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

139278 An ideal gas has pressure $P$ and the kinetic energy of the unit volume of the gas is $E$. $P$ and $E$ are related as:

1 $\mathrm{P}=\mathrm{E}$
2 $P=\frac{2}{3} E$
3 $P=\frac{E}{2}$
4 $P=\frac{2}{5} E$
Kinetic Theory of Gases

139189 The r.m.s. speed of oxygen molecule in a gas is ' $u$ '. If the temperature is doubled and the molecules dissociate into two atoms, the r.m.s. speed will be

1 $4 \mathrm{u}$
2 $\mathrm{u} \sqrt{2}$
3 $2 \mathrm{u}$
4 $\mathrm{u}$
Kinetic Theory of Gases

139197 Three closed vessels $A, B$ and $C$ are at the same temperature $T$ and contain gases. Vessel $A$ contains only $\mathrm{O}_{2}$, B contains only $\mathrm{N}_{2}$ and $\mathrm{C}$ contains a mixture of equal quantities of $\mathrm{O}_{2}$ and $\mathrm{N}_{2}$. If the rms speed of $\mathrm{O}_{2}$ molecules in Vessel $A$ is $v_{1}$ and that of $N_{2}$ molecules in vessel $B$ is $v_{2}$ then the rms speed of $\mathrm{O}_{2}$ molecules in vessel $C$ is

1 $\left(\frac{\mathrm{v}_{1}+\mathrm{v}_{2}}{2}\right)$
2 $\mathrm{v}_{1}$
3 $\left(\mathrm{v}_{1} \mathrm{v}_{2}\right)$
4 $\frac{\mathrm{v}_{1}}{2}$
Kinetic Theory of Gases

139203 The temperature of an ideal gas is increased from $100 \mathrm{~K}$ to $400 \mathrm{~K}$. If the rms speed of the gas molecule is $v$ at $100 \mathrm{~K}$, then at $400 \mathrm{~K}$ it becomes

1 $2 \mathrm{v}$
2 $4 \mathrm{v}$
3 $0.5 \mathrm{v}$
4 $0.25 \mathrm{v}$
5 $\mathrm{v}$
Kinetic Theory of Gases

139278 An ideal gas has pressure $P$ and the kinetic energy of the unit volume of the gas is $E$. $P$ and $E$ are related as:

1 $\mathrm{P}=\mathrm{E}$
2 $P=\frac{2}{3} E$
3 $P=\frac{E}{2}$
4 $P=\frac{2}{5} E$
Kinetic Theory of Gases

139189 The r.m.s. speed of oxygen molecule in a gas is ' $u$ '. If the temperature is doubled and the molecules dissociate into two atoms, the r.m.s. speed will be

1 $4 \mathrm{u}$
2 $\mathrm{u} \sqrt{2}$
3 $2 \mathrm{u}$
4 $\mathrm{u}$
Kinetic Theory of Gases

139197 Three closed vessels $A, B$ and $C$ are at the same temperature $T$ and contain gases. Vessel $A$ contains only $\mathrm{O}_{2}$, B contains only $\mathrm{N}_{2}$ and $\mathrm{C}$ contains a mixture of equal quantities of $\mathrm{O}_{2}$ and $\mathrm{N}_{2}$. If the rms speed of $\mathrm{O}_{2}$ molecules in Vessel $A$ is $v_{1}$ and that of $N_{2}$ molecules in vessel $B$ is $v_{2}$ then the rms speed of $\mathrm{O}_{2}$ molecules in vessel $C$ is

1 $\left(\frac{\mathrm{v}_{1}+\mathrm{v}_{2}}{2}\right)$
2 $\mathrm{v}_{1}$
3 $\left(\mathrm{v}_{1} \mathrm{v}_{2}\right)$
4 $\frac{\mathrm{v}_{1}}{2}$
Kinetic Theory of Gases

139203 The temperature of an ideal gas is increased from $100 \mathrm{~K}$ to $400 \mathrm{~K}$. If the rms speed of the gas molecule is $v$ at $100 \mathrm{~K}$, then at $400 \mathrm{~K}$ it becomes

1 $2 \mathrm{v}$
2 $4 \mathrm{v}$
3 $0.5 \mathrm{v}$
4 $0.25 \mathrm{v}$
5 $\mathrm{v}$
Kinetic Theory of Gases

