The use of the secondary sodium circuit to separate steam from radio­active primary sodium carries the disadvantage of a loss of thermal efficiency due to the increase of entropy as heat is transferred from primary to secondary sodium. The extent of the loss can be estimated very conveniently in terms of the available energy (sometimes called the exergy). The specific steady-flow available energy a, is given by

a — h — T0s,

where h and s are specific enthalpy and entropy respectively, and T0 is the dead-state or environmental temperature.

If the working fluid in a cyclic power plant circulates at a rate M and receives heat as it changes from state 1 to state 2, the rate at which it receives heat is

Q — M(h — h2)

and the maximum work output Pmax is given by

^max — M(a1 a2 )•

The maximum thermal efficiency is Pmax/Q. Pmax is attained only if all the processes taking place in the plant are reversible. Equation 4.7 shows that Pmax is the rate of increase of available energy of the work­ing fluid as it receives heat. Every time heat is transferred — from the fuel to the primary coolant, from primary to secondary coolant and from secondary to water and steam — enthalpy is conserved but entropy is increased and therefore the available energy is decreased (equation 4.5).

Table 4.1 shows the steady increase of entropy of the fuel, the primary coolant, the secondary and the steam in a 3600 MW (heat) plant. The entropy of the fuel is greater than that of the source of the energy in the fission fragments, because their kinetic energy has been turned into disorganised thermal agitation (i. e. into heat). The other increases in entropy are due to the transfers of heat from higher to lower temperatures.

Table 4.2 shows the lost potential for doing work represented by each increase in entropy (assuming an environmental temperature of 300 °K). The increase in available energy of the steam in the steam generator is 1860 MW, and this would be the net power output if the steam cycle were reversible. There are, however, various irreversibilit­ies — in the turbine for example, due to pressure losses in pipes, and in the feed train — so that the actual net work output would be 1490 MW.

The overall efficiency of the plant is 41%. It is of interest to note that the greatest sources of loss of thermal efficiency — i. e. the greatest

sources of entropy production — are the change of the kinetic energy of the fission fragments into heat in the fuel, and the transfer of that heat from the fuel to the coolant. In contrast the loss of efficiency due to the presence of the secondary sodium circuit is a mere 0.2%, which is small compared with the losses due to irreversibility within the steam plant. The flow of available energy is shown diagrammatically in Figure 4.16.