Diathermal container

Figure 3.9 Schematic representation of (a) an adiabatic container, allowing PV work by movement of a piston, but unaffected by other changes in the surroundings (b) a diathermal (nonadiabatic) container, allowing thermal equilibration with the surroundings.

An enclosure, such that the equilibrium of a system contained within it can only be disturbed by mechanical means, is adiabatic, otherwise it is diathermic. For instance, stirring, or the passage of an electric current, constitute mechanical means." A system Kf] in an adiabatic enclosure is adiabatically isolated, but this does not preclude mechanical interactions with the surroundings. Its transitions are then called adiabatic. 

Such a system will be called a standard system (n — 1 enclosures in diathermic contact, each containing a simple fluid, may serve as example. x being any one of the pressures)... 

Let us now carry out a change of state (A —> B) on the system with each type of container and measure the mechanical work (wadiabatic, diathermal) associated with each. From these two measurements, we can define heat q = gA B absorbed in this process as... 

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). 

We next examine an isolated compound system with a fixed total volume containing a sliding partition that is initially locked and that provides for adiabatic insulation of two compartments at pressures P and P", temperatures T and 7", and individual volumes V and V". The system is allowed to relax after slowly releasing the lock and slowly rendering the partition diathermic. Entropy changes in both compartments can now occur in accord with the relation dS — T [dE -t- PdV], no other forms of work being allowed. The constraints wedV + dV" = 0 (rather than dV = dV" = 0, as before) and dE dE" = 0. By the procedure adopted before we write... 

A simple system is one that has no internal boundaries and thus allows all of its parts to be in contact with each other with respect to the exchange of mass, work, and heat. An example would be a mole of a substance inside a container. A composite system consists of simple systems separated by boundaries. An example would be a box divided into two parts by a firm wall. The construction of the wall would determine whether the two parts can exchange mass, heat, and work. For example, a permeable wall would allow mass transfer, a diathermal wall would allow heat transfer, and so on. 

Solution In (a) we have a tank that contains a liquid and a vapor. This system is inhomogeneous, because it consists of two phases closed, because it cannot exchange mass with the surroundings and simple, because it does not contain any internal walls. Although the liquid can exchange mass with the vapor, the exchange is internal to the system. There is no mention of insulation. We may assume, therefore, that the system is diathermal. 

Figure 3.22 on the next page shows the initial state of an apparatus consishng of an ideal gas in a bulb, a stopcock, a porous plug, and a cylinder containing a frictionless piston. The walls are diathermal, and the surroundings are at a constant temperature of 300.0 K and a constant pressure of 1.00 bar. 

Walls that permit heating as a mode of transfer of energy are called diathermic (Fig. 1.3). A metal container is diathermic and so is our skin or any biological membrane. Walls that do not permit heating even though there is a difference in temperature are called adiabatic. The double walls of a vacuum flask are... 

The energy and entropy, which are related in this equation to the molecular partition function, are statistical entities, defined by particles which do not interact except to maintain the equilibrium conditions. To obtain similar relationships for real systems, it is necessary to apply statistical mechanics to the calculation of the thermodynamic entities, which correspond to the molar quantities of particles, or that is N approaches 1 this treatment it is convenient to use the canonical ensemble already discussed and presented in Figure n.l. This ensemble consists of a very large number of systems, N, each containing 1 mol of molecules and separated from the others by diathermic walls, which allow heat conduction but do not allow particles to pass. The set of all the systans is isolated from the outside and has a fixed energy E, which is the energy of the canonical ensemble. 

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