At what temperature will the RMS speed of oxygen molecules become just sufficient for escaping from the earth's atmosphere?

(Given : Mass of oxygen molecule (m) = 2.76 x 10^{-26 }kg, Boltzmann's constant k_{B} = 1.38 × 10^{-23} J K^{-1}):

1. $2.508\times {10}^{4}$ $K$

2. $8.360\times {10}^{4}$ $K$

3. $5.016\times {10}^{4}$ $K$

4. $1.254\times {10}^{4}$ $K$

Subtopic: Types of Velocities |

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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 |

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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 |

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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) $R$

NEET - 2016

Subtopic: Specific Heat |

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The molecules of a given mass of gas have r.m.s velocity of 200 ms^{-1} at 27°C and 1.0 x 10^{5} Nm^{-2} pressure. When the temperature and pressure of the gas are increased to ,respectively, 127°C and 0.05 X 10^{5 }Nm^{-2} , r.m.s 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 |

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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 |

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

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