CBSE Class 11 Physics Exemplar NCERT Solutions Chapter 12: Kinetic Theory

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NCERT Solutions PDF Class 11 PDF

This chapter delves into the Kinetic Theory of Gases, explaining the behavior of gases at a molecular level. The NCERT Solutions for Class 11 Physics Exemplar, Chapter 12, cover fundamental concepts such as the relationship between pressure, volume, and temperature of gases, molecular motion, and the ideal gas law. These solutions provide step-by-step explanations for multiple-choice questions, helping students grasp the underlying principles. By working through these problems, students will understand how macroscopic properties of gases arise from the microscopic behavior of molecules. This resource is designed to aid in exam preparation by clarifying complex topics and reinforcing understanding of the kinetic theory, crucial for excelling in physics examinations.

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BoardCBSE
ClassClass 11
SubjectPhysics Exemplar
Session2026
LanguageEnglish
TypeNCERT Solutions
ChapterChapter 12

Chapter summary

Chapter 12, Kinetic Theory, focuses on the molecular basis of gas behavior. The NCERT Solutions provided here address key concepts like the ideal gas law, Boyle's Law, and Charles's Law, explaining how molecular motion relates to observable properties like pressure and temperature. The solutions clarify the impact of external factors on gas behavior and the principles governing molecular collisions with container walls, offering a solid foundation for understanding thermodynamics.

Learning outcomes

  • Understand the relationship between molecular motion and macroscopic gas properties.
  • Apply the ideal gas law and its related laws (Boyle's, Charles's) to solve problems.
  • Analyze the effect of molecular collisions on the pressure exerted by a gas.
  • Explain how temperature changes affect the volume and pressure of a gas under constant pressure conditions.
  • Differentiate between various thermodynamic processes based on their applicability to gas laws.

Topics covered

Paper topics

  • Kinetic Theory of Gases
  • Ideal Gas
  • NTP Conditions
  • Molecular Motion
  • RMS Velocity
  • Gas Pressure
  • Boyle's Law
  • Isothermal Process
  • Charles's Law
  • Frictionless Piston
  • Molecular Collisions
  • Momentum Transfer

Important topics

  • Kinetic Theory of Gases Principles
  • Ideal Gas Law (pV=nRT)
  • Boyle's Law and Isothermal Processes
  • Pressure-Volume-Temperature Relationships
  • Molecular Collisions and Momentum Transfer

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Questions and Solutions

Question 1

A cubic vessel (with face horizontal + vertical) contains an ideal gas at NTP. The vessel is being carried by a rocket which is moving at a speed of 500 m s-1 in vertical direction. The pressure of the gas inside the vessel as observed by us on the ground
Solution: The pressure exerted by a gas on the walls of its container is due to the collisions of the gas molecules with the walls. The speed of the rocket (500 m/s) is significantly smaller than the root-mean-square (vrms) speed of the gas molecules at NTP. The motion of the vessel as a whole does not alter the relative velocities of the gas molecules with respect to the walls. Therefore, the frequency and force of molecular collisions with the walls remain unchanged. Consequently, the pressure of the gas inside the vessel, as observed from the ground, remains the same.

Question 2

1 mole of an ideal gas is contained in a cubical volume V, ABCDEFGH at 300K. One face of the cube (EFGH) is made up of a material which totally absorbs any gas molecule incident on it. At any given time,
Solution: In an ideal gas, when a molecule collides elastically with a wall, the momentum transferred to the wall is twice the magnitude of its normal momentum component. For the face EFGH, which totally absorbs the gas molecules, the momentum transfer is different from an elastic collision. Specifically, if we consider the momentum change of the molecule, it is related to the impulse given by the wall. For a perfectly absorbing surface, the molecule's momentum component normal to the surface becomes zero after incidence. The pressure exerted by the gas is proportional to the rate of momentum transfer. Since the face EFGH absorbs molecules, it does not exert an equal and opposite force as an elastic collision would. The pressure on EFGH would be less than that on a wall experiencing elastic collisions. If we assume that the average momentum transfer per molecule to the absorbing wall is half of that to an elastically colliding wall, then the pressure on EFGH would be half the pressure on a wall like ABCD, which experiences elastic collisions.

