GATE 2026 BT – Question 59
A batch sterilizer is being operated at 121 $^o$C for sterilizing a medium containing microbial cells. Assume that the thermal deactivation of cells is a first order process with a death rate constant of 0.69 min$^{-1}$ at 121 $^o$C. If the initial concentration of microbes in the medium is $10^{10}$ cells m$^{-3}$, the time taken to reduce the microbial load to a final concentration of 10 cells m$^{-3}$ is _________ min. (rounded off to the nearest integer)
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 30
Explanation
For first-order death, $N = N_0e^{-k_dt}$, so $t = \frac{1}{k_d}\ln\frac{N_0}{N} = \frac{\ln 10^9}{0.69} = \frac{20.72}{0.69} = 30$ min.