Question

A capillary tube of area of cross-section $A$ is dipped in water vertically. The amount of heat evolved as the water rises in the capillary tube up to height $h$ is : (The density of water is $\rho$ ) (a) $\frac{A p g h^{2}}{2}$ (b) $A g h^{2} \rho$ (c) $2 A g h^{\overline{2}} \rho$ (d) none of these

Name: Problem 42, Chapter 12: Arihant AIEEE Physics
Uploaded: 2021-09-11T06:14:45-08:00
Duration: 1 min 5 s
Channel: Narayan Hari
Description: A capillary tube of area of cross-section A is dipped in water vertically. The amount of heat evolved as the water rises in the capillary tube up to height h is : (The density of water is ρ) (a) (A p g h^2)/(2) (b) A g h^2 ρ(c) 2 A g h^2 ρ(d) none of these

   A capillary tube of area of cross-section $A$ is dipped in water vertically. The amount of heat evolved as the water rises in the capillary tube up to height $h$ is : (The density of water is $\rho$ )
(a) $\frac{A p g h^{2}}{2}$
(b) $A g h^{2} \rho$
(c) $2 A g h^{\overline{2}} \rho$
(d) none of these

Arihant AIEEE Physics

D.B. Singh 2006 Edition

Chapter 12, Problem 42

Instant Answer

Solved by Expert Narayan Hari

09/11/2021

Step 1

Step 1: First, we need to understand that the heat evolved in this process is equal to the potential energy of the water. Show more…

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A capillary tube of area of cross-section $A$ is dipped in water vertically. The amount of heat evolved as the water rises in the capillary tube up to height $h$ is : (The density of water is $\rho$ ) (a) $\frac{A p g h^{2}}{2}$ (b) $A g h^{2} \rho$ (c) $2 A g h^{\overline{2}} \rho$ (d) none of these

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Key Concepts

Gravitational Potential Energy

This concept is about the energy an object acquires when it is raised in a gravitational field. In contexts like a capillary tube where water rises by a height h, each infinitesimal mass element of water gains potential energy proportional to its weight and the height it reaches. The total energy change reflects the sum (integral) of the energy gains of all these mass elements.

Integration Over a Continuous Distribution

When dealing with fluids or any continuous mass distribution, calculating the total work or energy change requires integrating the contributions of each infinitesimal element. In the case of water rising in a capillary tube, the integration accounts for the fact that different layers of water (from the bottom to the top of the column) are raised by different distances, leading to an overall energy change determined by this incremental summation process.

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