Test: Law of Equipartition of Energy


10 Questions MCQ Test Physics Class 11 | Test: Law of Equipartition of Energy


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QUESTION: 1

How many degrees of freedom do non linear triatomic gas molecules has?

Solution:

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.

QUESTION: 2

If a gas has n degree of freedom, ratio of principal specific heats of the gas is

Solution:

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​)

QUESTION: 3

 O2  is a __________ molecule , and has __________ translational degrees of freedom

Solution:

Oxygen molecule is a diatomic molecule and  has 3 translational and 2 rotational degrees of freedom

QUESTION: 4

What is law of equipartition of energy?

Solution:

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.

QUESTION: 5

The degree of freedom for diatomic gas is:

Solution:

For monoatomic gas degrees of freedom are 3, while for diatomic gas is it 5, and for triatomic gas it is 7.

QUESTION: 6

1calorie = ?

Solution:

1 calorie = 4.184 joules. That is the conversion rate, no explanation.

QUESTION: 7

The degree of freedom for tri atomic gas is:

Solution:

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).

QUESTION: 8

On which of the following factors, does the average kinetic energy of gas molecules depend?

Solution:

The average K.E. of gas molecules depends only on the absolute temperature of the gas and is directly proportional to it.

QUESTION: 9

The mean free path is the ____________

Solution:
QUESTION: 10

The average distance a molecule can travel without colliding is called

Solution:

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.

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