12.2 Thermal equilibrium

Equilibrium in mechanics means that the net external force and torque on a system are zero. The term ‘equilibrium’ in thermodynamics appears in a different context: we say the state of a system is an equilibrium state if the macroscopic variables that characterize the system do not change in time. For example, a gas inside a closed rigid container, completely insulated from its surroundings, with fixed values of pressure, volume, temperature, mass, and composition that do not change with time, is in a state of thermodynamic equilibrium.

In general, whether or not a system is in a state of equilibrium depends on the surroundings and the nature of the wall that separates the system from the surroundings.

Consider two gases A and B occupying two different containers. We know experimentally the pressure and volume of a given mass of gas can be chosen to be its two independent variables. 

Let the pressure and volume of the gases be \(\left(P_A, V_A\right)\) and \(\left(P_B, V_B\right)\) respectively. Suppose first that the two systems are put in proximity but are separated by an adiabatic wall – an insulating wall (can be movable) that does not allow flow of energy (heat) from one to another. The systems are insulated from the rest of the surroundings also by similar adiabatic walls. The situation is shown schematically in Fig. \(12.1\) (a). In this case, it is found that any possible pair of values \(\left(P_A, V_A\right)\) will be in equilibrium with any possible pair of values \(\left(P_B, V_B\right)\).

Next, suppose that the adiabatic wall is replaced by a diathermic wall – a conducting wall that allows energy flow (heat) from one to another. It is then found that the macroscopic variables of the systems \(A\) and \(B\) change spontaneously until both systems attain equilibrium states. After that, there is no change in their states. The situation is shown in Fig. 12.1(b). The pressure and volume variables of the two gases change to \(\left(P_B^{\prime}, V_B{ }^{\prime}\right)\) and \(\left(P_A{ }^{\prime}, V_A{ }^{\prime}\right)\) such that the new states of \(A\) and \(B\) are in equilibrium with each other. There is no more energy flow from one to another. We then say that system \(A\) is in thermal equilibrium with system \(B\). In thermal equilibrium, the temperatures of the two systems are equal.

Note: Thermodynamics may also involve other variables that are not so obvious to our senses e.g. entropy, enthalpy, etc., and they are all macroscopic variables. However, a thermodynamic state is specified by five state variables viz., pressure, volume, temperature, internal energy, and entropy. Entropy is a measure of disorderness in the system. Enthalpy is a measure of the total heat content of the system.