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Zeroth Law of Thermo- Dynamics: Preliminary Concepts

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Zeroth Law of Thermo- Dynamics: Preliminary Concepts 4 Zeroth Law of Thermo- CHAPTER dynamics: Preliminary Concepts 4.1 INTRODUCTION Thermodynamics is a branch of physics that deals with the inter-relations between heat and other forms of energy. It is based on principles, which has been formulated by generalizing experimental observations made on a variety of physical systems. It makes no attempt about what is going on at microscopic (atomic or molecular) level. It is a macroscopic (large-scale) theory of natural phenomena. Its aim is to establish relationship between directly observed macroscopic quantities viz. pressure, volume, temperature, concentration, electric field, magnetic field, polarization, magnetization, etc. which define the state of the system under investigation. As the name itself suggests, it employs both thermal and mechanical concepts. Its principles are widely used in design of heat engines, nuclear power stations, rocket propulsion, biological phenomena etc. One of the shortcomings of thermodynamics is that it gives no picture of the internal mechanism of phenomena. The kinetic theory, on the other hand, attempts to establish relationships between macroscopic quantities and microscopic quantities. In this method, the laws of mechanics are applied to the motion of individual molecule and macroscopic properties (such as heat capacity, expansion coefficient, viscosity, diffusion, etc.) are deduced. In statistical mechanics, no attention is paid to individual molecule, instead the assembly of microscopic particles is treated statistically. This approach of describing behavior of system will be discussed in a separate chapter. 4.2 THERMODYNAMIC SYSTEM AND SURROUNDINGS To study the behavior of a substance thermodynamically, we select a finite portion of that substance. The portion that is set aside (in imagination) on which we pay our attention or on which experimental observations are made is called system. Everything outside this portion which has direct bearing on the behavior of the system is called surroundings. The system and the surroundings comprise what we call universe. The boundary which separates the system from surroundings is called wall. The wall of the system may or may not allow it to interact with the surroundings. A wall, which prevents any exchange of matter and energy between the system and surroundings is called isolating wall and the system is said to be isolated. Such a system will not be affected by its surrounding and is not of much importance from thermodynamic point of view. 70 Thermal and Statistical Physics If the boundary of the system permits exchange of matter and energy, the system is called open system. On the other hand, if the exchange of energy and not matter occurs between the system and surroundings, the system is called closed system. A wall which prevents thermal interaction is known as adiabatic wall and a system enclosed within an adiabatic wall is called thermally isolated. If exchange of heat takes place between the system and surroundings through the boundary wall, the boundary is called diathermic wall. 4.3 THERMODYNAMIC VARIABLES There are, in general, two points of view to study the behavior of the system or its interactions with the surroundings or both: macroscopic point of view and microscopic point of view. The macroscopic description of system involves the specification of a few fundamental measurable properties of the system such as volume, pressure, temperature, amount of substance etc., without considering the internal structure of the system. The macroscopic quantities refer to gross characteristics or large- scale properties of the system and are called macroscopic thermodynamic coordinates (variables or parameters). Of the many thermodynamic variables, only a few variables are needed for the description of the system. In microscopic description of a system assumptions are made about the structure of matter under investigation. It postulates the existence of molecules, their motion, their energy states, their interactions etc. Thus a large number of quantities, which refer to small-scale properties of the system, needed to specify the state of the system. These are called microscopic coordinates (variables or parameters). These variables cannot be measured in laboratory. A thermodynamic system is one whose state can be described in terms of thermodynamic variables. The variables defining the state of a thermodynamic system differ from system to system. For instance, the state of a gas enclosed in a vessel is described by its pressure, volume, temperature and mass. The state of a metal bar is described by its length, cross-section, tension, temperature, the state of a liquid film by its area, surface tension etc. A dielectric and a magnetic system need additional variables such as polarization and magnetization