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228 PHYSICS adiabatic wall – an insulating wall (can be law in 1931 long after the first and second Laws movable) that does not allow flow of energy (heat) ofthermodynamicswerestatedandsonumbered. from one to another. The systems are insulated The Zeroth Law clearly suggests that when two from the rest of the surroundings also by similar systems A and B, are in thermal equilibrium, adiabatic walls. The situation is shown there must be a physical quantity that has the schematically in Fig. 11.1 (a). In this case, it is same value for both. This thermodynamic found that any possible pair of values (A , A ) will variable whose value is equal for two systems in be in equilibrium with any possible pair of values (P , V ). Next, suppose that the adiabatic wall is thermal equilibrium is called temperature (T ). B B Thus, if A and B are separately in equilibrium replacedbyadiathermicwall – aconductingwall with C, T A T C and T B T .CThis implies that thatallowsenergyflow(heat)fromonetoanother. T = T i.e. the systems A and B are also in It is then found that the macroscopic variables of A B thermal equilibrium. the systems A and B change spontaneously until We have arrived at the concept of temperature both the systems attain equilibrium states. After formally via the Zeroth Law. The next question that there is no change in their states. The is : how to assign numerical values to situation is shown in Fig. 11.1(b). The pressure and volume variables of the two gases change to temperaturesofdifferentbodies? Inotherwords, how do we construct a scale of temperature ? (PB′, VB′) and (A ′, A ′) such that the new states Thermometry deals with this basic question to of A and B are in equilibrium with each other *. There is no more energy flow from one to another. which we turn in the next section. We then say that the system A is in thermal equilibrium with the system B. What characterises the situation of thermal equilibriumbetweentwosystems?Youcanguess the answer from your experience. In thermal equilibrium, the temperatures of the two systems are equal. We shall see how does one arrive at the concept of temperature in thermodynamics? The Zeroth law of thermodynamics provides the clue. 11.3 ZEROTH LAW OF THERMODYNAMICS (a) Imagine two systems A and B, separated by an adiabaticwall,whileeachisincontactwithathird systemC, via a conducting wall [Fig. 11.2(a)]. The states of the systems (i.e., their macroscopic variables) will change until both A and B come to thermalequilibriumwithC.Afterthisisachieved, suppose that the adiabatic wall between A and B isreplacedbyaconductingwallandCisinsulated from A and B by an adiabatic wall [Fig.11.2(b)]. It is found that the states of A and B change no (b) further i.e. they are found to be in thermal Fig. 11.2 (a) Systems A and B are separated by an equilibrium with each other. This observation adiabatic wall, while each is in contact forms the basis of the Zeroth Law of with a third system C via a conducting Thermodynamics, which states that ‘two wall. (b) The adiabatic wall between A systems in thermal equilibrium with a third and B is replaced by a conducting wall, system separately are in thermal equilibrium while C is insulated from A and B by an adiabatic wall. with each other’. R.H. Fowler formulated this * Both the variables need not change. It depends on the constraints. For instance, if the gases are in containers of fixed volume, only the pressures of the gases would change to achieve thermal equilibrium. Reprint 2026-27