he column of mercury in a barometer (see Figure below) has a height of 0.760 m when the pressure is one atmosphere and the temperature is 0.0 °C. Ignoring any change in the glass containing the mercury, what will be the height of the mercury column for the same one atmosphere of pressure when the temperature rises to 36.6 °C on a hot day? Hint: The pressure in the barometer is Pressure = ρgh, and the density ρ changes when the temperature changes.
3 answers
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Volume thermal expansion coef Hg 0.000181/K
∆V = αᵥV∆T, αᵥ is volume thermal expansion coef
∆V = αᵥV∆T
∆V/V = αᵥ∆T,
because cross sectional area is fixed
∆V/V = ∆h/h = αᵥ∆T,
∆h = hαᵥ∆T, = (760mm)(0.000181/K)(36.6K) = 5.03 mm
new h = (760+5.03) = 765.03mm
∆V = αᵥV∆T, αᵥ is volume thermal expansion coef
∆V = αᵥV∆T
∆V/V = αᵥ∆T,
because cross sectional area is fixed
∆V/V = ∆h/h = αᵥ∆T,
∆h = hαᵥ∆T, = (760mm)(0.000181/K)(36.6K) = 5.03 mm
new h = (760+5.03) = 765.03mm
ans is right.
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