Question

The density of liquid gallium is 6.09 g/cm3 at 35c. If this element is employed in a barometer instead of mercury, what is the height of a column of gallium sustained in the barometer at 1 atm pressure?

Answer 1

Using formula,

$h_{Ga}\rho_{Ga}=h_{Hg}\rho_{Hg}$

where $h_{Ga}$ represents height of gallium in barometer, $\rho_{Ga}$ represents density of gallium , $h_{Hg}$ represents height of mercury in barometer and $\rho_{Hg}$ represents density of mercury.

given, density of gallium = 6.09 g/cm³

we know, height of mercury column at 1atm pressure is 760mm or 76cm.

and density of mercury = 13.6 g/cm³

now, $h_{Ga}$ × 6.09 g/cm³ = 76cm × 13.6 g/cm³

or, $h_{Ga}$ = 76 × 13.6/6.09= 169.72 cm

hence, height of gallium column sustained in the barometer at 1 atm pressure is 169.72cm