quantities on both sides are extensive * . (The

product of an intensive variable like P and an extensive quantity ∆ V is extensive.) . THERMODYNAMIC PROCESSES . . Quasi-static process Consider a gas in thermal and mechanical equilibrium with its surroundings.

The pressure of the gas in that case equals the external pressure and its temperature is the same as that of its surroundings. Suppose that the external pressure is suddenly reduced (say by lifting the weight on the movable piston in the container). The piston will accelerate outward. During the process, the gas passes through states that are not equilibrium states.

The non- equilibrium states do not have well-defined pressure and temperature. In the same way, if a finite temperature difference exists between the gas and its surroundings, there will be a rapid exchange of heat during which the gas will pass through non-equilibrium states. In due course, the gas will settle to an equilibrium state with well-defined temperature and pressure equal to those of the surroundings. The free expansion of a gas in vacuum and a mixture of gases undergoing an explosive chemical reaction, mentioned in section .

are also examples where the system goes through non- equilibrium states. Non-equilibrium states of a system are difficult to deal with. It is, therefore, convenient to imagine an idealised process in which at every stage the system is an equilibrium state. Such a * As emphasised earlier, Q is not a state variable.

However, ∆ Q is clearly proportional to the total mass of system and hence is extensive. process is, in principle, infinitely slow, hence the name quasi-static (meaning nearly static). The system changes its variables ( P , T , V ) so slowly that it remains in thermal and mechanical equilibrium with its surroundings throughout. In a quasi-static process, at every stage, the difference in the pressure of the system and the external pressure is infinitesimally small.

The same is true of the temperature difference between the system and its surroundings (Fig. . ). To take a gas from the state ( P , T ) to another state ( P ′ , T ′ ) via a quasi-static process, we change the external pressure by a very small amount, allow the system to equalise its pressure with that of the surroundings and continue the process infinitely slowly until the system achieves the pressure P ′ .

Similarly, to change the temperature, we introduce an infinitesimal temperature difference between the system and the surrounding reservoirs and by choosing reservoirs of progressively different temperatures T to T ′ , the system achieves the temperature T ′ . Fig. . In a quasi-static process, the temperature of the surrounding reservoir and the external pressure differ only infinitesimally from the temperature and pressure of the system.

A quasi-static process is obviously a hypothetical construct. In practice, processes that are sufficiently slow and do not involve accelerated motion of the piston, large temperature gradient, etc., are reasonably approximation to an ideal quasi-static process. We shall from now on deal with quasi-static processes only, except when stated otherwise. A process in which the temperature of the system is kept fixed throughout is called an isothermal process .

The expansion of a gas in a metallic cylinder placed in a large reservoir of fixed temperature is an example of an isothermal process. (Heat transferred from the reservoir to the system does not materially affect the temperature of the reservoir, because of its very large heat capacity.) In isobaric processes the pressure is constant while in isochoric processes the volume is constant. Finally, if the system is insulated from the surroundings and no heat flows between the system and the surroundings, the process is adiabatic . The definitions of these special processes are summarised in Table.

. Table . Some special thermodynamic processes We now consider these processes in some detail :