There are three common temperature scales, that each scale has its uses and conversion formulas between them are available (Helmenstine, 2019 ). Here illustrations how to obtain the formulas are given.
Notice three different temperature scales in following figure.
Figure 1. Temperature scales and some references points (LivePhysics, 2023 ).
The ratios holds for any temperature scales are as follow
F − 32 212 − 32 = C − 0 100 − 0 = K − 273.15 373.15 − 273.15 , (1) \tag{1}
\frac{F - 32}{212 - 32} = \frac{C - 0}{100 - 0} = \frac{K - 273.15}{373.15 - 273.15},
212 − 32 F − 32 = 100 − 0 C − 0 = 373.15 − 273.15 K − 273.15 , ( 1 )
which are obtained from Figure 1. Equation (1) can produce
F = 212 − 32 100 − 0 ( C − 0 ) + 32 = 180 100 C + 32 = 9 5 C + 32 (2) \tag{2}
\begin{array}{rcl}
F & = & \displaystyle \frac{212 - 32}{100 - 0} (C - 0) + 32 \newline
&&\newline
& = & \displaystyle \frac{180}{100} C + 32 \newline
&&\newline
& = & \displaystyle \frac{9}{5} C + 32
\end{array}
F = = = 100 − 0 212 − 32 ( C − 0 ) + 32 100 180 C + 32 5 9 C + 32 ( 2 )
and
C = 100 − 0 212 − 32 ( F − 32 ) + 0 = 100 180 ( F − 32 ) = 5 9 ( F − 32 ) , (3) \tag{3}
\begin{array}{rcl}
C & = & \displaystyle \frac{100 - 0}{212 - 32} (F - 32) + 0 \newline
&&\newline
& = & \displaystyle \frac{100}{180} (F - 32) \newline
&&\newline
& = & \displaystyle \frac{5}{9} (F - 32),
\end{array}
C = = = 212 − 32 100 − 0 ( F − 32 ) + 0 180 100 ( F − 32 ) 9 5 ( F − 32 ) , ( 3 )
which we are already very familiar with.
What are the important points, related to water, which can be considered as points used in the temperature conversion formulas? Try to obtain the formula C = C ( K ) C = C(K) C = C ( K ) K = K ( C ) K = K(C) K = K ( C ) F = F ( K ) F = F(K) F = F ( K ) K = K ( F ) K = K(F) K = K ( F )