# Defining temperature using mercury column

After one defines 0th law of thermodynamics w/ thermal equilibrium using temperature. Then a quantitative description of temperature can be made. We can measure temperature by finding another property which changes monotonically with temperature.

In my textbook " concept of physics by HC verma" on pg.2, He states that we measure temperature as a function of the height of a mercury column and he assumes the temperature as a linear relation which is:

$$t=al+b$$ ( where t is temperature, l is length and 'a' and 'b' are some constants)

And then he states that change of one degree in temperature will mean a change in $$\frac{l_2 - l_1}{t_2 - t_1}$$ in the length of the mercury column

I can not understand the second statement...

I know that slope of $$\frac{\Delta t}{\Delta l} = a$$ but how does this relate to change in one degree of temperature?

Given the linear relation you can subtract the relations for a temperature difference of 1, namely: $$(t+1)-t=\left(al_f+b\right)-\left(al_i+b\right)\\ \Rightarrow 1=a\Delta l\\ \Rightarrow \Delta l=\frac{1}{a}$$