Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up.
Sign up to join this community
A new temperature scale is to be sued where freezing and boiling temperature of water is at -100 deg N and 100 deg N respectively. Calculate Absolute Zero in Degree N
Answer is -992.6 Degree N
Absolute Zero in C = 273.15 C
I use Ratio and Proportion:
Total Scale in N = 100 - - 100 = 200
Total Scale in C = 100 - 0 = 100
( Current Temp ) / (Overall Scale) = x/200 = 273.15/100
x = 546.3 N
What am I doing wrong? Any Hint? Am I not supposed to use Ratio and Proportion?
We would assume that the new scale is an affine transformation of others (this is not explicitly stated, which is problematic because without this assumption there is no way to solve the problem).
Therefore it's simple: come up with an affine function which relates Celsius to the new system:
$$ f(x) = ax + b $$
They give you two points. The freezing point is $-100$ and the boiling point is $+100$. Since we know that this corresponds to $0^\circ\ C$ and $100^\circ\ C$ this gives:
$$ f(0) = b = -100 \\ f(100) = 100a + b = 100 \rightarrow 100a - 100 = 100 \rightarrow a = \frac{200}{100} = 2 $$
Therefore:
$$ f(x) = 2x - 100 $$
This gives that $f(-273.15) = -646.3$.
As you found, the size of an $N$ degree is $1/2$ a $C$ degree, so it takes twice as many $N$ degrees to be the same interval as $C$ degrees. You missed the fact that $-100 N$ corresponds to $0 C$, so since absolute zero is $273.15$ below $0 C$, it is $2 \cdot 273.15$ below $-100 N$, which says absolute zero is $-100 -2 \cdot 273.15=-646.3 N$ Yes, that disagrees with your book. It looks like the book used degrees F somehow-that gets close.
