out of the nernst cell hence from equation 7 with ip 0 and equation 8 from these equations the air fuel lambda ratio u03bb can be written as the rich case indicated by ip lt 0 is more complex mathematically because of the assumption that v 4 0 that is there is no excess oxygen however the basic equation 1 still holds and the balance equations result in oxygen 2 v 1 v 2 v 5 c u03c6 2 xo 11 because there is an extra unknown another equation is needed this is the water balance equation obtained from the dissociation of h 2 o and co 2 into h 2 and co expressed by equation 13 v u2062 u2062 2 u00b7 v u2062 u2062 5 v u2062 u2062 1 u00b7 v u2062 u2062 6 kp 13 where kp is the equilibrium constant a function of exhaust temperature for a typical value of 1740 k kp is 3 5 the measured sensor current for the rich case is given by equation 14 ip u2212 kco p co u2212 kh 2 p h 2 u2212 p tot u03c3vi u00b7 kco v 5 kh 2 v 6 14 which includes two additional sensitivity calibrations kco and kh 2 substituting in the component expressions from equations 9 to 12 yields equation 15 also from equations 9 to 11 v 1 v 2 and v 6 can be written in terms of v 5 and u03c6 as follows from equation 11 v 2 c u03c6 2 xo u2212 2 v 1 u2212 v 5 c u03c6 2 xo u2212 2 a u03c6 v 5 from equation 10 v 6 b u03c6 2 u2212 v 2 b u03c6 2 u2212 c u03c6 u2212 2 xo.