Work done by the system

Flere the subscripts and/refer to the initial and final states of the system and the work is defined as the work perfomied on the system (the opposite sign convention—with as work done by the system on the surroundings—is also in connnon use). Note that a cyclic process (one in which the system is returned to its initial state) is not introduced as will be seen later, a cyclic adiabatic process is possible only if every step is reversible. Equation (A2.1.9), i.e. the mtroduction of t/ as a state fiinction, is an expression of the law of conservation of energy. 

Since is defined as work done on the system, the minimum amount of work necessary to produce a given change in the system is that in a reversible process. Conversely, the amount of work done by the system on the surroundings is maximal when the process is reversible. 

Qh = heat supplied to a system W( = work done by the system AE = change in energy of the system... 

If the work term W( is expanded to breakdown shaft work done to or from the system and the work done by the system, then... 

The -W signifies work done to the system, a driven machine, as contrasted to -l-W, which would indicate work done by the system as with a driver. 

Net work done by the system ineluding both meehanieal and eleetrieal work, W,. 

Note that the definition of R is arbitrary. However, the present choice seems simplest and has a transparent physical interpretation. The work done by the system in an infinitesimal reversible transformation at constant S, N, A, s, and ayiy is given by... 

Assume isothermal operation, and that no work done by the system. Then the fust law simplifies to ... 

In this change there will be in general a finite amount of heat withdrawn by the system from its environment, which may be absorbed in various parts. The total absorbed heat we shall denote by YQ. At the same time the parts of the system, exerting forces on external bodies, may perform mechanical work. The total mechanical work done by the system on external bodies we shall denote by 2A. 

A consideration of the same example also illustrates the result established in treatises on dynamics that the condition for stable, unstable, or neutral equilibrium of a mechanical system is that, for any small displacement which does not violate the constraints, the change of potential energy shall vanish to the first order, and be positive, negative, or zero respectively to the second order. When the system is in stable, unstable, or neutral equilibrium, the potential energy is a minimum, a maximum, or stationary respectively (Theorem of Dirichlet). Thus the work done by the system in any infinitesimal displacement is zero to the first order, and negative, positive, or zero to the second order, for the three cases. All these conditions refer only to a par-... 

A being the solubility of the gas. p is therefore a function of x. The work done by the system during the whole second operation is ... 

For a stationary material the change in the internal energy is equal to the difference between the net amount of heat added to the system and the net amount of work done by the system on its surroundings. For an infinitesimal change ... 

For reactions involving heat effects, the total and component mass balance equations must be coupled with a reactor energy balance equation. Neglecting work done by the system on the surroundings, the energy balance is expressed by... 

When a process is carried out at a constant pressure, P, the work done by the system can be represented as... 

It is clear from the entire matter described above that in chemical systems conservation of energy is usually handled in terms of three quantities (i) work done by the system on the surroundings which is taken as plus (+) w or the work done by the surroundings on the system which is taken as (-) w (ii) heat gained by the system (+q) and heat lost by the system (-q) and (iii) the increase (+A U) or decrease (—A (7) in the internal energy of the system as a result of the process carried through. 

The convention adopted here is that 8uj is negative if work is done by the system. However, in some textbooks the first law of thennodynamics is written in the form dE = q — 5m, in which case the work done by the system is positive. 

Here the work is negative, -200J, because the work done by the system is removed from the system. 

In this case, the energies in different units had to be converted to the same unit before addition. The work done by the system, a loss of energy to the system, is negative. 

But back to our subject the first law of thermodynamics deals with energy and is also known as the law of the conservation of energy. It can be formulated as follows The increase in the internal energy of a thermodynamic system is equal to the amount of heat energy added to the system minus the work done by the system on the surroundings. Energy can occur in various forms, for example, chemical,... 

The pressure work term is also made up of all of the species. However, let us first consider it for a single species and not include any subscripts. Since W has the convention of work done by the system on the surroundings and the definition of work is the product of force times distance moved in the direction of the force, we can show from Figure 3.9 that... 

First Law of Thermodynamics energy is conserved quantitatively, AE = q — w, where q is heat added to the system and w is work done by the system. 

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