Capacity returned - temperature curves

Capacity returned (discharged capacity)-dischargetemperature curves and percentage withdrawabie capacity returned-temperature curves... 

Capacity returned (dischruged capaciity)-discharge temperature curves and percentage withdrawable capacity retumed-lemperature curves 31/8... 

The analysis can be carried out at several levels. The most elementary is by making some assumption regarding the trend r " as a function of x. For instance, one could empirically try to account for the fully symmetrical case of fig. 4.2a by letting = r x(l- x), where T is a kind of capacity concentration, to which we shall return below. If this is substituted in [4.2.8b], with dp = RTdx/x it is found that at fixed temperature dy/dx is a constant, i.e. the linear case of fig. 4.1 is retrieved. However, this model is unrealistic because, if surface and bulk are both ideal, there is no reason why the one component would enrich the interface over the other, i.e. r - 0 and y - y when two liquids are identical they must have identical surface tensions. In practice this implies that trend (1) in fig. 4.1 is found only in the limiting case of horizontallty of the y(x) line. This limit is never fully attained. Hence we should start at a higher level to account for the more frequently encountered y(x) curves. 

In the first case, the rate of heat loss (line 1) intersects the exponential heat production curve at two points. A and B, where the chemical heat production rate is balanced by the heat removal capacity. The low temperature point A represents a stable situation which can be illustrated by considering an increase in temperature to point C. At this temperature the rate of heat loss is greater than the rate of heat production and the temperature will return to point A. In contrast, point B is unstable as any slight increase in temperature will cause an increase in the rate of heat production not matched by the rate of heat loss and an accelerating runaway will occur. 

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