Tag: degree of freedom: law of equipartition of energy

Questions Related to degree of freedom: law of equipartition of energy

How many degrees of freedom the gas molecules have if under STP the gas density $\rho = 1.3 kg/m^3$ and the velocity of sound propagation in it is $330 ms^{-1}$?

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

  1. $3$

  2. $5$

  3. $7$

  4. $8$

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Correct Option: B

At room temperature (27$^0$ C) the rms speed of the moleculesof certain diatomic gas is found to be 1920 ms$^{-1}$ then the molecule is:

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

  1. $H _2$

  2. $F _2$

  3. $O _2$

  4. $Cl _2$

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Correct Option: A
Explanation:
Let the room temperature is $T = 27^0C=27+273=300K$
Now, $V _{rms}=\sqrt{\dfrac{3RT}{m}}$
$\Rightarrow M=\dfrac{3RT}{V _{rms}^2}$
By putting the value we get,
$M=\dfrac{3\times8.314\times300}{1920^2}=2\times10^{-3}kg=2g$
Thus, it is an Hydrogen.

If temperature of body increases by 10%, then increase in radiated energy of the body is :

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

  1. 10 %

  2. 40 %

  3. 46 %

  4. 1000 %

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Correct Option: C

The law of equipartition of energy was given by :

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

  1. Claussius

  2. Maxwell

  3. Boltzmann

  4. Carnot

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Correct Option: A
Explanation:

The law is given by Claussius which states that for any dynamical system in a thermal equilibrium, the total energy is equally divided among the degrees of freedom.

The value of $\gamma$ for gas X is 1.66, then x is :

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

  1. Ne

  2. O$ _3$

  3. N$ _2$

  4. H$ _2$

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Correct Option: A
Explanation:

Given that value of gamma is 1.66 i.e $\dfrac{5}{3}$ which implies that it is a monoatomic gas, and Neon (Ne) is the only monoatomic gas among the given options.

An ant is moving on a plane horizontal surface. The number of degrees of freedom of the ant will be

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

  1. 1

  2. 2

  3. 3

  4. 6

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Correct Option: B

Gas exerts pressure on the walls of container because the molecules-

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

  1. Are loosing the kinetic energy

  2. Are getting stuck to the walls

  3. Are transferring their momentum to walls

  4. Are accelerated toward walls.

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Correct Option: C
Explanation:

Gas molecules are in random motion having some momentum and while colliding with the walls they transfer their momentum to the walls and this collective transfer of momentum from all the molecules to the walls appears as pressure exerted by gas on the container wall.

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

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

  1. 1

  2. 2

  3. 3

  4. more than 3

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Correct Option: C
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.

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 :

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

  1. 3 NK

  2. N/3K

  3. 3 N/K

  4. 3N - K

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Correct Option: D
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.

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

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

  1. $R = NK^2$

  2. $K = NR$

  3. $N = RK$

  4. $R=NK$

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Correct Option: D
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 $