Tag: behavior of perfect gas and kinetic theory

Questions Related to behavior of perfect gas and kinetic theory

Hydrogen is a diatomic gas. Its molar specific heat at constant volume is very nearly

  1. $\frac { 3 R } { 2 }$

  2. $\frac { 5 R } { 2 }$

  3. $\frac { 7 R } { 2 }$

  4. (b) or (c) depending on the temperature.


Correct Option: D

$T _1$ is the temperature of oxygen enclosed in a cylinder. The temperature is increased to $T _2$ and Maxwellan distribution curves for $O _2$ at temperature $T _1$ and $T _2$ are plotted. If $A _1$ and $A _2$ are the areas under the curves and the speed axis, in both cases , then 

  1. $A _1 > A _2$

  2. $A _1 < A _2$

  3. A_1 = A_2$

  4. $A _1=\sqrt {A _2}$


Correct Option: A

let A and B the two gases and given :
$\frac{{T} _{A}}{{M} _{A}}$ = 4. $\frac{{T} _{B}}{{M} _{B}}$  Where T is the temperature and M is molecular mass. If ${C} _{A}$ and  ${C} _{B}$ are the r.m.s. speed, then the ratio $\frac{{C} _{A}}{{C} _{B}}$ will be equal to:

  1. 2

  2. 4

  3. 1

  4. 0.5


Correct Option: A

A mixture of ideal gases 7 kg of nitrogen and 11 Kg of $ CO _2 $ then (Take $\gamma$ for nitrogen and $CO _2$ as 1.4 and 1.3 respectively)

  1. Equivalent molecular weight of the mixture is 36.

  2. Equivalent molecular weight of the mixture is 18.

  3. $ \gamma $ for the mixture is 5/2

  4. $ \gamma $ for the mixture is 47/35


Correct Option: A,D

$3$ mole of gas ''X"  and $2$ moles of gas "Y" enters from end "P" and "Q" of the cylinder respectively. The cylinder has the area of cross section , shown as
under 
The length of the cylinder is $150cm$. The gas "X" intermixes with gas "Y" at the point . If the molecular weight of the gases X and Y is $20$ and $80$ respectively, then what will be the distance of point A from Q?

  1. $75cm$

  2. $50cm$

  3. $37.5$

  4. $90cm$


Correct Option: B
Explanation:

$\begin{array}{l} \frac { { rx } }{ { ry } } =\frac { { { w _{ x } } } }{ { { n _{ y } } } } \sqrt { \frac { { { M _{ y } } } }{ { { M _{ x } } } }  }  \ =\frac { 3 }{ 2 } \sqrt { \frac { { 80 } }{ { 20 } }  } =\frac { 3 }{ 1 } =3:1 \ \therefore \frac { { dis\tan  ce\, \, travelled\, \, by\, \, gas\, \, X } }{ { dis\tan  ce\, \, travelled\, \, by\, \, gas\, \, Y } } =3:1 \ \therefore dis\tan  ce\, \, of\, \, A\, \, from\, \, Q=\frac { { 150 } }{ 3 } =50\, \, cms \end{array}$

Hence, OPtion $B$ is correct.

The lowest pressure(the best Vaccum) that can be created in laboratory at 27 degree is $10^{-11} $ mm of Hg. At this pressure, the number of ideal gass molecules per $cm^{3}$ will be

  1. $3.22 \times 10 ^{12} $

  2. $1.61 \times 10 ^{12} $

  3. $3.21 \times 10 ^{6} $

  4. $3.22 \times 10 ^{5} $


Correct Option: A

If $P=10^6kT$, then the number of molecules per unit volume of the gas is:

  1. 1

  2. $10^2$

  3. $10^3$

  4. $10^6$


Correct Option: D

A sample of gas is at $0^{\circ}C$. To what temperature must it be raised in order to double the rms speed of its molecules?

  1. $102^{\circ}C$

  2. $273^{\circ}C$

  3. $819^{\circ}C$

  4. $1092^{\circ}C$


Correct Option: C

One mole of gas occupies 10 ml at 50 mm pressure. The volume of 3 moles of the gas at 100 mm pressure and same temperature is 

  1. 15 ml

  2. 100 ml

  3. 200 ml

  4. 500 ml


Correct Option: A

2 moles of an ideal monoatomic gas at temperature $T _0$ is mixed wth 4 moles of another ideal monoatomic gas at temperature $2T _0$ then  the temperature of the mixture is:

  1. $\frac{5}{3} T _0$

  2. $\frac{3}{2} T _0$

  3. $\frac{4}{3} T _0$

  4. $\frac{5}{4} T _0$


Correct Option: A