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

139298 The temperature of a gas is raised from $27^{\circ} \mathrm{C}$ to $927^{\circ} \mathrm{C}$. The root mean square speed

1 is $\sqrt{\left(\frac{927}{27}\right)}$ times the earlier value
2 remains the same
3 gets halved
4 gets doubled
Kinetic Theory of Gases

139299 The mean free path of molecules of a gas, (radius $r$ ) is inversely proportional to

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

139300 The molecules of a given mass of a gas have r.m.s. velocity of $200 \mathrm{~ms}^{-1}$ at $27^{\circ} \mathrm{C}$ and $1.0 \times 10^{5}$ $\mathrm{Nm}^{-2}$ pressure. When the temperature and pressure of the gas are respectively, $127^{\circ} \mathrm{C}$ and $0.05 \times 10^{5} \mathrm{Nm}^{-2}$ the rms velocity of its molecules in $\mathrm{ms}^{-1}$ is

1 $\frac{400}{\sqrt{3}}$
2 $\frac{100 \sqrt{2}}{3}$
3 $\frac{100}{3}$
4 $100 \sqrt{2}$
Kinetic Theory of Gases

139301 The r.m.s speed of hydrogen gas molecules at a certain temperature is $200 \mathrm{~ms}^{-1}$. If the absolute temperature of the gas is doubled and the hydrogen gas dissociates into atomic hydrogen, then the r.m.s speed will become

1 $200 \mathrm{~ms}^{-1}$
2 $400 \mathrm{~ms}^{-1}$
3 $600 \mathrm{~ms}^{-1}$
4 $800 \mathrm{~ms}^{-1}$
Kinetic Theory of Gases

139302 When the temperature of an ideal gas is increased by $600 \mathrm{~K}$, the velocity of sound in the gas becomes $\sqrt{3}$ times the initial velocity in it. The initial temperature of the gas is:

1 $-73^{\circ} \mathrm{C}$
2 $27^{\circ} \mathrm{C}$
3 $127^{\circ} \mathrm{C}$
4 $327^{\circ} \mathrm{C}$
Kinetic Theory of Gases

139298 The temperature of a gas is raised from $27^{\circ} \mathrm{C}$ to $927^{\circ} \mathrm{C}$. The root mean square speed

1 is $\sqrt{\left(\frac{927}{27}\right)}$ times the earlier value
2 remains the same
3 gets halved
4 gets doubled
Kinetic Theory of Gases

139299 The mean free path of molecules of a gas, (radius $r$ ) is inversely proportional to

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

139300 The molecules of a given mass of a gas have r.m.s. velocity of $200 \mathrm{~ms}^{-1}$ at $27^{\circ} \mathrm{C}$ and $1.0 \times 10^{5}$ $\mathrm{Nm}^{-2}$ pressure. When the temperature and pressure of the gas are respectively, $127^{\circ} \mathrm{C}$ and $0.05 \times 10^{5} \mathrm{Nm}^{-2}$ the rms velocity of its molecules in $\mathrm{ms}^{-1}$ is

1 $\frac{400}{\sqrt{3}}$
2 $\frac{100 \sqrt{2}}{3}$
3 $\frac{100}{3}$
4 $100 \sqrt{2}$
Kinetic Theory of Gases

139301 The r.m.s speed of hydrogen gas molecules at a certain temperature is $200 \mathrm{~ms}^{-1}$. If the absolute temperature of the gas is doubled and the hydrogen gas dissociates into atomic hydrogen, then the r.m.s speed will become

1 $200 \mathrm{~ms}^{-1}$
2 $400 \mathrm{~ms}^{-1}$
3 $600 \mathrm{~ms}^{-1}$
4 $800 \mathrm{~ms}^{-1}$
Kinetic Theory of Gases

139302 When the temperature of an ideal gas is increased by $600 \mathrm{~K}$, the velocity of sound in the gas becomes $\sqrt{3}$ times the initial velocity in it. The initial temperature of the gas is:

1 $-73^{\circ} \mathrm{C}$
2 $27^{\circ} \mathrm{C}$
3 $127^{\circ} \mathrm{C}$
4 $327^{\circ} \mathrm{C}$
Kinetic Theory of Gases

139298 The temperature of a gas is raised from $27^{\circ} \mathrm{C}$ to $927^{\circ} \mathrm{C}$. The root mean square speed

1 is $\sqrt{\left(\frac{927}{27}\right)}$ times the earlier value
2 remains the same
3 gets halved
4 gets doubled
Kinetic Theory of Gases

139299 The mean free path of molecules of a gas, (radius $r$ ) is inversely proportional to

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

139300 The molecules of a given mass of a gas have r.m.s. velocity of $200 \mathrm{~ms}^{-1}$ at $27^{\circ} \mathrm{C}$ and $1.0 \times 10^{5}$ $\mathrm{Nm}^{-2}$ pressure. When the temperature and pressure of the gas are respectively, $127^{\circ} \mathrm{C}$ and $0.05 \times 10^{5} \mathrm{Nm}^{-2}$ the rms velocity of its molecules in $\mathrm{ms}^{-1}$ is

