Everything so far has been definitions. This lesson is the payoff, and it is the reason UHT milk exists.

The rule, first, in one line: ten degrees hotter, one tenth the time — for an organism whose z is 10 C°. That is not a rule of thumb, it is the z-value read out loud. Twenty degrees hotter is one hundredth of the time. The arithmetic is $t_2 = t_1 \times 10^{-(T_2 - T_1)/z}$, where $t_1$ is the hold that already works at $T_1$, and $t_2$ the hold that matches it at $T_2$. It is the F-value equation with the existing, proven hold playing the part of the lethality to be matched.

So far this only says you can trade. Here is why you would want to.

Recall from lesson three: z belongs to the thing being heated. The spore's z is about 10 C°. The pigment that gives a purée its colour, the vitamin C in a juice, the proteins that decide texture — their z-values run 25 to 45 C°. A large z means indifferent to temperature. So when the process climbs 10 C°, the spore's death rate goes up tenfold and the colour's damage rate goes up by only about $10^{10/33} \approx 2$. Cut the hold to a tenth to keep the kill identical, and the colour damage comes out at roughly a fifth of what it was.

Same kill. A fifth of the damage. That single inequality between two z-values is the entire commercial case for high-temperature short-time processing, and it is why UHT milk is held for seconds at 140 °C rather than half an hour at 100 °C.

Two limits, because the trade is not free. Going hotter means the equipment must actually reach and hold the temperature at the cold spot, and in a can that is a slow business — which is why HTST belongs to flowing products in hold tubes and plate exchangers, not to retorted solids. And a shorter hold makes residence time the critical control: in a hold tube, the FASTEST particle sets the process, not the average one, so the design is written against the fastest streamline and nothing else.