The Question is from neet-chemistry chemical-thermodynamics liquid-state, and it was created by the author Mr. S M HUSSAIN

Question

A liquid confined within a capillary tube of radius 'r' shows a capillary rise 'h'. If the angle of contact is zero and the surface tension is 'T', which of the following expressions correctly represents the density 'ρ' of the liquid?

Mr. S M HUSSAIN · Accepted Answer

## CORE INFORMATION
✓ **Answer**: C
## CONCEPT FRAMEWORK
	**Primary Concept**: Capillary action and its relation to surface tension, density, and radius of the capillary tube.
	**Related Topics**: Fluid mechanics, surface tension, cohesive and adhesive forces.
	**Prerequisites**: Understanding of surface tension, pressure difference across a curved surface (Young-Laplace equation), and hydrostatic pressure.
## SOLUTION PATHWAY
**Given Information**:
		Radius of capillary tube = r
		Capillary rise = h
		Angle of contact = 0°
		Surface tension = T
		Density of liquid = ρ (to be determined)
**Method & Steps**:
	1. Consider the pressure difference across the meniscus of the liquid in the capillary tube.  Since the angle of contact is zero, the meniscus is hemispherical.
		Reasoning: The pressure inside the liquid just below the meniscus is less than the atmospheric pressure due to the surface tension.
		Formula/Rule: The pressure difference ΔP across a curved surface is given by the Young-Laplace equation:  $ΔP = \frac{2T}{r}$, where r is the radius of curvature (equal to the radius of the capillary tube in this case).
	2. Equate the pressure difference to the hydrostatic pressure due to the liquid column of height h.
		Working: The hydrostatic pressure is given by $P = ρgh$, where g is the acceleration due to gravity.  Therefore, $ρgh = \frac{2T}{r}$ 
		Key Point:  The pressure difference due to surface tension is balanced by the hydrostatic pressure of the liquid column.
	3. Solve for the density ρ.
		Result: Rearranging the equation, we get $ρ = \frac{2T}{rgh}$
		Verification: The units are consistent: $[ρ] = \frac{[T]}{[r][g][h]} = \frac{N/m}{m \cdot m/s^2 \cdot m} = kg/m^3$, which is the correct unit for density.
## OPTION ANALYSIS
[A] :x: Incorrect. This option has the numerator and denominator inverted.
[B] :x: Incorrect. This option has the numerator and denominator inverted and lacks a factor of 2.
[C] ✓: Correct. This option accurately represents the density of the liquid derived from the Young-Laplace equation and hydrostatic pressure balance.
[D] :x: Incorrect. This option has the numerator and denominator inverted and lacks a factor of 2.
## LEARNING AIDS
	**Common Mistakes**:
		1. Incorrectly applying the Young-Laplace equation: Remember that the pressure difference is 2T/r for a hemispherical meniscus (zero contact angle).
		2. Forgetting to consider hydrostatic pressure: The surface tension effect is balanced by the weight of the liquid column.
	**Quick Tips**:
		1. Draw a diagram to visualize the pressure difference and the liquid column.
		2. Remember the Young-Laplace equation and the formula for hydrostatic pressure.

Mr. S M HUSSAIN · Answer

ρ = T/2rhg

Mr. S M HUSSAIN · Answer

ρ = rhg/2T

Mr. S M HUSSAIN · Answer

The correct Option is "ρ = 2T/rhg"

Mr. S M HUSSAIN · Answer

ρ = 2rhg/T

NEET Chemistry States Of Matter Liquid State MCQs

Select Topic

Question Tags

Question Tags

Question Tags

Question Tags

Question Tags

Question Tags

Question Tags

Question Tags

Question Tags

Question Tags

NEET Subjects

Our Bots

Company