I'd like to learn what the part "for the preservation of food" modifies in the following sentence, the noun "heat" or the whole phrase "the value of heat" .
What do you think?
I think "for the preservation of food" refers to the whole phrase "the value of heat".
"What value of heat?" "The value of heat for the preservation of food".
Do you agree with me on it? Thank you
It's ambiguous.
The value of heat for the preservation of food has been known for a long time.
One reading is that the kind of heat we are talking about is food-preservation heat. Then [heat for the preservation of food] is a phrase.
Imagine this expanded into a dialogue:
The other reading is that we are talking about what heat-in-general is valuable for: the value [of heat] [for the preservation of food]. Expanded as follows:
Without any context I would guess the second reading is more likely.
The 'value' being spoken of here is not just the value of 'heat', but specifically its use for the preservation of food.
If you asked simply "what is the value of heat?", it could refer to the cost of generating heat, ie the price of fossil fuels. In your example, it is not talking about monetary value at all. A secondary meaning of 'value' is "the importance or worth of something for someone". So, heat is important in the process of food preservation.
Penicillin's value for the treatment of infection ...
Can be restated:
The value of penicillin for the treatment of infection...
The noun value is modified by the prepositional phrase, for the treatment of infection, identifying the context for the value. It is not value "as a long term investment", say, or "for stopping squeaks in machinery" or any other kind of value.
The periphrastic genitive and genitive construction (of penicillin, penicillin's) indicate the thing that possesses the value, penicillin.
Compare:
Tom's trick for making light and fluffy scrambled eggs is to beat air bubbles into the eggs and to cook them quickly over fairly high heat.