1 $\frac{400}{\sqrt{3}}$
2 $\frac{100 \sqrt{2}}{3}$
3 $\frac{100}{3}$
4 $100 \sqrt{2}$
Kinetic Theory of Gases

139301 The r.m.s speed of hydrogen gas molecules at a certain temperature is $200 \mathrm{~ms}^{-1}$. If the absolute temperature of the gas is doubled and the hydrogen gas dissociates into atomic hydrogen, then the r.m.s speed will become

1 $200 \mathrm{~ms}^{-1}$
2 $400 \mathrm{~ms}^{-1}$
3 $600 \mathrm{~ms}^{-1}$
4 $800 \mathrm{~ms}^{-1}$
Kinetic Theory of Gases

139302 When the temperature of an ideal gas is increased by $600 \mathrm{~K}$, the velocity of sound in the gas becomes $\sqrt{3}$ times the initial velocity in it. The initial temperature of the gas is:

1 $-73^{\circ} \mathrm{C}$
2 $27^{\circ} \mathrm{C}$
3 $127^{\circ} \mathrm{C}$
4 $327^{\circ} \mathrm{C}$
Kinetic Theory of Gases

139298 The temperature of a gas is raised from $27^{\circ} \mathrm{C}$ to $927^{\circ} \mathrm{C}$. The root mean square speed

1 is $\sqrt{\left(\frac{927}{27}\right)}$ times the earlier value
2 remains the same
3 gets halved
4 gets doubled
Kinetic Theory of Gases

139299 The mean free path of molecules of a gas, (radius $r$ ) is inversely proportional to

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

139300 The molecules of a given mass of a gas have r.m.s. velocity of $200 \mathrm{~ms}^{-1}$ at $27^{\circ} \mathrm{C}$ and $1.0 \times 10^{5}$ $\mathrm{Nm}^{-2}$ pressure. When the temperature and pressure of the gas are respectively, $127^{\circ} \mathrm{C}$ and $0.05 \times 10^{5} \mathrm{Nm}^{-2}$ the rms velocity of its molecules in $\mathrm{ms}^{-1}$ is

1 $\frac{400}{\sqrt{3}}$
2 $\frac{100 \sqrt{2}}{3}$
3 $\frac{100}{3}$
4 $100 \sqrt{2}$
Kinetic Theory of Gases

139301 The r.m.s speed of hydrogen gas molecules at a certain temperature is $200 \mathrm{~ms}^{-1}$. If the absolute temperature of the gas is doubled and the hydrogen gas dissociates into atomic hydrogen, then the r.m.s speed will become

1 $200 \mathrm{~ms}^{-1}$
2 $400 \mathrm{~ms}^{-1}$
3 $600 \mathrm{~ms}^{-1}$
4 $800 \mathrm{~ms}^{-1}$
Kinetic Theory of Gases

139302 When the temperature of an ideal gas is increased by $600 \mathrm{~K}$, the velocity of sound in the gas becomes $\sqrt{3}$ times the initial velocity in it. The initial temperature of the gas is:

1 $-73^{\circ} \mathrm{C}$
2 $27^{\circ} \mathrm{C}$
3 $127^{\circ} \mathrm{C}$
4 $327^{\circ} \mathrm{C}$
Kinetic Theory of Gases

139298 The temperature of a gas is raised from $27^{\circ} \mathrm{C}$ to $927^{\circ} \mathrm{C}$. The root mean square speed

1 is $\sqrt{\left(\frac{927}{27}\right)}$ times the earlier value
2 remains the same
3 gets halved
4 gets doubled
Kinetic Theory of Gases

139299 The mean free path of molecules of a gas, (radius $r$ ) is inversely proportional to

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

139300 The molecules of a given mass of a gas have r.m.s. velocity of $200 \mathrm{~ms}^{-1}$ at $27^{\circ} \mathrm{C}$ and $1.0 \times 10^{5}$ $\mathrm{Nm}^{-2}$ pressure. When the temperature and pressure of the gas are respectively, $127^{\circ} \mathrm{C}$ and $0.05 \times 10^{5} \mathrm{Nm}^{-2}$ the rms velocity of its molecules in $\mathrm{ms}^{-1}$ is

1 $\frac{400}{\sqrt{3}}$
2 $\frac{100 \sqrt{2}}{3}$
3 $\frac{100}{3}$
4 $100 \sqrt{2}$
Kinetic Theory of Gases

139301 The r.m.s speed of hydrogen gas molecules at a certain temperature is $200 \mathrm{~ms}^{-1}$. If the absolute temperature of the gas is doubled and the hydrogen gas dissociates into atomic hydrogen, then the r.m.s speed will become

1 $200 \mathrm{~ms}^{-1}$
2 $400 \mathrm{~ms}^{-1}$
3 $600 \mathrm{~ms}^{-1}$
4 $800 \mathrm{~ms}^{-1}$
Kinetic Theory of Gases

139302 When the temperature of an ideal gas is increased by $600 \mathrm{~K}$, the velocity of sound in the gas becomes $\sqrt{3}$ times the initial velocity in it. The initial temperature of the gas is:

1 $-73^{\circ} \mathrm{C}$
2 $27^{\circ} \mathrm{C}$
3 $127^{\circ} \mathrm{C}$
4 $327^{\circ} \mathrm{C}$