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

139254 The molecules in an ideal gas at $27^{\circ} \mathrm{C}$ have a certain mean velocity. At what approximate temperature, will the mean velocity be doubled?

1 $54^{\circ} \mathrm{C}$
2 $327^{\circ} \mathrm{C}$
3 $1200^{\circ} \mathrm{C}$
4 $927^{\circ} \mathrm{C}$
Kinetic Theory of Gases

139256 The energy per mole per degree of freedom of an ideal gas is

1 $\frac{3}{2} \mathrm{k}_{\mathrm{B}} \mathrm{T}$
2 $\frac{1}{2} \mathrm{k}_{\mathrm{B}} \mathrm{T}$
3 $\frac{3}{2} \mathrm{RT}$
4 $\frac{1}{2} \mathrm{RT}$
Kinetic Theory of Gases

139257 A mixture of two gases is contained in a vessel. The gas 1 is mono atomic and gas 2 is diatomic and the ratio of their molecular masses $M_{1} / M_{2}$ $=1 / 4$. What is the ratio of root mean square speeds of the molecules of two gases?

1 2
2 4
3 8
4 16
Kinetic Theory of Gases

139258 The average kinetic energy of a gas molecule at $27^{\circ} \mathrm{C}$ is $6.21 \times 10^{-21} \mathrm{~J}$, then its average kinetic energy at $227^{\circ} \mathrm{C}$ is:

1 $10.35 \times 10^{-21} \mathrm{~J}$
2 $11.35 \times 10^{-21} \mathrm{~J}$
3 $52.2 \times 10^{-21} \mathrm{~J}$
4 $5.22 \times 10^{-21} \mathrm{~J}$
Kinetic Theory of Gases

139259 A cubical box with porous walls containing an equal number of $\mathrm{O}_{2}$ and $\mathrm{H}_{2}$ molecules is placed in a large evacuated chamber. The entire system is maintained at constant temperature $T$. The ratio of $V_{\text {rms of }} \mathrm{O}_{2}$ molecules to that of the $V_{\text {rms }}$ of $\mathrm{H}_{2}$ molecules, found in the chamber outside the box after a short interval is

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

139254 The molecules in an ideal gas at $27^{\circ} \mathrm{C}$ have a certain mean velocity. At what approximate temperature, will the mean velocity be doubled?

1 $54^{\circ} \mathrm{C}$
2 $327^{\circ} \mathrm{C}$
3 $1200^{\circ} \mathrm{C}$
4 $927^{\circ} \mathrm{C}$
Kinetic Theory of Gases

139256 The energy per mole per degree of freedom of an ideal gas is

1 $\frac{3}{2} \mathrm{k}_{\mathrm{B}} \mathrm{T}$
2 $\frac{1}{2} \mathrm{k}_{\mathrm{B}} \mathrm{T}$
3 $\frac{3}{2} \mathrm{RT}$
4 $\frac{1}{2} \mathrm{RT}$
Kinetic Theory of Gases

139257 A mixture of two gases is contained in a vessel. The gas 1 is mono atomic and gas 2 is diatomic and the ratio of their molecular masses $M_{1} / M_{2}$ $=1 / 4$. What is the ratio of root mean square speeds of the molecules of two gases?

1 2
2 4
3 8
4 16
Kinetic Theory of Gases

139258 The average kinetic energy of a gas molecule at $27^{\circ} \mathrm{C}$ is $6.21 \times 10^{-21} \mathrm{~J}$, then its average kinetic energy at $227^{\circ} \mathrm{C}$ is:

1 $10.35 \times 10^{-21} \mathrm{~J}$
2 $11.35 \times 10^{-21} \mathrm{~J}$
3 $52.2 \times 10^{-21} \mathrm{~J}$
4 $5.22 \times 10^{-21} \mathrm{~J}$
Kinetic Theory of Gases

139259 A cubical box with porous walls containing an equal number of $\mathrm{O}_{2}$ and $\mathrm{H}_{2}$ molecules is placed in a large evacuated chamber. The entire system is maintained at constant temperature $T$. The ratio of $V_{\text {rms of }} \mathrm{O}_{2}$ molecules to that of the $V_{\text {rms }}$ of $\mathrm{H}_{2}$ molecules, found in the chamber outside the box after a short interval is

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

139254 The molecules in an ideal gas at $27^{\circ} \mathrm{C}$ have a certain mean velocity. At what approximate temperature, will the mean velocity be doubled?

1 $54^{\circ} \mathrm{C}$
2 $327^{\circ} \mathrm{C}$
3 $1200^{\circ} \mathrm{C}$
4 $927^{\circ} \mathrm{C}$
Kinetic Theory of Gases

139256 The energy per mole per degree of freedom of an ideal gas is

1 $\frac{3}{2} \mathrm{k}_{\mathrm{B}} \mathrm{T}$
2 $\frac{1}{2} \mathrm{k}_{\mathrm{B}} \mathrm{T}$
3 $\frac{3}{2} \mathrm{RT}$
4 $\frac{1}{2} \mathrm{RT}$
Kinetic Theory of Gases

139257 A mixture of two gases is contained in a vessel. The gas 1 is mono atomic and gas 2 is diatomic and the ratio of their molecular masses $M_{1} / M_{2}$ $=1 / 4$. What is the ratio of root mean square speeds of the molecules of two gases?

