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

139226 Five gas molecules chosen at random are found to have speeds of $500,600,700,800$ and 900 $\mathrm{m} / \mathrm{s}$. Then which of the following statements is correct?

1 The root mean square speed and the average speed are the same.
2 The root mean square speed is $14 \mathrm{~m} / \mathrm{s}$ higher than the average speed.
3 The root mean square speed is $14 \mathrm{~m} / \mathrm{s}$ lower than the average speed.
4 The root mean square speed is $\sqrt{ } 14 \mathrm{~m} / \mathrm{s}$ higher than the average speed.
Kinetic Theory of Gases

139228 If $m$ represents the mass of each molecule of a gas and $T$, its absolute temperature, then the root mean square velocity of the gaseous molecule is proportional to

1 $\mathrm{mT}$(e) $\mathrm{mT}^{-1 / 2}$
2 $\mathrm{m}^{1 / 2} \mathrm{~T}^{1 / 2}$
3 $\mathrm{m}^{-1 / 2} \mathrm{~T}$
4 $\mathrm{m}^{-1 / 2} \mathrm{~T}^{1 / 2}$
Kinetic Theory of Gases

139232 During an experiment, an ideal gas is found to obey an additional law $\mathrm{VP}^{2}=$ constant. The gas is initially at temperature $T$ and volume $V$. What will be the temperature of the gas when it expand to a volume $2 \mathbf{V}$ ?

1 $\sqrt{3} \mathrm{~T}$
2 $\mathrm{T} \sqrt{1 / 2}$
3 $\mathrm{T} \sqrt{2}$
4 $\mathrm{T} \sqrt{3}$
Kinetic Theory of Gases

139233 The molecules of a given mass of gas have a root mean square velocity of $200 \mathrm{~m} \mathrm{~s}^{-1}$ at $27^{\circ} \mathrm{C}$ and $1.0 \times 10^{5} \mathrm{~N} \mathrm{~m}^{-2}$ pressure. When the temperature is $127^{\circ} \mathrm{C}$ and the pressure is $0.5 \times$ $10^{5} \mathrm{Nm}^{-2}$, the root mean square velocity in $\mathrm{ms}^{-}$ 1 , is

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

139226 Five gas molecules chosen at random are found to have speeds of $500,600,700,800$ and 900 $\mathrm{m} / \mathrm{s}$. Then which of the following statements is correct?

1 The root mean square speed and the average speed are the same.
2 The root mean square speed is $14 \mathrm{~m} / \mathrm{s}$ higher than the average speed.
3 The root mean square speed is $14 \mathrm{~m} / \mathrm{s}$ lower than the average speed.
4 The root mean square speed is $\sqrt{ } 14 \mathrm{~m} / \mathrm{s}$ higher than the average speed.
Kinetic Theory of Gases

139228 If $m$ represents the mass of each molecule of a gas and $T$, its absolute temperature, then the root mean square velocity of the gaseous molecule is proportional to

1 $\mathrm{mT}$(e) $\mathrm{mT}^{-1 / 2}$
2 $\mathrm{m}^{1 / 2} \mathrm{~T}^{1 / 2}$
3 $\mathrm{m}^{-1 / 2} \mathrm{~T}$
4 $\mathrm{m}^{-1 / 2} \mathrm{~T}^{1 / 2}$
Kinetic Theory of Gases

139232 During an experiment, an ideal gas is found to obey an additional law $\mathrm{VP}^{2}=$ constant. The gas is initially at temperature $T$ and volume $V$. What will be the temperature of the gas when it expand to a volume $2 \mathbf{V}$ ?

1 $\sqrt{3} \mathrm{~T}$
2 $\mathrm{T} \sqrt{1 / 2}$
3 $\mathrm{T} \sqrt{2}$
4 $\mathrm{T} \sqrt{3}$
Kinetic Theory of Gases

139233 The molecules of a given mass of gas have a root mean square velocity of $200 \mathrm{~m} \mathrm{~s}^{-1}$ at $27^{\circ} \mathrm{C}$ and $1.0 \times 10^{5} \mathrm{~N} \mathrm{~m}^{-2}$ pressure. When the temperature is $127^{\circ} \mathrm{C}$ and the pressure is $0.5 \times$ $10^{5} \mathrm{Nm}^{-2}$, the root mean square velocity in $\mathrm{ms}^{-}$ 1 , is

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

139226 Five gas molecules chosen at random are found to have speeds of $500,600,700,800$ and 900 $\mathrm{m} / \mathrm{s}$. Then which of the following statements is correct?

