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If someone says "resistance decreases with temperature", is it possible to interpret the relationship between resistance and temperature? Does it mean that as temperature falls, resistance falls together? Or is it the other way round - resistance falls as temperature rises?

john
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  • It is not a complete sentence, unless you insist that "temperature" means "a decrease in temperature", and if you understand that one is talking about the usual case; however this is a question in the domain of physics or electrical engineering, not English. – LPH Nov 30 '21 at 11:06
  • I’m voting to close this question because it belong to an SE site on physics or EE. – LPH Nov 30 '21 at 11:07
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    @LPH: I think it *is* a perfectly good "complete sentence". Just as it's fine to ask the question *Why does mass increase with velocity as an object approaches the speed of light?*, which imho clearly legitimises the assertion *Mass increases with velocity. In these parallel constructions, the implication is If one increases, so does the other* (plus the corollary If one decreases, so does the other). – FumbleFingers Nov 30 '21 at 14:23
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    @EdwinAshworth I am not sure that the relationship is always one of parallelism (↓↓, ↑↑); instead it can be of this type: "↓↑, ↓↓". That is, the second quantity is taken as increasing (implicitly). This reference shows this latter usage: "We know that for metals, resistance increases with temperature, but for semiconductors, resistance decreases with temperature obeying an exponential relationship as shown in Eq. (8.47) ln R = R͚ exp(c/T)". (The eq. does show that T must increase in order for R to decrease. (1/2) – LPH Nov 30 '21 at 18:58
  • @EdwinAshworth url of reference https://www.google.fr/books/edition/Fundamentals_of_Electroceramics/24B_DwAAQBAJ?hl=fr&gbpv=1&dq=%22resistance+decreases+with+temperature%22&pg=PA207&printsec=frontcover (2/2) – LPH Nov 30 '21 at 18:58
  • @FumbleFingers I am aware of this formulation for the "all increasing" case, but I think ther is no such established convention for the "decreasing - decreasing" case; see my comment to user Edwin Ashworth. – LPH Nov 30 '21 at 19:01
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    @LPH Yes, 'immune response decreases with age' must be read as 'y decreases as x increases'. Contrast 'chances of survival in the sea decrease as the temperature decreases'. This shows that 'y decreases as x increases' is far better. Or 'y is a monotonically decreasing function of x'. – Edwin Ashworth Nov 30 '21 at 19:35
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    A less ambiguous way to express this is resistance varies directly with temperature if the numeric values move in the same direction. If they move in opposite directions, resistance varies inversely with temperature. You can make the statement more precise by saying linearly or by using other qualifiers. – Jack O'Flaherty Nov 30 '21 at 23:51
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    "resistance decreases with temperature" this means that the (electrical) resistance of an object is directly proportional to its temperature, i.e. a cold object has less resistance than a similar hot object. – Greybeard Dec 01 '21 at 14:39
  • @Jack O'Flaherty 'A less ambiguous way to express this is resistance varies directly with temperature if the numeric values move in the same direction.' But monotonically increasing or constantly increasing functions need not be proportionalities. – Edwin Ashworth Dec 01 '21 at 15:57
  • @EdwinAshworth No; if they are, it's linearly. It could also be 'as the square of' or 'logarithmically'. – Jack O'Flaherty Dec 01 '21 at 18:06
  • @Jack O'Flaherty So you need 'A less ambiguous way to express this is resistance varies directly with temperature if the numeric values move in the same direction ... provided the relationship is a proportionality.' – Edwin Ashworth Dec 02 '21 at 11:26
  • @EdwinAshworth More usual expressions would be resistance varies directly with temperature and inversely as the square of its diameter, for example, or inversely as the logarithm of temperature, for metal wires and semiconductors respectively. – Jack O'Flaherty Dec 02 '21 at 15:03
  • @Jack O'Flaherty But in everyday usage we have expressions like 'immunity decreases with age', with no implication of exact inverse proportionality. – Edwin Ashworth Dec 02 '21 at 16:02
  • @EdwinAshworth True. The decrease speeds up, later on. You could say resistance falls with age, then. Especially, resistance to temperatures less than 72F. – Jack O'Flaherty Dec 02 '21 at 16:29

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It is a perfectly good sentence. With temperature is understood as as temperature increases.

Edit: two people have chosen to downvote this answer, without giving any reason. I guess it's because I didn't provide any sources to back up my answer.

In the iWeb corpus, there are 237 instances of "increases with temperature" and 61 of "decreases with temperature". On inspection, nearly all of these are like the given example, having no further specification. Here are some examples from the corpus:

While we know that evaporation increases with temperature...

This electrical resistance in metals increases with temperature

With thermistors, resistance decreases with temperature and with RTD's, resistance increases.

Air density also decreases with temperature. Warm air is less dense than cold air... (this example confirms my interpretation)

Bed expansion increases with flow rate and decreases with temperature.

Colin Fine
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