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All questions of Kinetic Theory for NEET Exam

Oxygen and nitrogen in two enclosures have the same mass, volume and pressure. The ratio of the temperature of oxygen to that of nitrogen is:
  • a)
    8/7
  • b)
    49/64
  • c)
    1
  • d)
    7/8
Correct answer is option 'A'. Can you explain this answer?

Neha Joshi answered
For same mass the ratio of moles of oxygen to that of nitrogen is 14:16 = 7:8
And we know that PV = nRT
Hence as V and P are also same, ratio of temperature of oxygen to that of nitrogen is inverse of the ratio of moles that is 8:7

Three moles of an ideal monoatomic gas is initially in the state A shown in the adjoining pressure-temperature graph. It is taken to state B without changing its pressure. If R is the universal gas constant, the work done by the gas in this process is 
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  • a)
    600 R
  • b)
    400 R
  • c)
    300 R
  • d)
    200 R
Correct answer is option 'A'. Can you explain this answer?

The work done by the gas in taking it from state A to state B = PΔV where ΔW is the increase in volume at constant pressure P. 
We have PV = μRT where p is the number of moles in the sample of the gas and R is the universal gas constant. 
Therefore we have PΔV = μR ΔT = 3 xR(450 - 250) = 600R 

Which one of the following quantities can be zero on an average for the molecules of an ideal gas in equilibrium?
  • a)
    Speed
  • b)
    Momentum
  • c)
    Kinetic Energy
  • d)
    Density
Correct answer is 'B'. Can you explain this answer?

Riya Banerjee answered
In case of ideal gases the average velocity is always zero. Hence the average momentum is zero. 
Whereas average speed is non- zero so the kinetic energy is also non-zero,  as these two are scalar quantities.

The degree of freedom of a molecule of a triatomic ga s is[1999]
  • a)
    2
  • b)
    4
  • c)
    6
  • d)
    8
Correct answer is option 'C'. Can you explain this answer?

Krish Khanna answered
No. of degree of freedom = 3 K – N where K is no. of atom and N is the number of relations between atoms. For triatomic gas, K = 3, N = 3C2 = 3
No. of degree of freedom = 3 (3) – 3 = 6

How many degrees of freedom do non linear triatomic gas molecules has?
  • a)
    two
  • b)
    six
  • c)
    three
  • d)
    five
Correct answer is option 'B'. Can you explain this answer?

Hansa Sharma answered
A triatomic nonlinear gaseous atom has 6 degrees of freedom, that are 3 in all transrational directions and three rotational barriers in all the three axises.

The number of degrees of freedom a diatomic molecule is
  • a)
    6
  • b)
    5.0
  • c)
    3
  • d)
    5.3
Correct answer is option 'D'. Can you explain this answer?

Akshara Chopra answered
Explanation:Degrees of freedom of a system refers to the possible independent motions a system can have.the total degrees of freedom describing the motion of a diatomic molecule is 5.3 for translation and 2 for rotation

Mean free path is the
  • a)
    maximum distance between collisions
  • b)
    minimum distance between collisions
  • c)
    average distance between collisions
  • d)
    (maximum distance + minimum distance )/ 2 between collisions
Correct answer is option 'C'. Can you explain this answer?

Explanation:the mean free path is the average distance traveled by a moving particle (such as an atom, a molecule, a photon) between successive impacts (collisions), which modify its direction or energy or other particle properties.

At absolute zero temperature may be defined as that temperature at which
  • a)
    Volume is maximum
  • b)
    Root mean square velocity of the gas molecule reduces to zero
  • c)
    Temperature is 273 K
  • d)
    Mass of molecules of gas is zero
Correct answer is option 'B'. Can you explain this answer?

Gaurav Kumar answered
At 0K temperature we know that there is no molecular motion, that is the KE of the particles gets 0. Thus we can say the combined KE of a gaseous system is zero, but as there combined mass cant be zero thus the combined of the square of velocities of the particles is zero, which means that the root mean square velocity of the gas is zero.

According to kinetic theory of gases, at absolute zero temperature [1990]
  • a)
    water freezes
  • b)
    liquid helium freezes
  • c)
    molecular motion stops
  • d)
    liquid hydrogen freezes
Correct answer is option 'C'. Can you explain this answer?

