Question

A Barometer with brass scale, which is correct at `0^(@)C`, reads `75cm` on a day when the air temperature is `20^(@)C`. Calculate correct reading at `0^(@)C`. (Coefficient of real expansion of mercury `=0.00018//^(@)C` and coefficient of linear expansion of brass `=0.000189//^(@)C`.)

Answer 1

We know `H_(0) cong H(1-(gamma-alpha)t)`.
In this problem, `H = 75cm, t = 20^(0)C`,
`gamma = 0.00018//^(0)C, alpha = 0.000018//^(0)C`
`H_(0)c = 75.000[1-(0.00018-0.0000189)20]`
`= 74.758 cm`