A mercury thermoeter read `80^(@)C` when the mercury is at `5.2cm` mark and `60^(@)` when the mercury is at `3.9cm` mark. Find the temperature when the mercury level is at `2.6cm` mark.

Explanation

`(l_(1)-l_(2))/(l_(1)-l_(3))=(alphal_(0)(T_(1)-T_(2)))/(alphal_(0)(T_(1)-T_(3)))=(T_(1)-T_(2))/(T_(1)-T_(3))`
`or (5.2-3.9)/(5.2-2.6)=(80-60)/(80-T_(3))`
`1.3(80-T_(3))=2.6(20) orT_(3)=40^(@)C`