Chapter 3 Properties of a Pure Substance n

Chapter 3 Properties of a Pure Substance n Three familiar properties of a substance in the previous chapter — – specific volume, – pressure, and – temperature.

3. 1 THE PURE SUBSTANCE has a homogeneous and invariable chemical composition, n exist in more than one phase, and n exist with no change of phase. n Examples : n – liquid water, – a mixture of ice and liquid water, – a mixture of gases, such as air n A mixture of liquid air and gaseous air – ( X) – Because the chemical composition of the liquid phase is different from that of the vapor phase. )

Simple Compressible Substances (system) n Those whose surface effects, magnetic effects, and electrical effects are insignificant when dealing with the substances. n But changes in volume, such as those associated with the expansion of a gas in a cylinder, are very important.

3. 2 VAPOR–LIQUID–SOLID-PHASE EQUILIBRIUM IN A PURE SUBSTANCE 0. 1 MPa 20 0 C, 1 kg Fig. 3. 1 Heat, ν 99. 6 0 C Heat , ν

n Saturation Temperature – The temperature at which vaporization takes place at a given pressure. n And this given pressure is called the Saturation Pressure for the given temperature.

Sub-cooled liquid Compressed liquid Fig. 3. 2 A vapor-pressure curve for a pure substance

n Saturated liquid (state) – A substance exists as liquid (state) at the saturation temperature and pressure. n Subcooled liquid (Compressed liquid) – If the temperature of the liquid is lower than the saturation temperature for the existing pressure, it is called either a subcooled liquid (implying that the temperature is lower than the saturation temperature for the given pressure) or a compressed liquid (implying that the pressure is greater than the saturation pressure for the given temperature).

n Quality of substance – When a substance exists as part liquid and part vapor at the saturation temperature, its quality is defined as the ratio of the mass of vapor to the total mass. n Quality has meaning only when the substance is in a saturated state.

n Saturated vapor – A substance exists as vapor at the saturation temperature. n The quality of dry saturated vapor is 100%.

n Superheated vapor is the vapor at a temperature greater than the saturation temperature. n Actually, the substances we call gases are highly superheated vapors.

o. C Supercritical fluid 20 Fig. 3. 3 Temperature–volume diagram for water showing liquid and vapor phases.

Table 3. 1

FIGURE 3. 4 T –v diagram for the two-phase liquid–vapor region to show the quality specific volume relation.

To Derivative the Quality, x n. V =Vliq +Vvap = mliq v f+mvap v g then divide the above equation by total mass m,

Table 3. 2

FIGURE 3. 5 Pressure temperature diagram for a substance such as water.

FIGURE 3. 6 Carbon dioxide phase diagram.

Fig. 3. 7 Water phase diagram.

3. 3 INDEPENDENT PROPERTIES OF A PURE SUBSTANCE • The state of a simple compressible pure substance is defined by two independent properties. • For example, if the specific volume and temperature of superheated steam are specified, the state of the steam is determined.

A exception, in a saturation state, should be noted. n Consider the saturated-liquid and saturatedvapor states of a pure substance. These two states have the same pressure and the same temperature, but they are definitely not the same state. Therefore, in a saturation state, pressure and temperature are not independent properties. n Two independent properties such as pressure and specific volume or pressure and quality are required to specify a saturation state of a pure substance.

n. A mixture of gases, such as air, has the same characteristics as a pure substance as long as only one phase is present, concerns precisely this point. n The state of air, which is a mixture of gases of definite composition, is determined by specifying two properties as long as it remains in the gaseous phase.

3. 4 TABLES OF THERMODYNAMIC PROPERTIES o. C Pg=1. 554 Pg=5. 0 Pg=1. 0 200 FIGURE 3. 8 Listing of the steam tables.

• Example Let us calculate the specific volume of saturated steam at 200 o. C having a quality of 70%. • <Solution> Using Eq. 3. 1, and looking up Table B. 1. 3 gives v = 0. 3 (0. 001 156) +0. 7 (0. 127 36) = 0. 0895 m 3 /kg

Example. 3. 1

Example 3. 2

continued

Example 3. 3

Example 3. 4 (p. 412)

3. 5 THERMODYNAMIC SURFACES

3. 6 THE P–V–T BEHAVIOR OF LOW- AND MODERATE-DENSITY GASES • At very low densities the average distances between molecules is so large that the intermolecular ( IM ) potential energy may effectively be neglected. • In such a case, the particles would be independent of one another, and the situation is referred to as an ideal gas. • Therefore, a very low density gas behaves according to the ideal gas equation of state.

n. R is a different constant for each particular gas. The value of R for a number of substances is given in Table A. 5 of Appendix A.

Example 3. 5

Example 3. 6

n Over what range of density will the ideal gas equation of state hold with accuracy? n How much does an actual gas at a given pressure and temperature deviate from ideal gas behavior?

As would be expected, at very low pressure or high temperature the error is small and the gas behavior becomes closer to the ideal gas model. n But this error becomes severe as the density increases (specific volume decreases). n

FIGURE 3. 14 Temperature-specific volume diagram for water that indicates the error in assuming ideal gas for saturated vapor and for superheated vapor.

Compressibility factor, Z n A more quantitative study of the question of the ideal-gas approximation n Z =1, for an ideal gas n The deviation of Z from unity is a measure of the deviation of the actual relation from the ideal-gas equation of state.

Fig. 3. 15 Compressibility of nitrogen

Is there a way in which we can put all of the substances on a common basis? To do so, we “reduce” the properties with respect to the values at the critical point.

Example 3. 7

Example 3. 8