See it is assumption only that at absolute zero temperature i.e 0 K temperature all type of molecular motion stopes since at earth it is impossible to achieve 0 K temp so i said it is mearly a assumption only . Though it is clear that all materials freeze at absolute 0 temperature so clearly water, liquid helium and liquid Hydrogen they all freezes . BUT ACCORDING TO THEORY OPTION C SEEMS TO BE MORE ACCURATE.

The degree of freedom for tri atomic gas is:
  • a)
    6
  • b)
    4
  • c)
    5
  • d)
    3
Correct answer is option 'A'. Can you explain this answer?

Hansa Sharma answered
Degrees of freedom are the ways in which a molecule of the gas can execute motion.
So in case of triatomic gas molecule:
1. It can translate (move) in all 3 dimensions, which accounts for 3 degrees of freedom (since there are 3 dimensions in which it could translate (move)).
2. This molecule can also revolve with Moment of Inertia ≠ 0 around all three axes, x, y, and z, which accounts for another 3 degrees of freedom (since there are 3 axes of rotation).

If a gas has n degree of freedom, ratio of principal specific heats of the gas is
  • a)
    1+ 2/n
  • b)
    2n
  • c)
    1 - 2/n
  • d)
    -2n
Correct answer is option 'A'. Can you explain this answer?

Pooja Shah answered
Let us consider 1 mole of an ideal gas at kelvin temperature T. It has N molecules (Avogadro's number). The internal energy of an ideal gas is entirely kinetic. The average KE per molecule of a ideal gas is ½ ​nkT (k is boltzman constant), where n is degree of freedom. Therefore, the internal energy of one mole of a gas would be
 
E=N(1/2​nKT)=1/2​nRT             (∵k=R/N​)
 
Now, Cv​=dE/dT​=n/2 ​R
 
and Cp​=n/2 ​R+R=(n/2​+1)R
 
​Cp/ Cv ​​=​(n/2​+1)R/n/2​=(1+2/n​)

The average distance a molecule can travel without colliding is called
  • a)
    Average distance
  • b)
    Mean free path
  • c)
    Mean drift
  • d)
    Mean distance
Correct answer is option 'B'. Can you explain this answer?

Rajat Patel answered
Mean free path is the average distance between the two successive collisions. Inside the gas there are several molecules which are randomly moving and colliding with each other. The distance which a particular gas molecule travels without colliding is known as mean free path.

When the temperature goes up, the pressure inside a rigid container will _____.
  • a)
    remain unchanged
  • b)
    go down
  • c)
    cause particles to cool
  • d)
    go up
Correct answer is option 'D'. Can you explain this answer?

Vijay Bansal answered
The pressure law states that for a constant volume of gas in a sealed container the temperature of the gas is directly proportional to its pressure. This can be easily understood by visualising the particles of gas in the container moving with a greater energy when the temperature is increased.

Calculate the change in internal energy of 3.00 mol of helium gas when its temperature is increased by 2.00 K.
  • a)
    85.0 J
  • b)
    95.0 J
  • c)
    65.0 J
  • d)
    75.0 J
Correct answer is option 'D'. Can you explain this answer?

Athira Chavan answered
Understanding Internal Energy Change
The internal energy change (ΔU) of an ideal gas can be calculated using the formula:
ΔU = n * C_v * ΔT
Where:
- n = number of moles
- C_v = molar specific heat at constant volume
- ΔT = change in temperature
Parameters for Helium Gas
- Helium is a monoatomic ideal gas.
- For monoatomic gases, C_v is approximately 3/2 R, where R is the ideal gas constant (8.314 J/mol·K).
Calculation Steps
1. Identify Variables:
- n = 3.00 mol (given)
- C_v = (3/2) * R = (3/2) * 8.314 J/mol·K = 12.471 J/mol·K
- ΔT = 2.00 K (given)
2. Plug in Values:
ΔU = n * C_v * ΔT
ΔU = 3.00 mol * 12.471 J/mol·K * 2.00 K
3. Perform the Calculation:
- ΔU = 3.00 * 12.471 * 2.00
- ΔU = 3.00 * 24.942
- ΔU = 74.826 J (approximately 75.0 J)
Conclusion
The calculated change in internal energy for 3.00 mol of helium gas when the temperature is increased by 2.00 K is approximately 75.0 J. Therefore, the correct answer is option 'D', which aligns with the calculated value.

