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Thermal death of microorganisms in the liquid medium follows first order kinetics. If the initial cell concentration in the fermentation medium is 108 cells / ml and the final acceptable contamination level is 10–3 cells, for how long should 1m3 medium be treated at temperature of 120° (thermal deactivation rate constant = 0.23 / min) to achieve acceptable load?
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- 48 min
- 11 min
- 110 min
- 20 min
Correct Option: C
Initial number of cells = 108 cells/ml * 1m3
But, we know, 1 m3 = 106 cm3
Also, 103 cm3 = 1000 ml
Therefore, total initial number of cells = 108 cells * 106 = 1014 cells
Final acceptance of contamination = 10–3 cells/ml or 103 cells/m3
Thus, using the first order rate constant equation :
t = 2.303 / K log10 [1014] /103
= 2.303/ 0.23 per min log10 (1014/103)
= 10 * 11 log10 (10)
t = 110 min.
