A barometer reads 75.0 cm on a steel scale. The room temperature is 30∘C. The scale is correctly graduated for 0∘C. The coefficient of linear expansion of steel is α = 1.2 × 10−5/∘C and the coefficient of volume expansion of mercury is γ = 1.8 × 10−4/∘C. Find the correct atmospheric pressure.
74.89 cm
The 75 cm length of steel at 0∘C will become lθ at 30∘C where,
Iθ = (75cm)[1+α(30∘C)]. ................(1)
The length of mercury column at 30∘C is lθ. Suppose the length of the mercury column, if it were at 0∘C, is l0. Then,
Iθ = I0[1+γ3(30∘C)]. ................(2)
By (1) and (2),
I0[1+γ3(30∘C)] = 75cm[1+(30∘C)]
Or, I0 = 75cm [1+α(30∘C)][1+γ3(30∘C)]
= 75 cm [1+(α−γ3)(30∘C)]
= 74.89 cm.