THE RUDOLF REPORT

7. ZYKLON B FOR THE KILLING OF HUMAN BEINGSprovided that the newly added gas (free of i) is ideally mixed with theold gas:dc idt= −a · c i (t) (8)i.e., that the concentration change of substance i is proportional tothe concentration c i (t) at time t.The modification of the equation yields:⌠ 1⌡c i (t) dc i = ⌡⌠−a · dt (9)After integration over dc and dt, resp., this yields:ln(c i (t)) = a' − a · t (10)orc i (t) = a"· e −at . (11)For t = 0, e −at = 1 and thusa" = c i (t=0) = c o (12)with c o as initial concentration (when the ventilation is started).This leads to:c i (t) = c o· e −at . (13)From equation (8) results the initial concentration changedc i (t=0)/dt:dc i (t=0)dt= –a · c o (14)Hence, we get for the constant a:–a = dc i(t=0)(dt · c 0 )(15)In case of a sufficiently low exchange volume dv per time intervaldt, the ratio of total volume V to the exchange volume dv can be introducedas initial concentration change (in case of infinitesimal transition(dt → 0) this is mathematically correct).For example, if the air exchange per time unit is 1 / 1,000 of the total, theconcentration change per time unit is1 / 1,000 , too.221