Diathermal walls

Consider a closed composite system consisting of two compartments separated by a rigid impermeable diathermal wall. The volumes and mole numbers of the two simple systems are fixed, but the energies fid1) and JV> may change, subject to the restriction f/0) + UV> = constant, imposed on the composite closed system. At equilibrium the values of f/0) and IfV) are such as to maximize the entropy. 

Consider the same composite system as before, but with the impermeable diathermal wall no longer fixed. Both internal energy as well as the volume and V may now change, subject to the extra closure condition, RP) + VP) = constant. 

Reconsider the equilibrium state of two systems separated by a rigid diathermal wall, but now permeable to one type of material (Ar1) and impermeable to all others. 

For two systems separated by a diathermal wall and with Xk = U, the affinity... 

STEREOCHEMICAL TERMINOLOGY, lUPAC RECOMMENDATIONS DIATHERMIC WALL ADIABATIC WALL... 

It is observed experimentally that, when two bodies having different temperatures are brought into contact with each other for a sufficient length of time, the temperatures of the two bodies approach each other. Moreover, when we form the contact between the two bodies by means of walls constructed of different materials and otherwise isolate the bodies from the surroundings, the rate at which the two temperatures approach each other depends upon the material used as the wall. Walls that permit a rather rapid rate of temperature change are called diathermic walls, and those that permit only a very slow rate are called adiabatic walls. The rate would be zero for an ideal adiabatic wall. In thermodynamics we make use of the concept of ideal adiabatic walls, although no such walls actually exist. 

ADIABATIC AND DIATHERMAL WALLS, AND FIXED-TEMPERATURE BATHS... 

The opposite of adiabatic is either diabatic or diathermal. The best way to provide diathermal walls is connect the system (inner vessel) to the surroundings (outer vessel) with metal (an excellent heat conductor) or water (a good thermal conductor with very large specific heat capacity) or diamond (the best heat conductor and, simultaneously, the best electrical insulator). 

Consider a system enclosed by diathermic walls. As explained in Sec. 1.1, these enclosures prevent exchange of matter but do permit changes in state of the system by manipulations of the surroundings. An example of this situation is provided by a Bunsen burner that is placed below a flask containing ice, water and vapor the diathermic glass walls of the beaker permit the ice to melt in response to the application of a flame exterior to the system (ice, water, steam) and boundary (flask). 

At fixed T and p, dG < 0 for an irreversible change in the system and dG = 0 for a reversible change. In the laboratory, the conditions for application of the Gibbs energy are met by a reactor with diathermal walls in contact with a... 

Now, consider changing the temperature of an ideal gas at constant volume from the point of view of thermodynamics. Because the volume is constant (the gas is confined in a vessel with rigid, diathermal walls), the pressure-volume work, w, must be zero therefore,... 

The diathermic wall is defined by the fact that two systems separated by such a wall cannot be at equilibrium... 

To make the differences between the two kinds of walls clearer, consider the situation where both are ideal gases, each satisfying the ideal-gas law pV= nRT. If the two were separated by a diathermic wall, one would... 

The concept of temperature derives from a fact of common experience, sometimes called the zeroth law of thermodynamics , namely, if two systems are each in thermal equilibrium with a third, they are in thermal equilibrium with each other. To clarify this point, consider the three systems shown schematically in figure A2.1.1, in which there are diathermic walls between systems a and y and between systems p and y, but an adiabatic wall between systems a and p. 

Figure A2.1.1. Illustration of the zeroth law. Three systems with two diathermic walls (solid) and one adiabatic wall (open).

Not all processes are adiabatic, so when a system is coupled to its environment by diathermic walls, the heat q absorbed by the system is defined as the difference between the actual work performed and that which would have been required had the change occurred adiabatically. 

If a system is coupled with its environment through an adiabatic wall free to move without constraints (such as the stops of the second example above), mechanical equilibrium, as discussed above, requires equality of the pressure p on opposite sides of the wall. With a diathermic wall, thermal equilibrium requires that the temperature 0 of the system equal that of its surroundings. Moreover, it will be shown later that, if the wall is permeable and permits exchange of matter, material equilibrium (no tendency for mass flow) requires equality of a chemical potential p. 

For a system composed of two subsystems a and P separated from each other by a diathermic wall and from the surroundings by adiabatic walls, the equation corresponding to equation (A2.1.12) is... 

Consider two ideal-gas subsystems a and P coupled by a movable diathermic wall (piston) as shown in figure A2.1.5. The wall is held in place at a fixed position / by a stop (pin) that can be removed then the wall is free to move to a new position I The total system (a + P) is adiabatically enclosed, indeed isolated q = w = 0), so the total energy, volume and number of moles are fixed. 

Figure A2.1.5. Irreversible changes. Two gases at different pressures separated by a diathermic wall, a piston that can be released by removing a stop (pin).

Consider the situation illustrated in figure A2.1.5. with the modification that the piston is now an adiabatic wall, so the two temperatures need not be equal. Energy is transmitted from subsystem a to subsystem p only in the form of work obviously dF = -dF so, in applying equation (A2.1.20), is df/ P equal to dV = dF or equal to dF , or is it something else entirely One can measirre the changes in temperature, yuf juand T — T and thus determine Af/ P after the fact, but could it have been predicted in advance, at least for ideal gases If the piston were a diathermic wall so the final temperatures are equal, the... 

Here p is the chemical potential just as the pressure pis a mechanical potential and the temperature Tis a thermal potential. A difference in chemical potential Ap is a driving force that results in the transfer of molecules through a permeable wall, just as a pressure difference Ap results in a change in position of a movable wall and a temperature difference AT produces a transfer of energy in the form of heat across a diathermic wall. Similarly equilibrium between two systems separated by a permeable wall must require equality of the chemical potential on the two sides. For a multicomponent system, the obvious extension of equation (A2.1.22) can be written... 

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