The pasteurisation ladder: D, z and F
Thermal processing · D, z, F on an HTST line
The lab establishes the baseline: held at 63 °C, the target organism falls 4 logs in 12 minutes. A second run at 72 °C measures a D-value of 0.27 minutes. Out on the HTST line, the holding tube gives 15 seconds — but today's chart shows it running at 71.7 °C instead of the specified 72. Build the ladder: the D-value at 63 °C, the z-value the two temperatures imply, and the F-value that says what today's 15 seconds at 71.7 °C is actually worth in 72 °C time.
Every number in this problem is editable — change any value below and the whole chain recalculates.
- t = 12 min — Holding time in the 63 °C run
- LR = 4 logs — Reduction achieved in that run
- D₂ = 0.27 min — Measured D-value at 72 °C
- t_p = 15 s — Holding tube residence time
- T = 71.7 °C — Today's process temperature
- T_ref = 72 °C — Specified reference temperature
- (a)the D-value at 63 °C
- (b)the z-value across the two temperatures
- (c)today's process time as equivalent minutes at 72 °C
A D-value is the price of one log: 12 minutes bought 4 logs, so each factor of ten costs 3 minutes at 63 °C. It is the survival curve compressed to a single number — and it silently assumes the curve IS a straight line in log-count, which real organisms mostly honour and spores test.
Carried onward at full precision, not this rounded figure.
Nine degrees dropped the D-value from 3 minutes to 0.27 — a factor of 11.1, just over one log — so z comes out at 8.6 C°: the temperature climb that makes killing ten times faster. Everything about trading time against temperature runs through this one constant.
Carried onward at full precision, not this rounded figure.
The F-value converts today's process into reference currency: 15 seconds at 71.7 °C is worth only 13.8 seconds at 72 °C. A drift of three-tenths of a degree quietly took 8 % of the lethality — the process LOOKS on-spec on time and is short on kill.
Carried onward at full precision, not this rounded figure.
Open the F-Value (Equivalent Time at Reference Temperature) solver →
Therefore D₆₃ = 3 minutes, z = 8.6 C°, and today's 15 seconds at 71.7 °C delivers an F of only 13.8 equivalent seconds — the line is running 8 % short of its specified lethality on a temperature error small enough to miss on a gauge.
Why this order
The three constants answer three different questions and only make sense in this order. D asks: at one temperature, how fast do they die? z asks: how does that speed change with temperature? F asks: given both, what is this actual, imperfect process worth in the reference temperature's currency? The ladder matters because regulation is written at the top of it — a pasteurisation standard is an F requirement — while everything a plant can measure lives at the bottom, in times and temperatures.
The ending is the lesson: lethality is exponential in temperature with z in the exponent, so small temperature errors are never small. Here −0.3 C° cost 8 %; a full degree low would cost 23 %. That asymmetry — time errors are linear, temperature errors are exponential — is why holding-tube thermometers are the most audited instruments in the building, and why the compliant-looking chart with a slightly lazy sensor is the most dangerous document in it.
Carried values move at full precision, not the rounded figure shown — chaining rounded numbers compounds error.