# Determining boiling point on a created temperature scale

1.Assume that you construct a thermometer using gallium as the fluid instead of mercury, and that you define the melting point of gallium as 0 °G and the boiling point of gallium as 1000 °G. What is the melting point of sodium chloride (801 °C) on the gallium scale?

First we determine the ratio of $^{\circ}\mathrm G/^{\circ}\mathrm C$ by dividing the melting points. This states that $0.4599\ ^{\circ}\mathrm G=1\ ^{\circ}\mathrm C$.

$$\dfrac{1000\ ^{\circ}\mathrm G-0\ ^{\circ}\mathrm G}{2204\ ^{\circ}\mathrm C-29.78\ ^{\circ}\mathrm C}=\dfrac{1000\ ^{\circ}\mathrm G}{2174.22\ ^{\circ}\mathrm C}=0.4599\ ^{\circ}\mathrm G/^{\circ}\mathrm C$$

To calculate the boiling point, this is done: $$T=0.4599\ ^{\circ}\mathrm G/^{\circ}\mathrm C\times\left(801\ ^{\circ}\mathrm C-29.78\ ^{\circ}\mathrm C\right)=355\ ^{\circ}\mathrm G$$

My question is, why are we subtracting by $29.78\ ^{\circ}\mathrm C$?

It zeroes things out. It is analogous to the use of "32" in the equation to convert Fahrenheit to Celsius, where "32" represents the melting point of ice on the Fahrenheit scale. In your G scale you must subtract the melting point of gallium in the Centigrade scale in order to get 0G at the melting point of gallium $$\ce{^{o}C = (^{o}F-32)*(5/9)}$$ $$\ce{^{o}G = (^{o}C-29.78)*(0.4599)}$$