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.
the ratios Link to heading
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
$$\tag{1} \frac{F - 32}{212 - 32} = \frac{C - 0}{100 - 0} = \frac{K - 273.15}{373.15 - 273.15}, $$
which are obtained from Figure 1. Equation (1) can produce
$$\tag{2} \begin{array}{rcl} F & = & \displaystyle \frac{212 - 32}{100 - 0} (C - 0) + 32 \newline &&\newline & = & \displaystyle \frac{180}{100} C + 32 \newline &&\newline & = & \displaystyle \frac{9}{5} C + 32 \end{array} $$
and
$$\tag{3} \begin{array}{rcl} C & = & \displaystyle \frac{100 - 0}{212 - 32} (F - 32) + 0 \newline &&\newline & = & \displaystyle \frac{100}{180} (F - 32) \newline &&\newline & = & \displaystyle \frac{5}{9} (F - 32), \end{array} $$
which we are already very familiar with.
challenges Link to heading
- 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 $C = C(K)$, $K = K(C)$ and $F = F(K)$, $K = K(F)$.