You decide to establish a new temperature scale on which the melting point of ammonia (-77.75 C ) is 0 A, and the boiling point of ammonia (-33.35 C ) is 200 A
What would be the temperature of absolute zero in A ?
..C...........K.......A
..100....|...373.....
.........|...........
.........|...........
.........|...........
.........|...........
...0.....|...273.....
.........|...........
.........|...........
.-33.35..|...........200
.........|...........
.........|...........
-77.75...|...........0
.........|...........
.........|...........
-273.15..|.....0.....?
----------------------
Not to scale. There are 200 divisions on the A scale vs 77.75-33.35 = 44.4 divisions on C scale. Therefore, to convert C to A we must multiply all of the readings by the factor 200/44.4. It is offset by 350.22 degrees. We can check it out to make sure we are right.
Let's convert -77.75C to A. The answer should be zero A.
-77.75 x (200/44.4) + 350.22 = -350.22+350.22 = 0. Right.
So what is -273.15 C on the A scale?
-273.15 x (200/44.4) + 350.22 = ?
Spacing is a problem on this forum but I think you can see that the vertical bar should be a line from top to bottom and represents a scale.
To determine the temperature of absolute zero in the newly established temperature scale, we need to understand the relationship between the Celsius scale and the newly established "A" scale.
First, let's find the temperature difference between the melting point and boiling point of ammonia on the Celsius scale:
Temperature difference on Celsius scale = boiling point - melting point
= (-33.35 C) - (-77.75 C)
= 44.4 C
Now, we can use the temperature difference on the Celsius scale to determine the temperature difference on the "A" scale:
Temperature difference on "A" scale = 200 A - 0 A
= 200 A
Since we know the temperature difference on the Celsius scale (44.4 C) and the temperature difference on the "A" scale (200 A), we can calculate the temperature of absolute zero on the "A" scale.
Temperature of absolute zero on "A" scale = (Temperature difference on "A" scale / Temperature difference on Celsius scale) * Absolute zero on Celsius scale
Temperature of absolute zero on "A" scale = (200 A / 44.4 C) * (-273.15 C)
Calculating this value:
Temperature of absolute zero on "A" scale = (200 A / 44.4 C) * (-273.15 C)
≈ -1229.73 A
Therefore, the temperature of absolute zero on the newly established "A" scale would be approximately -1229.73 A.