. The tube of a mercury barometer is 1 cm in diameter. What correction due to capillarity with effect of miniscus is to be applied to barometer reading if surface tension of mercury is 435.5 dyne/cm and angle of contact of mercury with glassis 140°? (density of mercury =13600 kg/m³)
Answers
Given :
T = 435.5 dyne/cm = 0.4355 N/m,
θ = 14 0
ρ = 13600 kg/m³
d = 1 cm
∴ r = 0.5 cm
= 5 × 10⁻³ m
T = rh ρ g/ 2 cos θ
h = 2T cos θ/ r g ρ
∴ h = 2 x0.4355x cos140⁰/ 5 x10⁻³x 13600 x9.8
= 0.8710x cos( 90 + 50 )/ 5x 13.6 x9.8
=0.8710( –sin 50 ) /5x 13.6 x9.8
=–0.8710x 0.7660/ 68.0x 9.8
= – 1.001 × 10⁻³m
∴ h = – 1.001 mm
here Negative sign indicates that mercury level will be lowered by 1.001 mm.
Hence to get correct reading h = 1.001 mm has to added.
∴ h = 1.001 mm
Explanation:
Given :
T = 435.5 dyne/cm = 0.4355 N/m,
θ = 14
0
ρ = 13600 kg/m³
d = 1 cm
∴ r = 0.5 cm
= 5 × 10⁻³ m
T = rh ρ g/ 2 cos θ
h = 2T cos θ/ r g ρ
∴ h = 2 x0.4355x cos140⁰/ 5 x10⁻³x 13600 x9.8
= 0.8710x cos( 90 + 50 )/ 5x 13.6 x9.8
=0.8710( –sin 50 ) /5x 13.6 x9.8
=–0.8710x 0.7660/ 68.0x 9.8
= – 1.001 × 10⁻³m
∴ h = – 1.001 mm
here Negative sign indicates that mercury level will be lowered by 1.001 mm.
Hence to get correct reading h = 1.001 mm has to added.
∴ h = 1.001 mm