Question

a liquid rises to a height of 5 cm in capillary tube and Mercury falls to a depth of 2cm in the same capillary tube.if the density of the liquid is 1.2 g/cc and mercury is 13.6g/cc.and angles of contact of liquid and Mercury with the capillary tube are 0° and 135° respectively.find the ratio of surface tension for mercury and liquid​

Answer 1

Explanation:

The height h through which a liquid will rise in a capillary tube of radius r is given by

h=

rρg

2Scosθ

where S is the surface tension, ρ is the density of the liquid and θ is the angle of contact.

For identical capillary tubes and two liquids ( water '1' & mercury '2')

h

2

h

1

=

rρ

1

g

2S

1

cosθ

1

×

2S

2

cosθ

2

rρ

2

g

⇒

h

2

h

1

=

ρ

1

S

1

cosθ

1

×

S

2

cosθ

2

ρ

2

⇒

S

2

S

1

=

h

2

h

1

×

cosθ

1

cosθ

2

×

ρ

2

ρ

1

⇒

S

2

S

1

=

−3.42

10

×

cos0

∘

cos135

∘

×

13.6

1

⇒

S

2

S

1

=

−3.42

10

×

1

−0.707

×

13.6

1

⇒

S

2

S

1

=0.152≈

6.5

1