Degree of Freedom, Various speeds of Gas Molecules
Kinetic Theory of Gases

139164 The average energy per mole of an ideal gas of number of degrees of freedom equal to $n$ at temperature $T$ is
#[Qdiff: Hard, QCat: Numerical Based, examname: AP EAMCET-23.09.2020,Shift-II#

1 $\frac{R T}{2 n}$
2 nRT
3 $\frac{2 R T}{n}$
4 $\frac{\mathrm{nRT}}{2}$
Kinetic Theory of Gases

139184 Mass of each molecule of gas ' $A$ ' containing ' $N$ ' molecules is ' $m$ ' and mass of each molecule of gas ' $\mathrm{B}$ ' containing ' $2 \mathrm{~N}$ ' molecules is ' $2 \mathrm{~m}$ '. These two gases are contained in a vessel which is maintained at a temperature $T$. The mean square velocity of the molecules of gas $B$ is denoted by ' $V^{2}$ ' and the mean square $X$ component of the velocity of gas $A$ is denoted by ' $w^{2}$ '. The value of $\frac{w^{2}}{v^{2}}$ is
#[Qdiff: Hard, QCat: Numerical Based, examname: AP EAMCET-24.04.2019,Shift-II#

1 $\frac{4}{3}$
2 $\frac{2}{3}$
3 $\frac{1}{3}$
4 $\frac{3}{4}$
Kinetic Theory of Gases

139186 The molecules of a monoatomic gas has r.m.s. speed $v$ at $27^{\circ} \mathrm{C}$. It is heated until the r.m.s. speed becomes $2 \mathrm{v}$. What is the new temperature?
#[Qdiff: Medium, QCat: Theory Based, examname: TS EAMCET 08.05.2019,Shift-II#

1 $1200 \mathrm{~K}$
2 $600 \mathrm{~K}$
3 $300 \mathrm{~K}$
4 $400 \mathrm{~K}$
Kinetic Theory of Gases

139204 The absolute temperature at which the rms speed of a hydrogen molecule is equal to its escape speed from the moon's surface is (where, $R$ is radius of moon, $g$ is acceleration due to gravity on Moon's surface, $m$ is mass of hydrogen molecules and $k$ is Boltzmann constant)
#[Qdiff: Hard, QCat: Numerical Based, examname: AP EAMCET (22.04.2018) Shift-II#

1 $\frac{m g R}{2 k}$
2 $\frac{2 m g R}{k}$
3 $\frac{3 m g R}{2 k}$
4 $\frac{2 m g R}{3 k}$
Kinetic Theory of Gases

139164 The average energy per mole of an ideal gas of number of degrees of freedom equal to $n$ at temperature $T$ is
#[Qdiff: Hard, QCat: Numerical Based, examname: AP EAMCET-23.09.2020,Shift-II#

1 $\frac{R T}{2 n}$
2 nRT
3 $\frac{2 R T}{n}$
4 $\frac{\mathrm{nRT}}{2}$
Kinetic Theory of Gases

139184 Mass of each molecule of gas ' $A$ ' containing ' $N$ ' molecules is ' $m$ ' and mass of each molecule of gas ' $\mathrm{B}$ ' containing ' $2 \mathrm{~N}$ ' molecules is ' $2 \mathrm{~m}$ '. These two gases are contained in a vessel which is maintained at a temperature $T$. The mean square velocity of the molecules of gas $B$ is denoted by ' $V^{2}$ ' and the mean square $X$ component of the velocity of gas $A$ is denoted by ' $w^{2}$ '. The value of $\frac{w^{2}}{v^{2}}$ is
#[Qdiff: Hard, QCat: Numerical Based, examname: AP EAMCET-24.04.2019,Shift-II#

1 $\frac{4}{3}$
2 $\frac{2}{3}$
3 $\frac{1}{3}$
4 $\frac{3}{4}$
Kinetic Theory of Gases

139186 The molecules of a monoatomic gas has r.m.s. speed $v$ at $27^{\circ} \mathrm{C}$. It is heated until the r.m.s. speed becomes $2 \mathrm{v}$. What is the new temperature?
#[Qdiff: Medium, QCat: Theory Based, examname: TS EAMCET 08.05.2019,Shift-II#

1 $1200 \mathrm{~K}$
2 $600 \mathrm{~K}$
3 $300 \mathrm{~K}$
4 $400 \mathrm{~K}$
Kinetic Theory of Gases

139204 The absolute temperature at which the rms speed of a hydrogen molecule is equal to its escape speed from the moon's surface is (where, $R$ is radius of moon, $g$ is acceleration due to gravity on Moon's surface, $m$ is mass of hydrogen molecules and $k$ is Boltzmann constant)
#[Qdiff: Hard, QCat: Numerical Based, examname: AP EAMCET (22.04.2018) Shift-II#

1 $\frac{m g R}{2 k}$
2 $\frac{2 m g R}{k}$
3 $\frac{3 m g R}{2 k}$
4 $\frac{2 m g R}{3 k}$
Kinetic Theory of Gases