In which case are the atoms relatively rigidly fixed?
  • a)
    gases
  • b)
    liquids and gases
  • c)
    solids
  • d)
    liquids
Correct answer is option 'C'. Can you explain this answer?

Pranav Saha answered
Explanation:
Atoms in a gas are well separated with no regular arrangement. Atoms vibrate and move freely at high speeds
Atoms in a liquid are close together with no regular arrangement. Atoms vibrate, move about, and slide past each other.
Atoms in a solid are tightly packed, usually in a regular pattern. Atoms vibrate (jiggle) but generally do not move from place to place.

According to Atomic Hypothesis: little particles of atom
  • a)
    attract each other when they are at small distance apart, but repel upon being squeezed into one another
  • b)
    repel each other when they are at small distance apart, but attract upon being squeezed into one another
  • c)
    repel each other when they are at small distance apart, but repel upon being squeezed into one another
  • d)
    repel each other when they are at large distance apart, but attract upon being separated from one another
Correct answer is option 'A'. Can you explain this answer?

Saikat Sharma answered
Explanation:At room temperature (=300K) the noble gases are all in the gas phase, they are banging around and colliding into one another like little pool balls. At this temperature, when the atoms collide they appear to elastically bounce off of one another, but this bounce is actually a result of atomic repulsion. The atoms are traveling so fast and they approach each other so quickly that their momentum 'squeezes' them together until the atomic repulsion pushes them back apart.

The average kinetic energy of a molecule in an ideal gas is
  • a)
    proportional to the pressure
  • b)
    depends on the nature of the ideal gas
  • c)
    proportional to the absolute temperature of the gas
  • d)
    proportional to the volume
Correct answer is option 'C'. Can you explain this answer?

Priya Patel answered
SHOW THAT THE AVERAGE TRANSLATIONAL KINETIC ENERGY OF THE MOLECULES OF A GAS IS DIRECTLY PROPORTIONAL TO ABSOLUTE TEMPERATURE. kinetic energy of the molecules of a gas is directly proportional to absolute temperature.

The mean free path is the ____________
  • a)
    average distance covered by a molecule between two successive collisions
  • b)
    length of the container that contains the gas
  • c)
    mean of the square of the average distance between two successive collisions
  • d)
    square of the average distance between two successive collisions
Correct answer is option 'A'. Can you explain this answer?

Anushka Das answered
Mean Free Path
The mean free path is a concept used in physics to describe the average distance traveled by a molecule or particle between two successive collisions. It is an important parameter in the study of gas behavior and is particularly relevant in the kinetic theory of gases.

Definition
The mean free path can be defined as the average distance covered by a molecule between two successive collisions. It represents the average distance a molecule travels before it interacts with another molecule or particle in a gas.

Explanation
To understand why the correct answer is option 'A', let's consider the behavior of gas molecules in a container. The gas molecules are in constant motion, moving in straight lines until they collide with other molecules or the walls of the container.

Each time a molecule collides with another molecule or the walls, its direction and velocity may change. The time it takes for a molecule to collide again depends on its speed and the density of the gas. Molecules with higher speeds will collide more frequently, while molecules in a denser gas will also collide more frequently.

The mean free path is an average value, calculated by considering the total distance covered by all the molecules in a gas and dividing it by the total number of collisions. Since the molecules move in random directions, the actual path of each molecule may be different.

Importance
The mean free path is a fundamental parameter in the kinetic theory of gases and is used to characterize the behavior of gas molecules. It provides valuable information about the average distance traveled by molecules, which is important for understanding diffusion, heat conduction, and other transport phenomena in gases.

Conclusion
In conclusion, the mean free path is the average distance covered by a molecule between two successive collisions. It is an important parameter in the study of gas behavior and helps to describe the motion and interactions of gas molecules. Option 'A' is the correct answer because it accurately defines the mean free path.

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