Tag: law of equipartition of energy

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Questions Related to law of equipartition of energy

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 de-Broglie wavelength of a particle accelerated with $150\ volt$ potential is $10^{-10}\ m$. If it accelerated by $600\ volts$ p.d. its wavelength will be

  1. $0.25\ A^{o}$

  2. $0. 5\ A^{o}$

  3. $1.5\ A^{o}$

  4. $2\ A^{o}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given,

$\lambda =\dfrac{hc}{eV}\ \ \ \ where,\ V=potential$

$\lambda \ \alpha \ \dfrac{1}{V}$

${{10}^{-10}}\ \alpha \ \dfrac{1}{150}\ ......\ (1)$

$\lambda \ \alpha \ \dfrac{1}{600}\ ......\ (2)$

Divide (2) by (1)

$ \dfrac{\lambda }{{{10}^{-10}}}=\dfrac{150}{600}=\dfrac{1}{4} $

$ \Rightarrow \lambda =0.25\times {{10}^{-10}}m\ =0.25\ {{A}^{o}} $ 

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

Three particles are situated on a light and rigid rod along Y-axis as shown in the figure. If the system is rotating with angular velocity of $2 rad/sec$ about X axis, then the total kinetic energy of the system is :

  1. $92 J $

  2. $184 J $

  3. $ 276 J $

  4. $46 J $
Reveal answer Fill a bubble to check yourself
A Correct answer
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 gas has molar heat capacity $C = 4.5\ R$ in the process $PT = constant$. Find the number of degrees of freedom (n) of molecules in the gas.

  1. $n = 7$

  2. $n = 3$

  3. $n = 5$

  4. $n = 2$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For a process PT = constant, P * (PV/nR) = constant, so P^2 * V = constant. This is a polytropic process PV^x = constant with x = 1/2. Molar heat capacity C = R/(gamma-1) + R/(1-x). 4.5R = R/(2/f) + R/(1-0.5) = fR/2 + 2R. 4.5 = f/2 + 2, so f/2 = 2.5, f = 5.

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 degrees of freedom of a triatomic gas is? (consider moderate temperature)

  1. $6$

  2. $4$

  3. $2$

  4. $8$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The general epression for degree of freedom is $DOF=3N-n$

here, DOF means degree of freedom, N is number of particle, and n is the number of holonomic constraints.
for a triatomic molecule, the number of particle is 3 and since the separation between three atoms are fixed so, the number of constraints is 3.
hence, $DOF=(3\times 3)-3$
$DOF=9-3$
$DOF=6$

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 vessel contains a non-linear triatomic gas. If $50$% of gas dissociate into individual atom, then find new value of degree of freedom by ignoring the vibrational mode and any further dissociation 

  1. $2.15$

  2. $3.75$

  3. $5.25$

  4. $6.35$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let's assume we have $1$ mole of triatomic gas

$\therefore 3Na$ is present
So, $0.5$ moles= $1.5 Na$ atoms
$1$ part of $0.5$ moles remains untouched
Degree of dissociation= $0.5 \times 6=3$
Degree of freedom for $0.5Na= 1.5 \times 0.5=0.75$
Total=$3+0.75=3.75$

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

For gas, if the ratio of specific heats at constants pressure $P$ and constant volume $V$ is $\gamma $, then the value of degree of freedom is:

  1. $\dfrac{\gamma +1}{\gamma -1}$

  2. $\dfrac{\gamma -1}{\gamma +1}$

  3. $\dfrac{1}{2}(\gamma-1)$

  4. $\dfrac{2}{\gamma-1}$
Reveal answer Fill a bubble to check yourself
A Correct answer
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 speed of a longitudinal wave in a mixture containing 4 moles of He and 1 mole of Ne at 300 K will be

  1. 930 m/s

  2. 541 m/s

  3. 498 m/s

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
The mixture contains $n _1=4\ mol$ of $He$ and $n _2=4\ mole$ of $Ne$ act. $T=300\ K$.
Forth $He$ and $Ne$ are monoatomic, so we take $r$ mix $=5/3\quad \left [r=\dfrac {cp}{cv}\right]$ 
$M'=\dfrac {M _1n _1+M _2n _2}{n _1+n _2}$
$=\dfrac {4\times 4+20\times 1}{4+1}=\dfrac {24}{5}=4.8\ g/mol$
$=4.8\times 10^{-3}\ kg/mol$
$\therefore \ $ Speed of sound through mixture
$v=\sqrt {\dfrac {vRT}{M'}}=\sqrt {\dfrac {5}{3}\times \dfrac {8.3\times 300}{4.8\times 10^{-3}}}\sim 929.83\ m/s$


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

$2$ grams of mono atomic gas occupies a volume of $2$ litres at a pressure of $8.3 \times 10^5$ Pa and $127^0C$. Find the molecular weight of the gas.

  1. $2$ grams/mole

  2. $16$ grams/mole

  3. $4$ grams/mole

  4. $32$ grams/mole
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Using PV = (m/M)RT, where m=2g, P=8.3e5 Pa, V=2e-3 m^3, T=400K, R=8.314. M = mRT/PV = (2 * 8.314 * 400) / (8.3e5 * 2e-3) = 6651.2 / 1660 = 4.006 g/mol.

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 vessel contains a non-linear triatomic gas. If $50$% of gas dissociate into individual atom, then find new value of degree of freedom by ignoring the vibrational mode and any further dissociation.

  1. 2.15

  2. 3.75

  3. 5.25

  4. 6.35
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Non-linear triatomic gas has f=6. If 50% dissociates into 3 atoms, the new mixture has 0.5 moles of triatomic (f=6) and 0.5 * 3 = 1.5 moles of monatomic (f=3). Average f = (0.5*6 + 1.5*3) / (0.5 + 1.5) = (3 + 4.5) / 2 = 7.5 / 2 = 3.75.