Chapter 3 Properties of a Pure Substance

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, exist in more than one phase, and exist with no change of phase.

Examples :

– liquid water,– a mixture of ice and liquid water,– a mixture of gases, such as air

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. )

Those whose surface effects, magnetic effects, and electrical effects are insignificant when dealing with the substances.

But changes in volume, such as those associated with the expansion of a gas in a cylinder, are very important.

Simple Compressible Substances(system)

3.2 VAPOR–LIQUID–SOLID-PHASE EQUILIBRIUM IN A PURE SUBSTANCE

Fig.3.1

0.1MPa

20 0C,1kgHeat, ν

99.6 0C

Heat ,ν

Saturation Temperature– The temperature at which

vaporization takes place at a given pressure.

And this given pressure is called the Saturation Pressure for the given temperature.

Fig. 3.2 A vapor-pressure curve for a pure substance

Sub-cooled liquid

Compressed liquid

Saturated liquid (state)– A substance exists as liquid (state) at the saturation

temperature and pressure.

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).

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.

Quality has meaning only when the substance is in a saturated state.

Saturated vapor– A substance exists as vapor at the

saturation temperature. The quality of dry saturated vapor

is 100%.

Superheated vaporis the vapor at a temperature greater than the saturation temperature.

Actually, the substances we call gases are highly superheated vapors.

Fig. 3.3 Temperature–volume diagram for water showing liquid and vapor phases.

20

oCSupercritical fluid

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

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.

Consider the saturated-liquid and saturated-vapor 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.

Two independent properties such as pressure and specific volume or pressure and quality are required to specify a saturation state of a pure substance.

A exception, in a saturation state, should be noted.

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.

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

FIGURE 3.8 Listing of the steam tables.

200

Pg=1.554

Pg=1.0

oC

Pg=5.0

• Example Let us calculate the specific volume of saturated steam at 200oC 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.

+

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

Over what range of density will the idealgas equation of state hold with accuracy?

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.

But this error becomes severe as the density increases (specific volume decreases).

FIGURE 3.14 Temperature-specific volume diagram for water that indicates the error in assuming ideal gas for saturated vapor and for superheated vapor.

A more quantitative study of the question of the ideal-gas approximation

Z =1, for an ideal gas

The deviation of Z from unity is a measure of the deviation of the actual relation from the ideal-gas equation of state.

Compressibility factor, Z

Fig.3.15 Compressibility of nitrogen

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

Example 3.7

Example 3.8