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The figure shows a plot of \(\dfrac{PV}{T}\) versus \(P\) for \(1.00\times10^{-3} \) kg of oxygen gas at two different temperatures.

Then relation between \(T_1\) and \(T_2\) is:

1. \(T_1=T_2\)

2. \(T_1<T_2\)

3. \(T_1>T_2\)

4. \(T_1 \geq T_2\)$\mathrm{}$

Subtopic: Ideal Gas Equation |

61%

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The figure shows a plot of \(\frac{PV}{T}\) versus \(P\) for \(1.00 \times 10^{- 3}~\text{kg}\) of oxygen gas at two different temperatures.

The value of \(\frac{PV}{T}\) where the curves meet on the \(y\)-axis is:

1. \(0.06~\text{JK}^{-1}\)

2. \(0.36~\text{JK}^{-1}\)

3. \(0.16~\text{JK}^{-1}\)

4. \(0.26~\text{JK}^{-1}\)

Subtopic: Ideal Gas Equation |

58%

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An oxygen cylinder of volume 30 litres has an initial gauge pressure of 15 atm and a temperature of 27 °C. After some oxygen is withdrawn from the cylinder, the gauge pressure drops to 11 atm, and its temperature drops to 17 °C. The mass of oxygen taken out of the cylinder is: $\left(\mathrm{R}=8.31{\mathrm{mol}}^{-1}{\mathrm{K}}^{-1},\mathrm{molecular}\mathrm{mass}\mathrm{of}{\mathrm{O}}_{2}=32\mathrm{u}\right)$

1. 0.14 kg

2. 0.16 kg

3. 0.18 kg

4. 0.21 kg

Subtopic: Ideal Gas Equation |

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An air bubble of volume 1.0 $c{m}^{3}$ rises from the bottom of a lake 40 m deep at a temperature of 12 °C. To what volume does it grow when it reaches the surface, which is at a temperature of 35 °C?

1. 5.3 cm^{3}

2. 4.0 cm^{3}

3. 3.7 cm^{3}

4. 4.9 cm^{3}

Subtopic: Ideal Gas Equation |

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What is the total number of air molecules (inclusive of oxygen, nitrogen, water vapor, and other constituents) in a room of capacity \(25.0\) m^{3 }at a temperature of \(27^\circ \text C\) and \(1\) atm pressure?

1. \(6.1\times10^{23}\) molecules

2. \(6.1\times10^{26}\) molecules

3. \(7.1\times10^{23}\) molecules

4. \(7.1\times10^{26}\) molecules

Subtopic: Ideal Gas Equation |

60%

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What is the average thermal energy of a helium atom at room temperature (\(27^{\circ}\text{C}\))?

1. | \(11 . 21 \times 10^{- 20}~\text{J}\) | 2. | \(3 . 09 \times 10^{- 16}~\text{J}\) |

3. | \( 6 . 21 \times 10^{- 21} ~\text{J} \) | 4. | \(5 . 97 \times 10^{- 19}~\text{J}\) |

Subtopic: Law of Equipartition of Energy |

64%

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At what temperature is the root mean square speed of an atom in an argon gas cylinder equal to the rms speed of a helium gas atom at \(-20^\circ \text{C}?\)

(Given the atomic mass of \(\mathrm{Ar}=39.9~\text{u}\) and of \(\mathrm{He}=4.0~\text{u}\)).

1. \(1.01 \times 10^3 ~\text{K} \)

2. \(3.15 \times 10^3 ~\text{K} \)

3. \(1.91 \times 10^3~ \text{K} \)

4. \(2.52 \times 10^3 ~\text{K}\)

Subtopic: Types of Velocities |

74%

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From a certain apparatus, the diffusion rate of hydrogen has an average value of 28.7 $c{m}^{3}{s}^{-1}$. The diffusion of another gas under the same conditions is measured to have an average rate of 7.2 $c{m}^{3}{s}^{-1}$. The unknown gas is:

1. Oxygen

2. Nitrogen

3. Helium

4. None of these

Subtopic: Types of Velocities |

60%

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Molar volume is the volume occupied by \(1\) mol of any (ideal) gas at standard temperature and pressure is:

(STP: \(1\) atmospheric pressure, \(0^{\circ} \text{C}\))

1. \(0\)

2. \(22.4\) litres

3. \(11.2\) litres

4. \(1\) litres

(STP: \(1\) atmospheric pressure, \(0^{\circ} \text{C}\))

1. \(0\)

2. \(22.4\) litres

3. \(11.2\) litres

4. \(1\) litres

Subtopic: Ideal Gas Equation |

87%

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The fraction of molecular volume to the actual volume occupied by oxygen gas at STP is: (Take the diameter of an oxygen molecule to be 3 Å).

1. 4 × 10^{−4}

2. 5 × 10^{−4}

3. 3 × 10^{−4}

4. 1 × 10^{−4}

Subtopic: Ideal Gas Equation |

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