Case Study Questions Class 11 Physics Chapter 13 Kinetic Theory
CBSE Class 11 Case Study Questions Physics Kinetic Theory. Important Case Study Questions for Class 11 Board Exam Students. Here we have arranged some Important Case Base Questions for students who are searching for Paragraph Based Questions Kinetic Theory.
At Case Study Questions there will given a Paragraph. In where some Important Questions will made on that respective Case Based Study. There will various types of marks will given 1 marks, 2 marks, 3 marks, 4 marks.
CBSE Case Study Questions Class 11 Physics Kinetic Theory
Case Study – 1
Boyle’s law is a gas law which states that the pressure exerted by a gas (of a given mass, kept at a constant temperature) is inversely proportional to the volume occupied by it. In other words, the pressure and volume of a gas are inversely proportional to each other as long as the temperature and the quantity of gas are kept constant. For a gas, the relationship between volume and pressure (at constant mass and temperature) can be expressed mathematically as follows.
P ∝ (1/V) Where P is the pressure exerted by the gas and V is the volume occupied by it. This proportionality can be converted into an equation by adding a constant, k.
Charles law states that the volume of an ideal gas is directly proportional to the absolute temperature at constant pressure. The law also states that the Kelvin temperature and the volume will be in direct proportion when the pressure exerted on a sample of a dry gas is held constant. Charles law and Boyle’s law applied to low density gas only. The total pressure of a mixture of ideal gases is the sum of partial pressures. This is Dalton’s law of partial pressures.
1) Boyle’s law is obeyed by high as well as low density gases. True or False?
a) True
b) False
2) Charles law is states that volume of an ideal gas is directly proportional to temperature at constant
a) Temperature
b) Pressure
c) Volume
d) None of these
3) State Daltons law of partial pressures
4) State Boyle’s law
5) State Charles law
Answer key – 1
1) a
2) b
3) The total pressure of a mixture of ideal gases is the sum of partial pressures exerted by all the molecules of gas. This is Dalton’s law of partial pressures.
4) Boyle’s law is a gas law which states that at constant temperature the pressure exerted by a gas is inversely proportional to the volume occupied by it. In other words, the pressure and volume of a gas are inversely proportional to each other as long as the temperature and the quantity of gas are kept constant. For a gas, the P ∝ (1/V) Where P is the pressure exerted by the gas and V is the volume occupied by it. This proportionality can be converted into an equation by adding a constant k.
5) Charles law states that the volume of an ideal gas is directly proportional to the absolute temperature at constant pressure.
Case Study – 2
Pressure of an Ideal Gas: according to kinetic theory of gases pressure is given by
P = 1/3 nmv2
Where, n is number of molecules per unit volume, m is mass and v2 is mean squared speed. Though we choose the container to be a cube, the shape of the vessel really is immaterial.
The average kinetic energy of a molecule is proportional to the absolute temperature of the gas; it is independent of pressure, volume or the nature of the ideal gas. This is a fundamental result relating temperature, a macroscopic measurable parameter of a gas (a thermodynamic variable as it is called) to a molecular quantity, namely the average kinetic energy of a molecule. The two domains are connected by the Boltzmann constant and given by E = kbT.
Where kb is Boltzmann constant having value of 1.38*10-23 joule per Kelvin.
We have seen that in thermal equilibrium at absolute temperature T, for each translational mode of motion, the average energy is ½ Kb T. The most elegant principle of classical statistical mechanics (first proved by Maxwell) states that this is so for each mode of energy: translational, rotational and vibrational. That is, in equilibrium, the total energy is equally distributed in all possible energy modes, with each mode having an average energy equal to ½ kB T. This is known as the law of equipartition of energy. Accordingly, each translational and rotational degree of freedom of a molecule contributes ½ kB T to the energy, while each vibrational frequency contributes 2 × ½ kB T = kB T, since a vibrational mode has both kinetic and potential energy modes.
1) Boltzmann constant has value of
a) 1.38*10-23 joule per Kelvin.
b) 1.38*10-28 joule per Kelvin.
c) 1.38*10-30 joule per Kelvin.
d) None of these
2) SI unit of Boltzmann constant is given by
a) Joules per meter
b) Joules per Kelvin
c) Joules per Newton
d) None of these
3) According to kinetic theory give formula for pressure of idea gas.
