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Two containers of equal volumes contain the same gas at pressures \(P_1\)${\mathrm{}}_{}$ and \(P_2\)${\mathrm{}}_{}$ and absolute temperatures \(T_1\)${\mathrm{}}_{}$ and \(T_2\)${\mathrm{}}_{}$, respectively. On joining the vessels, the gas reaches a common pressure \(P\) and common temperature \(T\). The ratio \(\frac{P}{T}\) is equal to:

1. | \(\frac{P_1}{T_1}+\frac{P_2}{T_2}\) | 2. | \(\frac{P_1T_1+P_2T_2}{(T_1+T_2)^2}\) |

3. | \(\frac{P_1T_2+P_2T_1}{(T_1+T_2)^2}\) | 4. | \(\frac{P_1}{2T_1}+\frac{P_2}{2T_2}\) |

Subtopic: Ideal Gas Equation |

52%

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The root mean square speed of the molecules of a diatomic gas is \(v\). When the temperature is doubled, the molecules dissociate into two atoms. The new root mean square speed of the atom is:

1. | \(\sqrt{2}v\) | 2. | \(v\) |

3. | \(2v\) | 4. | \(4v\) |

Subtopic: Types of Velocities |

67%

From NCERT

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A vessel contains a mixture of one mole of oxygen and two moles of nitrogen at \(300\) K. The ratio of the average rotational kinetic energy per ${\mathrm{O}}_{2}$ molecule to that per ${\mathrm{N}}_{2}$ molecule is:

1. | 1 : 1 |

2. | 1 : 2 |

3. | 2 : 1 |

4. | depends on the moments of inertia of the two molecules |

Subtopic: Law of Equipartition of Energy |

71%

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An experiment is carried out on a fixed amount of gas at different temperatures and at high pressure such that it deviates from the ideal gas behaviour. The variation of $\frac{\mathrm{PV}}{\mathrm{RT}}$ with P is shown in the diagram. The correct variation will correspond to: (Assuming that the gas in consideration is nitrogen)

1. | Curve A | 2. | Curve B |

3. | Curve C | 4. | Curve D |

Subtopic: Ideal Gas Equation |

59%

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The figure below shows the graph of pressure and volume of a gas at two temperatures ${\mathrm{T}}_{1}$ and ${\mathrm{T}}_{2}$. Which one, of the following, inferences is correct?

1. | \(\mathrm{T}_1>\mathrm{T}_2\) |

2. | \(\mathrm{T}_1=\mathrm{T}_2\) |

3. | \(\mathrm{T}_1<\mathrm{T}_2\) |

4. | No inference can be drawn |

Subtopic: Ideal Gas Equation |

85%

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An ideal gas is initially at temperature T and volume V. Its volume increases by $\u2206\mathrm{V}$ due to an increase in temperature $\u2206\mathrm{T}$, pressure remaining constant. The quantity $\mathrm{\delta}=\u2206\mathrm{V}/\left(\mathrm{V}\u2206\mathrm{T}\right)$ varies with temperature as:

1. | 2. | ||

3. | 4. |

Subtopic: Ideal Gas Equation |

56%

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Which one, of the following, graphs represents the behaviour of an ideal gas at constant temperature?

1. | 2. | ||

3. | 4. |

Subtopic: Ideal Gas Equation |

77%

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The average translational kinetic energy of \(O_2\) (molar mass \(32\)) molecules at a particular temperature is \(0.048~\text{eV}\). The translational kinetic energy of \(N_2\) (molar mass \(28\)) molecules in \(\text{eV}\) at the same temperature is:

1. \(0.0015\)

2. \(0.003\)

3. \(0.048\)

4. \(0.768\)

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

82%

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The translatory kinetic energy of a gas per \(\text{g}\) is:

1. | \({3 \over 2}{RT \over N}\) | 2. | \({3 \over 2}{RT \over M}\) |

3. | \({3 \over 2}RT \) | 4. | \({3 \over 2}NKT\) |

Subtopic: Kinetic Energy of an Ideal Gas |

61%

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For hydrogen gas \(C_P-C_V=a\) and for oxygen gas \(C_P-C_V=b\) where molar specific heats are given. So the relation between \(a\) and \(b\) is given by: (where \(C_p\) and \(C_V\) in J mol^{-1} K^{-1})

1. \(a=16b\)

2. \(b=16a\)

3. \(a=4b\)

4. \(a=b\)

Subtopic: Specific Heat |

63%

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