Physics Question about Temperature, Pressure & Volume, please show workings if possible!?

Question

A column of mercury in a barometer 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 37.5 °C on a hot day?

(This hint was given with the question: The pressure in the barometer is Pressure = ρgh, and the density ρ changes when the temperature changes.)

billrussell42 · Answer

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)(37.5K) = 5.2 mm
new h = 765.2 mm

Michael E · Answer

If you look at rho as a function of temprature, .76*rho(0)g=rho(37.5)gh
If you know rho as a function of temp, that will give h = rho(37.5)/rho(0)/.76

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Physics Question about Temperature, Pressure & Volume, please show workings if possible!?

2 Answers