We would like to perpare a scale whose length does not change with temperature. It is proposed to prepare a unit scale f this type whose length remains, say 10 cm. We can use a bimetallic strip made of brass and iron each of different length (both components) would change in such a way that differnece between theri lenght rermain constant. If `alpha_(iron) = 1.2 xx 10^(-5)//K and alpha_(brass) = 1.8 xx 10^(-5)//K,` what should we take as lenght of each strip ?

Explanation

According to question `l_("iron") - l_("brass") = 10 cm` = constant at all temperatures
Let `l_(0)` be length at temperature `0^(@)C` and l be the length after change in temperature of `Delta t`.
Now, we can write `l_("iron")-l_("brass") = 10 cm` at all temperatures
`l_("iron") (1+ alpha_("iron") Delta t) - l_("brass") (1+alpha_("brass")Delta t) = 10 cm`
`l_("iron") alpha_("iron") = l_("brass") alpha_("brass")`
`:. (l_("iron"))/(l_("brass")) = (1.8)/(1.2) = (3)/(2)`
`:. (1)/(2) l_("brass") = 10 cm`
`rArr l_("brass") = 20 cm` and `l_("iron") 30 cm`