Tag: behaviour of perfect gas and kinetic theory of gases

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

The speed of a longitudinal wave in a mixture containing 4 moles of He and 1 mole of Ne at 300 K 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. 930 m/s

  2. 541 m/s

  3. 498 m/s

  4. None of these

Show answer
Correct Option: A
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
$v=\sqrt {\dfrac {vRT}{M'}}=\sqrt {\dfrac {5}{3}\times \dfrac {8.3\times 300}{4.8\times 10^{-3}}}\sim 929.83\ m/s$


$2$ 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.

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. $2$ grams/mole

  2. $16$ grams/mole

  3. $4$ grams/mole

  4. $32$ grams/mole

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Correct Option: C

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.

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. 2.15

  2. 3.75

  3. 5.25

  4. 6.35

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Correct Option: B

When an ideal monoatomic  gas is heated zt constant pressure , which of the following may be true

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. $\dfrac {dU}{dQ} = \frac {3}{5}$

  2. $\dfrac {dW}{dQ} = \frac {2]}{5}$

  3. $\dfrac {dU}{dQ} = \frac {4}{5}$

  4. $dW + dU = dQ $

Show answer
Correct Option: D

If $\gamma $ be the ration of specific heats of a perfect gas, the number of degree of freedom of a molecule of the gas 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. $\dfrac{{25}}{2}\left( {\gamma - 1} \right)$

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

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

  4. $\dfrac{9}{2}(\gamma - 1)$

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Correct Option: C

The degree of freedom of a diatomic gas at normal temperature 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. $7$

  2. $6$

  3. $5$

  4. $4$

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Correct Option: C

The magnetic monment of a diamagnetic atom 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. Much greater than one

  2. 1

  3. Between zero and one

  4. Equal to zero

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Correct Option: D

On increasing temperature of the reacting system by $10$ degrees the rate of reaction almost doubles. The most appropriate reason for this 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. collision frequency increases

  2. activation energy decreases by increases in temperatuer

  3. the fraction of molecules having energy equal to threshold energy or more increase

  4. the value of threshold energy decreases

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Correct Option: A

An ant is walking on the horizontal surface. The number of degree of freedom of 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: C

n moles of an ideal monoatomic gas undergoes an isothermal expansion at temperature T during which its volume becomes 4 times. The work done on the gas and change in internal energy of the gas respectively 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. n RT Ln 4,0

    • n RT Ln 4,0

  3. n RT Ln 4 $\frac { 3 n R T } { 2 }$

    • n RT Ln 4, $\frac { 3 n R T } { 2 }$
Show answer
Correct Option: A
Explanation:

$\begin{array}{l} w=nRT\, \, \, \ln { \left( { \frac { { 4v } }{ v }  } \right)  }  \ =nRT\, \, \ln { 4 } \, \, \, \, \, \, & \, \, \, \Delta u=0 \end{array}$

$\therefore$ Option $A$ is correct.