4) According to kinetic theory what is average kinetic energy of molecules of ideal gas ?
5) What is law of equipartition of energy ?
Answer key – 2
1) a
2) b
3) According to kinetic theory of gases pressure is given by P = 1/3 nmv2 Where, n is number of molecules per unit volume, m is mass and v2 is mean squared speed. Though we choose the container to be a cube, the shape of the vessel really is immaterial.
4) The average kinetic energy of a molecule is proportional to the absolute temperature of the gas; it is independent of pressure, volume or the nature of the ideal gas and given by E = 3/2 kbT.
Where kb is Boltzmann constant having value of 1.38*10-23 joule per Kelvin.
5) We know that for each translational mode of motion, the average energy is ½ Kb T. classical statistical mechanics states that in equilibrium, the total energy is equally distributed in all possible energy modes, with each mode having an average energy equal to ½ kBT. This is known as the law of equipartition of energy. Accordingly, each translational and rotational degree of freedom of a molecule contributes ½ kBT to the energy, while each vibrational frequency contributes 2 × ½ kB T = kBT, since a vibrational mode has both kinetic and potential energy modes.
Case Study – 3
SPECIFIC HEAT CAPACITY
Monatomic Gases: The molecule of a monatomic gas has only three translational degrees of freedom. Thus, the average energy of a molecule at temperature T is (3/2) kBT. The total internal energy of a mole of such a gas is U = (3/2) RT.
The molar specific heat at constant volume cv is given by
Cv = dU/dT = (3/2) R
For an ideal gas,
Cp – Cv = R
Where Cp is the molar specific heat at constant pressure. Thus, CP= (5/2) R
The ratio of specific heats IS γ= cp/cv = 5/3.
Diatomic Gases: a diatomic molecule treated as a rigid rotator, like a dumbbell, has 5 degrees of freedom: 3 translational and 2 rotational. Using the law of equipartition of energy, the total internal energy of a mole of such a gas is U = (5/2) RT.
The molar specific heat at constant volume cv is given by
Cv = dU/dT = (5/2) R
For an ideal gas,
Cp – Cv = R
Where Cp is the molar specific heat at constant pressure. Thus, CP= (7/2) R
The ratio of specific heats IS γ( for rigid diatomic)= cp/cv = 7/5.
For non rigid diatomic molecules they have additional mode of vibrations therefore
γ= cp/cv = 9/7
Polyatomic Gases: In general a polyatomic molecule has 3 translational, 3 rotational degrees of freedom and a certain number ( f ) of vibrational modes. According to the law of equipartition of energy, it is easily seen that one mole of such a gas has
Cv= (3+f) R and Cp= (4+f) R and γ= (4+f)/ (3+f).
1) For monatomic molecules ratio of specific heats is γ
a) 5/3
b) 7/5
c) 9/5
d) None of these
2) For diatomic rigid molecules ratio of specific heats is γ
a) 5/3
b) 7/5
c) 9/7
d) None of these
3) For diatomic non rigid molecules ratio of specific heats is γ
- 5/3
- 7/5
- 9/7
- None of these
4) Give cp and cv values and ratio of specific heat for monatomic gas molecules.
5) Give cp and cv values and ratio of specific heat for polyatomic gas molecules
Answer key – 3
1) a
2) b
3) c
4) Monatomic Gases: The molecule of a monatomic gas has only three translational degrees of freedom. Thus, the average energy of a molecule at temperature T is (3/2) kBT. The total internal energy of a mole of such a gas is U = (3/2) RT.
The molar specific heat at constant volume cv is given by
Cv = dU/dT = (3/2) R
For an ideal gas,
Cp – Cv = R
Where Cp is the molar specific heat at constant pressure. Thus, CP= (5/2) R
The ratio of specific heats IS γ= cp/cv = 5/3.
Polyatomic Gases: In general a polyatomic molecule has 3 translational, 3 rotational degrees of freedom and a certain number ( f ) of vibrational modes. According to the law of equipartition of energy, it is easily seen that one mole of such a gas has
Cv= (3+f) R and Cp= (4+f) R and γ= (4+f)/ (3+f).
Class 11 Physics Kinetic Theory