temperatures. The term was coined as an alternative to the still widely
used description commercially sterilewhich was objected to on the
grounds that sterility is not a relative concept; a material is either sterile
or it is not. An appertized or commercially sterile food is not necessarily
sterile – completely free from viable organisms. It is however free from
organisms capable of growing in the product under normal storage
conditions. Thus for a canned food in temperate climates, it is not a
matter of concern if viable spores of a thermophile are present as the
organism will not grow at the prevailing ambient temperature.
4.1.2 Quantifying the Thermal Death of Micro-organisms: D and z
Values
In Chapter 3 we described how a micro-organism can grow only over a
restricted range of temperature, defined by three cardinal temperatures.
When the temperature is increased above the maximum for growth, cells
are injured and killed as key cellular components are destroyed and
cannot be replaced. This occurs at an increasing rate as the temperature
increases.
The generally accepted view is that thermal death is a first order
process, that is to say, at a given lethal temperature, the rate of death
depends upon the number of viable cells present. We can express this
mathematically as:
dN=dt¼cN ð 4 : 1 Þwhere dN/dtis the rate of death,Nis the number of viable cells present
andcis a proportionality constant. The minus sign signifies thatNis
decreasing.
To obtain information about the number of cells surviving after
different periods of heating, this equation can be integrated between
time zero and timetto give:
logeðN=N 0 Þ¼ct ð 4 : 2 Þor
N¼N 0 ect ð 4 : 3 ÞwhereNandN 0 are the numbers of viable cells present at timestand 0
respectively.
It is more convenient to represent Equation (4.2) in terms of loga-
rithms to the base 10 as:
log 10 ðN=N 0 Þ¼kt ð 4 : 4 Þwherek¼c/loge 10 ¼c/2.303.
66 The Microbiology of Food Preservation