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At what temperature will the \(\text{rms}\) speed of oxygen molecules become just sufficient for escaping from the earth's atmosphere?

(Given: Mass of oxygen molecule \((m)= 2.76\times 10^{-26}~\text{kg}\), Boltzmann's constant \(k_B= 1.38\times10^{-23}~\text{J K}^{-1}\)):

1. \(2.508\times 10^{4}~\text{K}\)

2. \(8.360\times 10^{4}~\text{K}\)

3. \(5.016\times 10^{4}~\text{K}\)

4. \(1.254\times 10^{4}~\text{K}\)

Subtopic: Types of Velocities |

63%

From NCERT

NEET - 2018

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A gas mixture consists of \(2\) moles of \(O_2\) and \(4\) moles of \(Ar\) at temperature \(T.\) Neglecting all the vibrational modes, the total internal energy of the system is:

1. | \(15RT\) | 2. | \(9RT\) |

3. | \(11RT\) | 4. | \(4RT\) |

Subtopic: Law of Equipartition of Energy |

77%

From NCERT

NEET - 2017

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A gas mixture consist of 2 moles of ${O}_{2}$ and 4 moles of Ar at temperature T. Neglecting all vibrational modes, the total internal energy of the system is:

(1)4RT

(2) 15RT

(3)9RT

(4)11RT

Subtopic: Kinetic Energy of an Ideal Gas | Law of Equipartition of Energy |

93%

From NCERT

NEET - 2017

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One mole of an ideal monatomic gas undergoes a process described by the equation $P{V}^{3}=$ constant. The heat capacity of the gas during this process is:

(1) $\frac{3}{2}R$

(2) $\frac{5}{2}R$

(3) $2R$

(4) $R$

Subtopic: Specific Heat |

NEET - 2016

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The molecules of a given mass of gas have rms velocity of 200 ms^{-1} at \(27^{\circ}\mathrm{C}\) and 1.0 x 10^{5} Nm^{-2} pressure. When the temperature and pressure of the gas are increased to, respectively, \(127^{\circ}\mathrm{C}\) and 0.05 X 10^{5 }Nm^{-2}, rms velocity of its molecules in ms^{-1} will become:

1. 400/√3

2. 100√2/3

3. 100/3

4.100√2

Subtopic: Types of Velocities |

79%

From NCERT

NEET - 2016

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A given sample of an ideal gas occupies a volume \(V\) at a pressure \(P\) and absolute temperature \(T\). The mass of each molecule of the gas is \(m\). Which of the following gives the density of the gas?

1. \(\frac{P}{kT}\)

2. \(\frac{Pm}{kT}\)

3. \(\frac{P}{kTV}\)

4. \(mkT\)

Subtopic: Ideal Gas Equation |

85%

From NCERT

NEET - 2016

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The molecules of a given mass of gas have rms velocity of \(200~\mathrm{ms^{-1}}\) at \(27^\circ \text{C}\) and \(1.0\times 10^{5}~\mathrm{Nm^{-2}}\) pressure. When the temperature and the pressure of the gas are respectively, \(127^\circ \text{C}\) and \(0.05\times10^{5}~\mathrm{Nm^{-2}}\), 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. \(100\sqrt{2}\)

1. \(\frac{400}{\sqrt{3}}\)

2. \(\frac{100\sqrt{2}}{3}\)

3. \(\frac{100}{3}\)

4. \(100\sqrt{2}\)

Subtopic: Types of Velocities |

82%

From NCERT

NEET - 2016

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