139278 An ideal gas has pressure $P$ and the kinetic energy of the unit volume of the gas is $E$. $P$ and $E$ are related as:

1 $\mathrm{P}=\mathrm{E}$
2 $P=\frac{2}{3} E$
3 $P=\frac{E}{2}$
4 $P=\frac{2}{5} E$
Kinetic Theory of Gases

139189 The r.m.s. speed of oxygen molecule in a gas is ' $u$ '. If the temperature is doubled and the molecules dissociate into two atoms, the r.m.s. speed will be

1 $4 \mathrm{u}$
2 $\mathrm{u} \sqrt{2}$
3 $2 \mathrm{u}$
4 $\mathrm{u}$
Kinetic Theory of Gases

139197 Three closed vessels $A, B$ and $C$ are at the same temperature $T$ and contain gases. Vessel $A$ contains only $\mathrm{O}_{2}$, B contains only $\mathrm{N}_{2}$ and $\mathrm{C}$ contains a mixture of equal quantities of $\mathrm{O}_{2}$ and $\mathrm{N}_{2}$. If the rms speed of $\mathrm{O}_{2}$ molecules in Vessel $A$ is $v_{1}$ and that of $N_{2}$ molecules in vessel $B$ is $v_{2}$ then the rms speed of $\mathrm{O}_{2}$ molecules in vessel $C$ is

1 $\left(\frac{\mathrm{v}_{1}+\mathrm{v}_{2}}{2}\right)$
2 $\mathrm{v}_{1}$
3 $\left(\mathrm{v}_{1} \mathrm{v}_{2}\right)$
4 $\frac{\mathrm{v}_{1}}{2}$
Kinetic Theory of Gases

139203 The temperature of an ideal gas is increased from $100 \mathrm{~K}$ to $400 \mathrm{~K}$. If the rms speed of the gas molecule is $v$ at $100 \mathrm{~K}$, then at $400 \mathrm{~K}$ it becomes

1 $2 \mathrm{v}$
2 $4 \mathrm{v}$
3 $0.5 \mathrm{v}$
4 $0.25 \mathrm{v}$
5 $\mathrm{v}$
Kinetic Theory of Gases

139278 An ideal gas has pressure $P$ and the kinetic energy of the unit volume of the gas is $E$. $P$ and $E$ are related as:

1 $\mathrm{P}=\mathrm{E}$
2 $P=\frac{2}{3} E$
3 $P=\frac{E}{2}$
4 $P=\frac{2}{5} E$
Kinetic Theory of Gases

139189 The r.m.s. speed of oxygen molecule in a gas is ' $u$ '. If the temperature is doubled and the molecules dissociate into two atoms, the r.m.s. speed will be

1 $4 \mathrm{u}$
2 $\mathrm{u} \sqrt{2}$
3 $2 \mathrm{u}$
4 $\mathrm{u}$
Kinetic Theory of Gases

139197 Three closed vessels $A, B$ and $C$ are at the same temperature $T$ and contain gases. Vessel $A$ contains only $\mathrm{O}_{2}$, B contains only $\mathrm{N}_{2}$ and $\mathrm{C}$ contains a mixture of equal quantities of $\mathrm{O}_{2}$ and $\mathrm{N}_{2}$. If the rms speed of $\mathrm{O}_{2}$ molecules in Vessel $A$ is $v_{1}$ and that of $N_{2}$ molecules in vessel $B$ is $v_{2}$ then the rms speed of $\mathrm{O}_{2}$ molecules in vessel $C$ is

1 $\left(\frac{\mathrm{v}_{1}+\mathrm{v}_{2}}{2}\right)$
2 $\mathrm{v}_{1}$
3 $\left(\mathrm{v}_{1} \mathrm{v}_{2}\right)$
4 $\frac{\mathrm{v}_{1}}{2}$
Kinetic Theory of Gases

139203 The temperature of an ideal gas is increased from $100 \mathrm{~K}$ to $400 \mathrm{~K}$. If the rms speed of the gas molecule is $v$ at $100 \mathrm{~K}$, then at $400 \mathrm{~K}$ it becomes

1 $2 \mathrm{v}$
2 $4 \mathrm{v}$
3 $0.5 \mathrm{v}$
4 $0.25 \mathrm{v}$
5 $\mathrm{v}$