Given below are two statements:
Statement 1: If a capillary tube is immersed first in cold water and then in hot water, the height of capillary rise will be smaller in hot water.
Statement 2: If a capillary tube is immersed first in cold water and then in hot water, the height of capillary rise will be smaller in cold water.
In the light of the above statements, choose the most appropriate option from the options given below:
Given below are two statements:
Statement 1: If a capillary tube is immersed first in cold water and then in hot water, the height of capillary rise will be smaller in hot water.
Statement 2: If a capillary tube is immersed first in cold water and then in hot water, the height of capillary rise will be smaller in cold water.
In the light of the above statements, choose the most appropriate option from the options given below:
- Both Statement I and Statement II are false
- Statement I is true but Statement II is false
- Both Statement I and Statement II are true
- Statement I is false but Statement II is true
The Correct Option is B
Approach Solution - 1
The question concerns the behavior of capillary rise when a tube is immersed in cold and hot water, and it poses two statements to evaluate which one is true.
The concept of capillary rise depends on the surface tension of the liquid. The formula for the height of capillary rise, \( h \), is given by:
\(h = \frac{2 \gamma \cos \theta}{\rho g r}\)
- \( \gamma \) is the surface tension of the liquid.
- \( \theta \) is the contact angle.
- \( \rho \) is the liquid's density.
- \( g \) is the acceleration due to gravity.
- \( r \) is the radius of the capillary tube.
When the temperature increases, such as immersing the tube in hot water, the surface tension \( \gamma \) decreases. Because the height of capillary rise is directly proportional to surface tension, an increase in temperature results in a decrease in the height of the capillary rise.
Now let's analyze the statements:
- Statement 1: If a capillary tube is immersed first in cold water and then in hot water, the height of capillary rise will be smaller in hot water.
- This statement is true because the surface tension decreases with an increase in temperature, leading to a smaller height of rise in hot water.
- Statement 2: If a capillary tube is immersed first in cold water and then in hot water, the height of capillary rise will be smaller in cold water.
- This statement is false because, as explained, the height will be larger in cold water due to higher surface tension.
Thus, the correct answer is: Statement I is true but Statement II is false.
Approach Solution -2
1. Understanding Capillary Rise
The height of capillary rise \(h\) is given by:
\[ h = \frac{2T \cos \theta}{\rho g r} \]
Where \(T\) is the surface tension, \(\theta\) is the contact angle, \(\rho\) is the density of the liquid, \(g\) is the acceleration due to gravity, and \(r\) is the radius of the capillary tube.
2. Effect of Temperature on Surface Tension
Surface tension \(T\) decreases as the temperature increases. Since \(h\) is directly proportional to \(T\), a decrease in \(T\) will lead to a decrease in the height of capillary rise.
3. Analyze Statements
Statement I is correct because in hot water (higher temperature), the surface tension is lower, resulting in a smaller height of capillary rise. Statement II is incorrect because the height of capillary rise is actually larger in cold water due to higher surface tension.
So, the correct option is: (2) Statement I is true but Statement II is false
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Concepts Used:
Thermodynamics
Thermodynamics in physics is a branch that deals with heat, work and temperature, and their relation to energy, radiation and physical properties of matter.
Important Terms
System
A thermodynamic system is a specific portion of matter with a definite boundary on which our attention is focused. The system boundary may be real or imaginary, fixed or deformable.
There are three types of systems:
- Isolated System – An isolated system cannot exchange both energy and mass with its surroundings. The universe is considered an isolated system.
- Closed System – Across the boundary of the closed system, the transfer of energy takes place but the transfer of mass doesn’t take place. Refrigerators and compression of gas in the piston-cylinder assembly are examples of closed systems.
- Open System – In an open system, the mass and energy both may be transferred between the system and surroundings. A steam turbine is an example of an open system.
Thermodynamic Process
A system undergoes a thermodynamic process when there is some energetic change within the system that is associated with changes in pressure, volume and internal energy.
There are four types of thermodynamic process that have their unique properties, and they are:
- Adiabatic Process – A process in which no heat transfer takes place.
- Isochoric Process – A thermodynamic process taking place at constant volume is known as the isochoric process.
- Isobaric Process – A process in which no change in pressure occurs.
- Isothermal Process – A process in which no change in temperature occurs.
Laws of Thermodynamics
Zeroth Law of Thermodynamics
The Zeroth law of thermodynamics states that if two bodies are individually in equilibrium with a separate third body, then the first two bodies are also in thermal equilibrium with each other.
First Law of Thermodynamics
The First law of thermodynamics is a version of the law of conservation of energy, adapted for thermodynamic processes, distinguishing three kinds of transfer of energy, as heat, as thermodynamic work, and as energy associated with matter transfer, and relating them to a function of a body's state, called internal energy.
Second Law of Thermodynamics
The Second law of thermodynamics is a physical law of thermodynamics about heat and loss in its conversion.
Third Law of Thermodynamics
Third law of thermodynamics states, regarding the properties of closed systems in thermodynamic equilibrium: The entropy of a system approaches a constant value when its temperature approaches absolute zero.