Suppose that you developed your own new temperature scale (denoted deg N). You chose 100.0 deg N as the temp?

Question

Suppose that you developed your own new temperature scale (denoted deg N). You chose 100.0 deg N as the temperature of freezing water (ice/water) and 170.0 deg N as the temperature of boiling water (water/steam) at one atmosphere pressure. What would be the temperature at which nitrogen boils (-196 deg C) on your new temperature scale?

need for test review thanks

Answer 1

If I assume that °N scale is built on base(10) and that one °N is proportional to one °C (not logarithmic scale), the boiling temperature of dinitrogen at a pressure of one atmosphere is:

100 - [ (196 x 70) / 100 ] = 100 - 137.2 = -37.2 °N


1 °N = 0.7 °C
1 °C = 10/7 °N.

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If I had to develop my own temperature scale, I would try to get some inspiration from °K scale:

O °K = atoms/molecules immobililty (according to which landmarks, though?)

Let's call my own personal temperature scale °A:

- that would be a centigrad scale like celsius's, kelvin's scales. Not logarithmic. Base-10 (we have 5 fingers on each hand. We start counting thanks to our fingers. Easier to memorize)

- well, I don't know what my "100 °A" would be but I really enjoy a 0°A = 0°C = freezing point of water at sea-level atmospheric conditions of pressure. Because I think it is very helpful for us Earthians to have a landmark from which we can guess if water can exist in frozen, liquid or gazeous state on our own planet, in life conditions for a human.

- well, I would keep that 100 °A = 100 °C = boiling/liquefying point of water at one atm. Because from "100", we start a new hundred in base-10 (symbolic boundary) and because life conditions are very different if water cannot stay in its liquid form.

- I would have a different temperature scale if I was living on Mars-planet (different pressure), and I would use a different temperature scale when I have to study theories of the universe. I wouldn't use a temperature scale actually, in such a field.

Answer 2

We know that 100.0 deg N = 0 deg C and 170.0 deg N = 100 deg C.

We need to be able to map 70 deg N onto 100 deg C.

Taking 100/70 would give us have many degrees C map onto each deg N, so a ratio of conversion would be 10C/7N.

To convert from deg C to deg N we would have to multiply by 7/10 and add 100. We multiply by 7/10 because there are only 7 deg N per each 10 deg C. If we think of the case when water freezes at 0 deg C, multiplying it by anything will leave it unchanged. We then offset by adding 100 to reach our freezing temp in deg N.

To test, water boils at 100 deg C,

100 deg C * (7/10) + 100 = 70 deg N + 100 = 170 deg N, which is what we wanted.

You should be able to apply this to your nitrogen boiling temperature. Yourself. As a check, your final answer should be negative decimal, with odd numbers in the ten's and one's column, and an even number of tenths.

--charlie

Answer 3

The answer is (170-100)/100*(-196)+100= -37.2