volume the existence of an absolute measure is obvious. Pressure and temperature also possess unequivocal states in which these properties vanish. The absolute character of these properties is best understood by considering the atomistic nature of matter, in particular of gases.

Pressure in a gas is a consequence of the momentum transferred to a wall by rebounding of impinging molecules. Such momentum transfers appear as a force on the surface, which, when scaled to a unit surface area, is the gas pressure. A common means of reducing pressure is by changing the density of the gas using a vacuum pump. This reduces the frequency of molecular impacts on the walls and as a consequence diminishes the rate of momentum transfer to the surface. Being a force per unit area, pressure in the SI (i.e., metric) system has units of Newtons (N) per square meter, or Pascals (Pa). Normal atmospheric pressure is 105 Pa, or 0.1 MPa.

The origin of pressure in a liquid is quite different from that in a gas. Molecular rebounding from the system walls is not a major contributor. Imagine a pressing on the top of a box filled with a liquidr, as in Fig. 1.11a. The force on top of the piston appears as a pressure in the liquid inside the box, evenly and isotropically distributed thoughout (hydrostatic pressure). The temperature and density of the liquid barely changed in this process. Pressure in a liquid is approximately analogous to the force on opposing walls of a box generated by connecting them with a turnbuckle (Fig. 1.11b).

Pressure

Fig. 1.10 Turnbuckle analogy of pressure in a liquid'

Fig. 1.10 Turnbuckle analogy of pressure in a liquid' 