Find an expression for how the daimeter of of glass cylinder containing the mercury must change with length for the height of the mercury column to vary linearly with temperature. Would this "tapering" of the cylinder be noticeable to the casual observer?
The temperature dependence of the volume of the mercury in thermometer:
V(T)=V0 (1+0.18182*10-3 T +0.0078*10-6 T2)
The temperature dependence of height of mercury in thermometer assuming constant diameter:
Now V(T) =pi/4*d2h(T)
So h(T) = V0/(pi/4*d2) (1+0.18182*10-3 T +0.0078*10-6 T2))
‘h(T)= C(1+0.18182*10-3 T +0.0078*10-6 T2)
Where C=( V0/(=pi/4*d2)
Hint: One way to start is by writing out an equation for V in terms of h and d(h). (Use your calculus skills!) Now you have an equation for h in terms of T and some function d(h), which is what you are looking for.