| |
|
|
| |
 |
| Thermodynamic Variables or Parameters |
|
| Thermodynamic variables are the quantities like pressure, volume and temperature, which help us to study the behavior of a thermodynamic system. There are some other thermodynamic variables such as entropy, internal energy, etc., but these thermodynamic variables can be expressed in terms of pressure, volume and temperature. |
| |
|
| The condition in which a particular material exists is described by physical quantities such as pressure, volume, temperature and amount of substance. For example, a tank of oxygen in a welding outfit has a pressure gauge and a label stating its volume. We could add a thermometer and place the tank on a scale to determine its mass. The variables that describe the state of the material and are called state variables. |
| |
| The volume V of a substance is usually determined by its pressure P, temperature T, and amount of substance, described by the mass m or number of moles n. Ordinarily, we can't change one of these variables without an increase in the pressure. If the tank gets too hot, it explodes. This happens occasionally with overheated steam boilers. |
| |
| In a few cases, where P, V, T and m (or n) have a simple relationship, we can express it as an equation called the equation of state. When it's too complicated for that, we can use graphs or numerical tables. Even then, the relation among the variables still exists. We call it an equation of state even when we do not know the actual equation. |
| |
Here's a simple (though approximate) equation of state for a solid material. The temperature coefficient of volume expansion b
is the fractional volume change  per unit temperature change, and
the compressibility k is the negative of the fractional volume change per
unit pressure change. If a certain amount of material has volume V0 when the pressure is P0 and the temperature is T0, the volume V at slightly differing pressure P and temperature T is approximately |
| |
 |
| |
| (There is a negative sign in front of the term k (P - Po) because an increase in pressure causes a decrease in the volume). Equation (1) is called an equation of state for the material. |
| |
|
| For a proper discussion of the three phases of matter, we require a three-dimensional diagram in which P, V and T should be plotted against three mutually perpendicular coordinate axes. This diagram, known as P-V-T diagram, is difficult to draw on paper. Hence, we generally ignore V and draw a graph between two variables P and T. This graph is known as pressure-temperature phase diagram. |
| |
| The figure(b) shown below represents the P-T diagram of those substances (such as CO2) that expand on melting. The figure(a) gives the P-T diagram for water. Water contracts on melting. |
| |
 |
| |
| In the figures a,b shown above, the curve PB represents the variation of melting point with pressure. The curve is generally called the fusion line. However, in the case of water, it is specifically called ice line. At pressure and temperature corresponding to any point on the fusion line, a substance C exists in equilibrium in solid and liquid phases. At pressure and temperature corresponding to any point on the fusion line, a substance coexists in equilibrium in solid and liquid phases. At pressure and temperature corresponding to any point on the left of the fusion line, a substance is in solid state. At pressure and temperature corresponding to any point on the right of fusion line, the substance exists in liquid state. When a certain amount of heat per unit mass, called latent heat of fusion is given to a substance, it crosses the fusion line at some point and the substance melts. Again, in figures a and b, the curve PA represents the variation of boiling point with pressure. This curve is called vaporization line. At pressure and temperature corresponding to any point on the vaporization line, a substance coexists in equilibrium in liquid and vapor phases. At pressure and temperature corresponding to any point above the vaporization line, a substance exists only in the liquid state. At pressure and temperature corresponding to any point below the vaporization line, a substance exists in vapor phase. When a certain amount of heat per unit mass, called the latent heat of vaporization is given to a substance, it crosses the vaporization line t some point and a change of state takes place. Again, in both the figures a and b, the curve PC is the sublimation line. In the case of water, it may be called hoar frost line. (Sublimation is a process in which a substance directly changes from solid to vapor state under suitable conditions of temperature and pressure.) At pressure and temperature corresponding to any point on the sublimation line, a substance co-exists in equilibrium in solid and vapor phases. |
| |
| The point P where the fusion line, vaporization line and sublimation line meet is called the triple point. The corresponding temperature and pressure are known as triple point temperature and triple point pressure respectively. At this temperature and pressure, a substance coexists in equilibrium in all the three phases. |
| |
|
|
| |
|
|
| |
|
|
|
