Tag: behaviour of perfect gas and kinetic theory of gases

Quizzes (2) Questions (105)

Questions Related to behaviour of perfect gas and kinetic theory of gases

Multiple choice physics behaviour of perfect gas and kinetic theory of gases degree of freedom: law of equipartition of energy law of equipartition of energy law of equipartition of energy and mean free path

A man is climbing up a spiral type staircase. His degrees of freedom are :

  1. 1

  2. 2

  3. 3

  4. more than 3
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

There will be three degrees of freedom. Two are along x-direction and y-directions due to translation and the last degree of freedom due to angular rotation as the  man climbs up.

Hence, Option C is correct.

Multiple choice physics behaviour of perfect gas and kinetic theory of gases degree of freedom: law of equipartition of energy law of equipartition of energy law of equipartition of energy and mean free path

A system consists of N particles, which have independent K relations among one another. The number of degrees of freedom of the system is given by :

  1. 3 NK

  2. N/3K

  3. 3 N/K

  4. 3N - K
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For a system of N particles having K independent relations among them, the degrees of freedom of the system is given by 3N-K. 3N  is due to three degrees of freedom associated with each particle if all the particles are independent of each other (i.e K=0) and due to K relation among them, degrees of freedom reduces to 3N-K

Hence, Option D is correct.

Multiple choice physics behaviour of perfect gas and kinetic theory of gases degree of freedom: law of equipartition of energy law of equipartition of energy law of equipartition of energy and mean free path

The correct relation connecting the universal gas constant (R), Avogadro number N$ _A$ and Boltzmann constant (K) is :

  1. $R = NK^2$

  2. $K = NR$

  3. $N = RK$

  4. $R=NK$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Units of R, N and K are $ Joule \times mole^{-1} \times K^{-1} $, $ mole^{-1} $ and $Joule \times  K^{-1}$
So $ R = N \times K $

Multiple choice physics behaviour of perfect gas and kinetic theory of gases degree of freedom: law of equipartition of energy law of equipartition of energy law of equipartition of energy and mean free path

A circular disc of mass $m$ and radius $r$ is rolling about its axis with a constant speed $v$. Its kinetic energy is 

  1. $\cfrac{1}{4}mv^2$

  2. $\cfrac{1}{2}mv^2$

  3. $\cfrac{3}{4}mv^2$

  4. $mv^2$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total kinetic energy = translational KE + rotational KE. For a rolling disc, K = (1/2)mv^2 + (1/2)I(omega^2). With I = (1/2)mr^2 and v = r*omega, K = (1/2)mv^2 + (1/2)(1/2)mr^2(v^2/r^2) = (1/2)mv^2 + (1/4)mv^2 = (3/4)mv^2.

Multiple choice physics behaviour of perfect gas and kinetic theory of gases degree of freedom: law of equipartition of energy law of equipartition of energy law of equipartition of energy and mean free path

The internal energy of a gas:

  1. is the sum total of kinetic and potential energies.

  2. is the total transitional kinetic energies

  3. is the total kinetic energy of randomly moving molecules.

  4. is the total kinetic energy of gas molecules
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

At a given temperature, the pressure of a container is determined by the number of times gas molecules strike the container walls. If the gas is compressed to a smaller volume, then the same number of molecules will strike against a smaller surface area; the number of collisions against the container will increase, and, by extension, the pressure will increase as well.
Increasing the kinetic energy of the particles will increase the pressure of the gas.
So, the internal energy of a gas Is the total kinetic energy of randomly moving molecules.
Hence, option C is correct.

Multiple choice physics behaviour of perfect gas and kinetic theory of gases degree of freedom: law of equipartition of energy law of equipartition of energy law of equipartition of energy and mean free path

State whether true or false:

Linear molecules have $3N-5$ vibrational degrees of freedom, whereas non linear molecules have $3N-6$ vibrational degrees of freedom, where N is no. of atoms present in a molecule.

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Vibrational degree of freedom:
(a) For linear molecule = 3N - 5.
(b) For non-linear molecule = 3N - 6. where N is no. of atoms present in a molecule.

Multiple choice physics behaviour of perfect gas and kinetic theory of gases degree of freedom: law of equipartition of energy law of equipartition of energy law of equipartition of energy and mean free path

To find out degree of freedom, the correct expression is :

  1. $f=\dfrac { 2 }{ \gamma -1 }$

  2. $f=\dfrac { \gamma +1 }{ 2 }$

  3. $f=\dfrac { 2 }{ \gamma +1 }$

  4. $f=\dfrac { 1 }{ \gamma +1 }$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\because \gamma =1+\dfrac { 2 }{ f } $
$\Longrightarrow \dfrac { 2 }{ f } =\gamma -1\Longrightarrow f=\dfrac { 2 }{ \gamma -1 } $