1 2
2 4
3 8
4 16
Kinetic Theory of Gases

139258 The average kinetic energy of a gas molecule at $27^{\circ} \mathrm{C}$ is $6.21 \times 10^{-21} \mathrm{~J}$, then its average kinetic energy at $227^{\circ} \mathrm{C}$ is:

1 $10.35 \times 10^{-21} \mathrm{~J}$
2 $11.35 \times 10^{-21} \mathrm{~J}$
3 $52.2 \times 10^{-21} \mathrm{~J}$
4 $5.22 \times 10^{-21} \mathrm{~J}$
Kinetic Theory of Gases

139259 A cubical box with porous walls containing an equal number of $\mathrm{O}_{2}$ and $\mathrm{H}_{2}$ molecules is placed in a large evacuated chamber. The entire system is maintained at constant temperature $T$. The ratio of $V_{\text {rms of }} \mathrm{O}_{2}$ molecules to that of the $V_{\text {rms }}$ of $\mathrm{H}_{2}$ molecules, found in the chamber outside the box after a short interval is

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

139254 The molecules in an ideal gas at $27^{\circ} \mathrm{C}$ have a certain mean velocity. At what approximate temperature, will the mean velocity be doubled?

1 $54^{\circ} \mathrm{C}$
2 $327^{\circ} \mathrm{C}$
3 $1200^{\circ} \mathrm{C}$
4 $927^{\circ} \mathrm{C}$
Kinetic Theory of Gases

139256 The energy per mole per degree of freedom of an ideal gas is

1 $\frac{3}{2} \mathrm{k}_{\mathrm{B}} \mathrm{T}$
2 $\frac{1}{2} \mathrm{k}_{\mathrm{B}} \mathrm{T}$
3 $\frac{3}{2} \mathrm{RT}$
4 $\frac{1}{2} \mathrm{RT}$
Kinetic Theory of Gases

139257 A mixture of two gases is contained in a vessel. The gas 1 is mono atomic and gas 2 is diatomic and the ratio of their molecular masses $M_{1} / M_{2}$ $=1 / 4$. What is the ratio of root mean square speeds of the molecules of two gases?

1 2
2 4
3 8
4 16
Kinetic Theory of Gases

139258 The average kinetic energy of a gas molecule at $27^{\circ} \mathrm{C}$ is $6.21 \times 10^{-21} \mathrm{~J}$, then its average kinetic energy at $227^{\circ} \mathrm{C}$ is:

1 $10.35 \times 10^{-21} \mathrm{~J}$
2 $11.35 \times 10^{-21} \mathrm{~J}$
3 $52.2 \times 10^{-21} \mathrm{~J}$
4 $5.22 \times 10^{-21} \mathrm{~J}$
Kinetic Theory of Gases

139259 A cubical box with porous walls containing an equal number of $\mathrm{O}_{2}$ and $\mathrm{H}_{2}$ molecules is placed in a large evacuated chamber. The entire system is maintained at constant temperature $T$. The ratio of $V_{\text {rms of }} \mathrm{O}_{2}$ molecules to that of the $V_{\text {rms }}$ of $\mathrm{H}_{2}$ molecules, found in the chamber outside the box after a short interval is

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

139254 The molecules in an ideal gas at $27^{\circ} \mathrm{C}$ have a certain mean velocity. At what approximate temperature, will the mean velocity be doubled?

1 $54^{\circ} \mathrm{C}$
2 $327^{\circ} \mathrm{C}$
3 $1200^{\circ} \mathrm{C}$
4 $927^{\circ} \mathrm{C}$
Kinetic Theory of Gases

139256 The energy per mole per degree of freedom of an ideal gas is

1 $\frac{3}{2} \mathrm{k}_{\mathrm{B}} \mathrm{T}$
2 $\frac{1}{2} \mathrm{k}_{\mathrm{B}} \mathrm{T}$
3 $\frac{3}{2} \mathrm{RT}$
4 $\frac{1}{2} \mathrm{RT}$
Kinetic Theory of Gases

139257 A mixture of two gases is contained in a vessel. The gas 1 is mono atomic and gas 2 is diatomic and the ratio of their molecular masses $M_{1} / M_{2}$ $=1 / 4$. What is the ratio of root mean square speeds of the molecules of two gases?

1 2
2 4
3 8
4 16
Kinetic Theory of Gases

139258 The average kinetic energy of a gas molecule at $27^{\circ} \mathrm{C}$ is $6.21 \times 10^{-21} \mathrm{~J}$, then its average kinetic energy at $227^{\circ} \mathrm{C}$ is:

1 $10.35 \times 10^{-21} \mathrm{~J}$
2 $11.35 \times 10^{-21} \mathrm{~J}$
3 $52.2 \times 10^{-21} \mathrm{~J}$
4 $5.22 \times 10^{-21} \mathrm{~J}$
Kinetic Theory of Gases

139259 A cubical box with porous walls containing an equal number of $\mathrm{O}_{2}$ and $\mathrm{H}_{2}$ molecules is placed in a large evacuated chamber. The entire system is maintained at constant temperature $T$. The ratio of $V_{\text {rms of }} \mathrm{O}_{2}$ molecules to that of the $V_{\text {rms }}$ of $\mathrm{H}_{2}$ molecules, found in the chamber outside the box after a short interval is

1 $\frac{1}{2 \sqrt{2}}$
2 $\frac{1}{4}$
3 $\frac{1}{\sqrt{2}}$
4 $\sqrt{2}$