respectively. Although it might seem that the macroscopic and microscopic points of view are entirely different and incompatible, there is nevertheless, a relation between them and when both points of view are applied to the same system, they lead to the same conclusion. The relation between the two points of view lies in the fact that the macroscopic properties are really averages over a long period of time of a large number of microscopic characteristics. For example the macroscopic quantity pressure is the average rate of change of momentum due to all the molecular collisions made on a unit area of the container of the gas. 4.4 EXTENSIVE AND INTENSIVE VARIABLES The state variables which are proportional to the mass of the system are called extensive variables. For instance, volume, internal energy, enthalpy, entropy, etc. are extensive variables. On the other hand, intensive variables are those which are independent of mass of the system. Temperature, pressure and density are intensive variables. Intensive variables are invariably denoted by capital letters such as T and P. Zeroth Law of Thermodynamics: Preliminary Concepts 71 The value of extensive variable per unit mass is called specific variable. Usually an extensive variable is denoted by capital letter and its specific value by small letter. The specific value of an extensive variable is independent of mass and hence is an intensive variable. If a system with mass m occupies a volume V, then its specific volume is denoted by v and given by V Specific volume, v = m The ratio of the value of an extensive variable to the number of moles of the system is called molar specific value. For example, molar specific volume is given by V Molar specific volume, v = , n is number of moles. n Writing thermodynamic equations in terms of specific values of extensive variables is convenient because they become independent of mass of the system. Table 4.1 Extensive and Intensive Variables Systems Extensive variables Specific value Intensive variables (1) Hydrostatic system Volume (V) v Pressure (P), Energy (U or E) u or e Temperature (T) Entropy (S) s Enthalpy (H) h (2) Stretched wire Length (L) l Tension (F) (3) Liquid film Area (A) a Surface tension (s) (4) Electric cell Charge (Q) q E.M.F. (e) (5) Dielectric slab Polarization (P) p Electric field (E) (6) Paramagnetic salt Magnetization (M) m Magnetic field (B or H) 4.5 THERMAL EQUILIBRIUM: ZEROTH LAW OF THERMODYNAMICS A system is said to be in thermal equilibrium if its thermodynamic coordinates remain unchanged. Consider two gaseous systems which are separated by a wall. If the change in thermodynamic coordinates of one system has no effect on those of the other system, then the wall separating the two systems is said to be adiabatic wall. On the other hand, if the changes in thermodynamic coordinates of one system causes changes in those of the other and the composite system attains a new equilibrium state, then the wall separating them is called diathermic or diathermal wall. Two systems separated by a diathermic wall are in equilibrium with each other. Now consider two systems A and B separated by an adiabatic wall and a third system C separated from A and B both by a diathermic wall as shown in Fig. 4.1. In this arrangement, system A and C will be in thermal equilibrium and so will be the systems B and C. Now if the adiabatic wall between A and B is replaced by a diathermic wall, it is found that A and B are also in thermal equilibrium. From this fact we come to conclusion that if system A is in thermal equilibrium with B and B is in thermal equilibrium with C, then A and C will also be in thermal equilibrium. This result is known as Zeroth law of thermodynamics and is stated as follows. 72 Thermal and Statistical Physics Adiabatic wall AB Diathermic wall C Fig. 4.1. When any two bodies or systems are each separately in thermal equilibrium with a third body, they are also in thermal equilibrium with each other and there exists a common useful scalar quantity called temperature which is a property of all thermodynamic systems in equilibrium states such that the temperature equality is a necessary and sufficient condition for thermal equilibrium. The above statement can also be stated in a mathematical form. Consider three systems 1, 2 and 3. Let X and Y be independent variables to describe their states. For the system 3, these variables are X3 and Y3. The condition for system 1 to be in thermal equilibrium with system 3 can be expressed in functional form as f1,3 (X1, Y1, X3, Y3) = 0 or X3 = F13 (X1, Y1, Y3) ...(4.1) That is, out of the four variables, only three are independent. Similarly, the condition of equilibrium of system 2 and 3 can be expressed as X3 = F23 (X2, Y2, Y3) ...(4.2) Eliminating X3 from Eqs. (4.1) and (4.2) we have F13 (X1, Y1, Y3) – F23 (X2, Y2, Y3) = 0 ...(4.3) But according to the zeroth law, system 1 and 2 will also be in thermal equilibrium with one another.
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