# Little temperature puzzle:

sonhouse
Posers and Puzzles 10 Feb '12 17:55
1. sonhouse
Fast and Curious
10 Feb '12 17:55
The ratio of temps between C and F is 1.6827. What is the temperature?
2. talzamir
Art, not a Toil
11 Feb '12 08:21
I think the answer you seek is 0 K.

Outside my window the ratio has been uncomfortably close to one a few times this winter.. the downside of living next door to Santa.
Who doesn&#039;t live on the North Pole, it&#039;s just disinformation given by the elves so that the big man can work in peace.
3. sonhouse
Fast and Curious
11 Feb '12 13:48
Originally posted by talzamir
[hidden]I think the answer you seek is 0 K.[/hidden]

Outside my window the ratio has been uncomfortably close to one a few times this winter.. the downside of living next door to Santa. [hidden]Who doesn't live on the North Pole, it's just disinformation given by the elves so that the big man can work in peace.[/hidden]
Your box has nothing in it, nothing comes up.
4. sonhouse
Fast and Curious
11 Feb '12 15:54
Another one: Can there be a temperature with a ratio=square root of 3?
5. joe shmo
Strange Egg
11 Feb '12 16:471 edit
Originally posted by sonhouse
Another one: Can there be a temperature with a ratio=square root of 3?
I'm going to say no such ratio can exist, but close enough happens @ -26.2 C
6. sonhouse
Fast and Curious
11 Feb '12 19:01
Originally posted by joe shmo
I'm going to say no such ratio can exist, but close enough happens @ -26.2 C
Pretty close, 1.728. I saw there was a range where only one temperature would have a particular ratio, on the positive C side, the numbers asymptote towards 1.8 but on the negative side, since -273.15 is absolute zero, the ratio can't get to 1.8. It can if you allow say -300,000 C, which of course is a nonsense number.

I was just playing with my casio calculator which has the C-F and F-C conversions and saw you could specify a ratio that would only work on the negative C side.
7. joe shmo
Strange Egg
11 Feb '12 19:24
Originally posted by sonhouse
Pretty close, 1.728. I saw there was a range where only one temperature would have a particular ratio, on the positive C side, the numbers asymptote towards 1.8 but on the negative side, since -273.15 is absolute zero, the ratio can't get to 1.8. It can if you allow say -300,000 C, which of course is a nonsense number.

I was just playing with my casio ca ...[text shortened]... F-C conversions and saw you could specify a ratio that would only work on the negative C side.
When I said

(C/F) =/= Sqrt(3)

Is because the irrational sqrt(3) cannot be expressed as the ratio of two integers
8. 13 Feb '12 10:56
Originally posted by joe shmo
When I said

(C/F) =/= Sqrt(3)

Is because the irrational sqrt(3) cannot be expressed as the ratio of two integers
But temperatures can have irrational values.
9. joe shmo
Strange Egg
13 Feb '12 16:15
Originally posted by deriver69
But temperatures can have irrational values.
But can you measure irrational values?
10. 14 Feb '12 01:422 edits
9C/5+32=F
C=160/(5F/C-9)
F=160/(5-9C/F)

I think temperature is a measure of the square of the average speed of a group of particles. As long as the particle speed can be irrational temperature can therefore be irrational, so this depends on whether speed is quantised or not.

Since there is no consensus on whether time and distance are quantised, nobody knows for sure whether speed is quantised, and so nobody knows whether an irrational temperature is possible.
11. 14 Feb '12 02:011 edit
Originally posted by joe shmo
But can you measure irrational values?
Interesting point with regard to temperature. You can measuire irrational lengths though for instance by using diagonals of rectangles with rational dimensions. Maybe I will have a word with the physics department see if they can come up with a plan (problem is they always want to round to a reasonable degree of accuracy).
12. 14 Feb '12 15:18
Originally posted by deriver69
Interesting point with regard to temperature. You can measuire irrational lengths though for instance by using diagonals of rectangles with rational dimensions. Maybe I will have a word with the physics department see if they can come up with a plan (problem is they always want to round to a reasonable degree of accuracy).
There is no mening to measure irrational values of temperatures. But this doesn't mean that irrational values of temperatures doesn't exist.

When a temp of 3 degree rises to 4 degrees, then every real value in between has been passed during the process. Even exactly pi degrees. Not for long though.
13. sonhouse
Fast and Curious
14 Feb '12 17:06
Originally posted by FabianFnas
There is no mening to measure irrational values of temperatures. But this doesn't mean that irrational values of temperatures doesn't exist.

When a temp of 3 degree rises to 4 degrees, then every real value in between has been passed during the process. Even exactly pi degrees. Not for long though.
Can you imagine the circuitry needed to make a temperature exactly PI C?
14. 14 Feb '12 19:491 edit
Originally posted by sonhouse
Can you imagine the circuitry needed to make a temperature exactly PI C?
You just need a thermometer calibrated in radians ðŸ™‚
15. sonhouse
Fast and Curious
14 Feb '12 22:27
Originally posted by iamatiger
You just need a thermometer calibrated in radians ðŸ™‚