Question 3

Boyle's law is applicable for an
  1. adiabatic process
  2. isothermal process
  3. isobaric process
  4. isochoric process
Solution: Boyle's law states that for a fixed amount of an ideal gas, the pressure and volume are inversely proportional, provided the temperature remains constant. Mathematically, this is expressed as pV = \text{constant}, where p is the pressure and V is the volume. A process that occurs at a constant temperature is known as an isothermal process. Therefore, Boyle's law is applicable only during an isothermal process.

Question 4

A cylinder containing an ideal gas is in vertical position and has a piston of mass M that is able to move up or down without friction. If the temperature is increased
  1. both p and V of the gas will change
  2. only p will increase according to Charles's law
  3. V will change but not p
  4. p will change but not V
Solution: Consider the forces acting on the piston. The downward forces are the atmospheric pressure acting on the top surface (p_a A, where A is the area of the piston) and the weight of the piston (Mg). The upward force is due to the pressure of the gas inside the cylinder (pA). Since the piston can move freely without friction, it is in equilibrium. Thus, the upward force must balance the downward forces:

pA = p_a A + Mg

This implies that the pressure of the gas inside the cylinder is constant:

p = p_a + \frac{Mg}{A}

When the temperature of the gas is increased, according to the ideal gas law (pV = nRT), if the pressure (p) is constant and the amount of gas (n) and the gas constant (R) are also constant, the volume (V) must increase proportionally to the absolute temperature (T). Therefore, the volume V will change, but the pressure p will remain constant.

Common mistakes

  • Confusing absolute temperature scales with Celsius or Fahrenheit.
  • Incorrectly applying gas laws when conditions like temperature or pressure are not constant.
  • Misinterpreting the effect of relative motion versus absolute motion on gas pressure.
  • Overlooking the specific conditions under which Boyle's Law is valid (isothermal process).

Revision tips

  • Focus on understanding the assumptions of the kinetic theory of gases.
  • Practice applying the ideal gas law (pV=nRT) and its derived forms.
  • Review the conditions for Boyle's Law and Charles's Law to be applicable.
  • Visualize molecular motion and its impact on pressure and temperature.
  • Pay attention to the units used in calculations involving gas properties.

Practice MCQs

Q1. A cubic vessel containing an ideal gas at NTP is carried by a rocket moving at 500 m/s vertically. How does the pressure of the gas inside the vessel, as observed from the ground, change?

Q2. In a cubical volume containing an ideal gas, one face is made of a material that totally absorbs gas molecules incident on it. What is the pressure on this absorbing face compared to the opposite face?

Q3. Boyle's Law, which states that for a fixed amount of gas at constant temperature, pressure is inversely proportional to volume (pV = constant), is applicable for which type of process?

Q4. An ideal gas in a cylinder with a frictionless piston is heated. The piston is free to move. What happens to the gas?

Frequently asked questions

What is the main concept covered in CBSE Class 11 Physics Exemplar Chapter 12?

Chapter 12, Kinetic Theory, explains the behavior of gases based on the motion of their molecules. It covers concepts like pressure, temperature, volume, and the ideal gas law.

How do these NCERT Solutions help students prepare for exams?

These solutions provide clear, step-by-step explanations for MCQs, reinforcing understanding of key principles and problem-solving techniques related to the kinetic theory of gases, which is crucial for physics exams.

What is the significance of the rocket's speed in Question 1?

Question 1 highlights that the macroscopic motion of a container does not affect the internal gas pressure if the container's speed is much less than the RMS speed of the gas molecules, as the relative motion between molecules and walls remains unchanged.

Why is Boyle's Law applicable only to isothermal processes?

Boyle's Law states that pressure is inversely proportional to volume at constant temperature. An isothermal process is one where the temperature remains constant, thus fulfilling the condition for Boyle's Law.

What does the frictionless piston scenario in Question 4 illustrate?

The scenario in Question 4 demonstrates that when a gas is heated in a cylinder with a frictionless piston, the pressure remains constant (due to external atmospheric pressure and piston weight), and the volume increases according to Charles's Law.

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