A barometer with brass scale which is correct at 0^(@)C reads 75 cm on a day at 20^(@)C. If Y_(real) of mercury - 0.00018 //^(@)C and a of brass is 0.000018//^(@)C, calculate the correct reading at 0^(@)C.

A barometer with brass scale which is correct at 0^(@)C reads 75 cm on

1.	A barometer with brass scale which is correct at 0^(@)C reads 75 cm on a day at 20^(@)C. If Y_(real) of mercury - 0.00018 //^(@)C and a of brass is 0.000018//^(@)C, calculate the correct reading at 0^(@)C.
Answer» Solution :Let `H _(0)` be the correct height at `0^(@)C,` H be the observed height at `t ^(@)C.` Let `alpha and gamma` be the coefficients of LINEAR EXPANSION and cubical expansion of BRASS and MERCURY. Let `p _(0) and p ` be the densities of mercury at `0^(@)C and t ^(@)C.` If we use correction for the expansion of the scale and change in density of mercury. We can write `H (1 + alpha t ) p g = H _(0) p _(0) g ` `H (1 + alpha t ) p = H _(0) p (1 + rt) implies H_(0) ~~ H ( 1 + alpha t) (1- gamma t ) = H {1- (gamma - alpha) t}` But `H = 75 cm, t = 20^(@)C, So, H _(0) = 74.758 cm`