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?
15
-
9@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).– FumbleFingersCommented Nov 30, 2021 at 14:23
-
2@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)– LPHCommented Nov 30, 2021 at 18:58
-
1@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 AshworthCommented Nov 30, 2021 at 19:35
-
1A 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'FlahertyCommented Nov 30, 2021 at 23:51
-
1"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.– GreybeardCommented Dec 1, 2021 at 14:39
|
Show 10 more comments
1 Answer
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.
answered Nov 30, 2021 at 23:29
