Diathermal boundary

We define a heat reservoir as any body, used as part of the surroundings of a particular system, whose only interaction with the system is across a diathermic boundary. A heat reservoir is then used to transfer heat to or from a thermodynamic system and to measure these quantities of heat. It may consist of one or more substances in one or more states of aggregation. In most cases a heat reservoir must be of such a nature that the addition of any finite amount of heat to the system or the removal of any finite amount of heat from the system causes only an infinitesimal change in the temperature of the reservoir. 

The absence of heat flow may be a result of the walls not permitting the transfer of thermal energy. Boundaries of this kind are called adiabatic. (Adiabatic walls are infinitely good thermal insulators.) If the walls are non-adiabatic (sometimes called diabatic or diathermal) and do permit heat transfer, but it does not occur, we say that the system is at thermal equilibrium with its surroundings. 

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). 

Diathermic boundaries. Boundaries that do not permit matter to be exchanged between systems and their surroundings but that permit changes to take place in properties of the system by heating or cooling of the surroundings. 

The most useful connection between thermodynamics and statistical thermodynamics is that established for a system at a given temperature T, volume V, and the number of particles N. The corresponding ensemble is referred to as the isothermal ensemble or the canonical ensemble. To obtain the T, V, N ensemble from the E, V, N ensemble, we replace the boundaries between the isolated systems by diathermal (i.e., heat-conducing) boundaries. The latter permits the flow of heat between the systems in the ensemble. The volume and the number of particles are still maintained constant. 

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. 

In (c) we have a condenser similar to those found in chemistry labs. Usually, hot vapor flows through the center of the condenser while cold water flows on the outside, causing the vapor to condense. This system is open because it allows mass flow through its boundaries. It is composite because of the waU that separates the two fluids. It is adiabatic because it is insulated from the surroundings. Even though heat is transferred between the inner and outer tube, this transfer is internal to the system (it does not cross the system bounds) and does not make the system diathermal. 

Comments In the condenser of part (c), we determined the system to be open and adiabatic. Is it not possible for heat to enter through the flow streams, making the system diathermal Streams carry enei with them and, as we will learn in Chapter 6. this is in the form of enthalpy. It is possible for heat to cross the boundary of the system inside the flow stream through conduction, due to different temperatures between the fluid stream just outside the system and the fluid just inside it. This heat flows slowly and represents a negligible amount compared to the energy carried by the flow. The main mode heat transfer is through the external surface of the system. If this is insulated, the system may be considered adiabatic. 

If the boundary allows heat transfer between the system and surroundings, the boundary is diathermal. An adiabatic boundary, on the other hand, is a boundary that does not allow heat transfer. We can, in principle, ensure that the boundary is adiabatic by surrounding the system with an adiabatic wall—one with perfect thermal insulation and a perfect radiation shield. 

An adiabatic process is one in which there is no heat transfer across any portion of the boundary. We may ensvure that a process is adiabatic either by using an adiabatic boundary or, if the boundary is diathermal, by continuously adjusting the external temperature to eliminate a temperature gradient at the boundary. 

Consider the thermal equilibration of two systems, with rigid boundaries, initially at temperatures T and T" that are joined via an adiabatic partition, which is allowed to become slightly diathermic (See Figure 2.2.1). The resulting heat transfer is assumed to proceed with all deliberate speed i.e., at a pace that permits us to assume that T and T", while individually variable, remain uniform within the two compartments, except very close to the interfacial partition. So long as the compoimd system remains isolated, interfacial phenomena may be ignored, and the energies and entropies remain additive, we find that... 

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