1 The root mean square speed and the average speed are the same.
2 The root mean square speed is $14 \mathrm{~m} / \mathrm{s}$ higher than the average speed.
3 The root mean square speed is $14 \mathrm{~m} / \mathrm{s}$ lower than the average speed.
4 The root mean square speed is $\sqrt{ } 14 \mathrm{~m} / \mathrm{s}$ higher than the average speed.
Kinetic Theory of Gases

139228 If $m$ represents the mass of each molecule of a gas and $T$, its absolute temperature, then the root mean square velocity of the gaseous molecule is proportional to

1 $\mathrm{mT}$(e) $\mathrm{mT}^{-1 / 2}$
2 $\mathrm{m}^{1 / 2} \mathrm{~T}^{1 / 2}$
3 $\mathrm{m}^{-1 / 2} \mathrm{~T}$
4 $\mathrm{m}^{-1 / 2} \mathrm{~T}^{1 / 2}$
Kinetic Theory of Gases

139232 During an experiment, an ideal gas is found to obey an additional law $\mathrm{VP}^{2}=$ constant. The gas is initially at temperature $T$ and volume $V$. What will be the temperature of the gas when it expand to a volume $2 \mathbf{V}$ ?

1 $\sqrt{3} \mathrm{~T}$
2 $\mathrm{T} \sqrt{1 / 2}$
3 $\mathrm{T} \sqrt{2}$
4 $\mathrm{T} \sqrt{3}$
Kinetic Theory of Gases

139233 The molecules of a given mass of gas have a root mean square velocity of $200 \mathrm{~m} \mathrm{~s}^{-1}$ at $27^{\circ} \mathrm{C}$ and $1.0 \times 10^{5} \mathrm{~N} \mathrm{~m}^{-2}$ pressure. When the temperature is $127^{\circ} \mathrm{C}$ and the pressure is $0.5 \times$ $10^{5} \mathrm{Nm}^{-2}$, the root mean square velocity in $\mathrm{ms}^{-}$ 1 , is

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

139226 Five gas molecules chosen at random are found to have speeds of $500,600,700,800$ and 900 $\mathrm{m} / \mathrm{s}$. Then which of the following statements is correct?

1 The root mean square speed and the average speed are the same.
2 The root mean square speed is $14 \mathrm{~m} / \mathrm{s}$ higher than the average speed.
3 The root mean square speed is $14 \mathrm{~m} / \mathrm{s}$ lower than the average speed.
4 The root mean square speed is $\sqrt{ } 14 \mathrm{~m} / \mathrm{s}$ higher than the average speed.
Kinetic Theory of Gases

139228 If $m$ represents the mass of each molecule of a gas and $T$, its absolute temperature, then the root mean square velocity of the gaseous molecule is proportional to

1 $\mathrm{mT}$(e) $\mathrm{mT}^{-1 / 2}$
2 $\mathrm{m}^{1 / 2} \mathrm{~T}^{1 / 2}$
3 $\mathrm{m}^{-1 / 2} \mathrm{~T}$
4 $\mathrm{m}^{-1 / 2} \mathrm{~T}^{1 / 2}$
Kinetic Theory of Gases

139232 During an experiment, an ideal gas is found to obey an additional law $\mathrm{VP}^{2}=$ constant. The gas is initially at temperature $T$ and volume $V$. What will be the temperature of the gas when it expand to a volume $2 \mathbf{V}$ ?

1 $\sqrt{3} \mathrm{~T}$
2 $\mathrm{T} \sqrt{1 / 2}$
3 $\mathrm{T} \sqrt{2}$
4 $\mathrm{T} \sqrt{3}$
Kinetic Theory of Gases

139233 The molecules of a given mass of gas have a root mean square velocity of $200 \mathrm{~m} \mathrm{~s}^{-1}$ at $27^{\circ} \mathrm{C}$ and $1.0 \times 10^{5} \mathrm{~N} \mathrm{~m}^{-2}$ pressure. When the temperature is $127^{\circ} \mathrm{C}$ and the pressure is $0.5 \times$ $10^{5} \mathrm{Nm}^{-2}$, the root mean square velocity in $\mathrm{ms}^{-}$ 1 , is

1 $\frac{400}{\sqrt{3}}$
2 $100 \sqrt{2}$
3 $\frac{100 \sqrt{2}}{3}$
4 $\frac{100}{3}$