SME
Microbiology · Problem type
Killing spores: the D-value
Use this for “With D₁₂₁ = 0.2 min, how long does a 12D cook take, and how many of 10⁶ spores survive?”
Chart
N(LR) = 1,000,000(0.1)ᴸᴿ
A log y-axis: an exponential draws as a straight line.
This is an example. Type your own values to start a new problem.
LR
=
t (min)
÷
D (min)
N₀
Starting spores
example
N
Survivors
calculated
Formulas
LR
=
t
D
12
=
2.4
0.2
N
=
N₀
÷
10LR
1 ×
10
-6
=
1 ×
10
6
10
12
Assumptions
•
At a fixed temperature, each D minutes kills 90% of the spores still alive: LR = t ÷ D log reductions leave N = N₀ ÷ 10ᴸᴿ.
•
D₁₂₁ is the D-value at 121 °C; a hotter cook has a smaller D.
•
A count below 1 is a chance: 10⁻⁶ survivors means one surviving spore in a million cans.
Step-by-step
WE KNOW
N₀ = 1 × 10⁶, D = 0.2 min, LR = 12
FIND
heating time (t), survivors (N)
Step 1 · Find heating time (t)
Use LR = t ÷ D
D
minutes
for
each
log
reduction.
t
=
LR
×
D
t
=
12
×
0.2
t
=
2.4
min
Step 2 · Find survivors (N)
Use N = N₀ ÷ 10ᴸᴿ
Each log reduction leaves a tenth of the spores.
N
=
10
6
10
12
N
=
10
-6
N
=
1 ×
10
-6
Check
Put the numbers back in. Both sides should match.
12
=
2.4
0.2
✓
1 ×
10
-6
=
10
6
10
12
✓
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