The coefficient of cubical expansion of mercury is 0.00018/°C and that of brass 0.00006 /°C. If a barometer having a brass scale were to read 74.5 cm at 30°C, find the true barometric height at 0°C. The scale is supposed to be correct at 15°C.

As,  αbrass =γbrass 3=0.000063                   =0.00002=2×10-5/C  ∘The brass scale is true at 15°C, therefore at 30°, its graduations will increase in length and hence, observed reading will be less than actual reading at 30°.∴The change in reading.                    Δl=lαbrass (ΔT)=74.5×2×10-5(30-15)                        = 0.02235 cm∴ Actual reading at 30°C,                      l30=lobserved +Δl=74.5+0.02235=74.522 cmAssuming area of cross-section to be constant, we have                     V0ρ0 = V30ρ30or                ah0ρ0 = ah30ρ30Therefore, true height at 0°C,                 h0=h30ρ30ρ0=h301+γHgΔT                      =74.5221+0.00018×30=74.5221.0054=74.122 cm