139164 The average energy per mole of an ideal gas of number of degrees of freedom equal to $n$ at temperature $T$ is
#[Qdiff: Hard, QCat: Numerical Based, examname: AP EAMCET-23.09.2020,Shift-II#

1 $\frac{R T}{2 n}$
2 nRT
3 $\frac{2 R T}{n}$
4 $\frac{\mathrm{nRT}}{2}$
Kinetic Theory of Gases

139184 Mass of each molecule of gas ' $A$ ' containing ' $N$ ' molecules is ' $m$ ' and mass of each molecule of gas ' $\mathrm{B}$ ' containing ' $2 \mathrm{~N}$ ' molecules is ' $2 \mathrm{~m}$ '. These two gases are contained in a vessel which is maintained at a temperature $T$. The mean square velocity of the molecules of gas $B$ is denoted by ' $V^{2}$ ' and the mean square $X$ component of the velocity of gas $A$ is denoted by ' $w^{2}$ '. The value of $\frac{w^{2}}{v^{2}}$ is
#[Qdiff: Hard, QCat: Numerical Based, examname: AP EAMCET-24.04.2019,Shift-II#

1 $\frac{4}{3}$
2 $\frac{2}{3}$
3 $\frac{1}{3}$
4 $\frac{3}{4}$
Kinetic Theory of Gases

139186 The molecules of a monoatomic gas has r.m.s. speed $v$ at $27^{\circ} \mathrm{C}$. It is heated until the r.m.s. speed becomes $2 \mathrm{v}$. What is the new temperature?
#[Qdiff: Medium, QCat: Theory Based, examname: TS EAMCET 08.05.2019,Shift-II#

1 $1200 \mathrm{~K}$
2 $600 \mathrm{~K}$
3 $300 \mathrm{~K}$
4 $400 \mathrm{~K}$
Kinetic Theory of Gases

139204 The absolute temperature at which the rms speed of a hydrogen molecule is equal to its escape speed from the moon's surface is (where, $R$ is radius of moon, $g$ is acceleration due to gravity on Moon's surface, $m$ is mass of hydrogen molecules and $k$ is Boltzmann constant)
#[Qdiff: Hard, QCat: Numerical Based, examname: AP EAMCET (22.04.2018) Shift-II#

1 $\frac{m g R}{2 k}$
2 $\frac{2 m g R}{k}$
3 $\frac{3 m g R}{2 k}$
4 $\frac{2 m g R}{3 k}$
Kinetic Theory of Gases

139164 The average energy per mole of an ideal gas of number of degrees of freedom equal to $n$ at temperature $T$ is
#[Qdiff: Hard, QCat: Numerical Based, examname: AP EAMCET-23.09.2020,Shift-II#

1 $\frac{R T}{2 n}$
2 nRT
3 $\frac{2 R T}{n}$
4 $\frac{\mathrm{nRT}}{2}$
Kinetic Theory of Gases

139184 Mass of each molecule of gas ' $A$ ' containing ' $N$ ' molecules is ' $m$ ' and mass of each molecule of gas ' $\mathrm{B}$ ' containing ' $2 \mathrm{~N}$ ' molecules is ' $2 \mathrm{~m}$ '. These two gases are contained in a vessel which is maintained at a temperature $T$. The mean square velocity of the molecules of gas $B$ is denoted by ' $V^{2}$ ' and the mean square $X$ component of the velocity of gas $A$ is denoted by ' $w^{2}$ '. The value of $\frac{w^{2}}{v^{2}}$ is
#[Qdiff: Hard, QCat: Numerical Based, examname: AP EAMCET-24.04.2019,Shift-II#

1 $\frac{4}{3}$
2 $\frac{2}{3}$
3 $\frac{1}{3}$
4 $\frac{3}{4}$
Kinetic Theory of Gases

139186 The molecules of a monoatomic gas has r.m.s. speed $v$ at $27^{\circ} \mathrm{C}$. It is heated until the r.m.s. speed becomes $2 \mathrm{v}$. What is the new temperature?
#[Qdiff: Medium, QCat: Theory Based, examname: TS EAMCET 08.05.2019,Shift-II#

1 $1200 \mathrm{~K}$
2 $600 \mathrm{~K}$
3 $300 \mathrm{~K}$
4 $400 \mathrm{~K}$
Kinetic Theory of Gases

139204 The absolute temperature at which the rms speed of a hydrogen molecule is equal to its escape speed from the moon's surface is (where, $R$ is radius of moon, $g$ is acceleration due to gravity on Moon's surface, $m$ is mass of hydrogen molecules and $k$ is Boltzmann constant)
#[Qdiff: Hard, QCat: Numerical Based, examname: AP EAMCET (22.04.2018) Shift-II#

1 $\frac{m g R}{2 k}$
2 $\frac{2 m g R}{k}$
3 $\frac{3 m g R}{2 k}$
4 $\frac{2 m g R}{3 k}$