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 kB = 1.38 × 10-23 J K-1):

1. $2.508×{10}^{4}$ $K$

2. $8.360×{10}^{4}$ $K$

3. $5.016×{10}^{4}$ $K$

4. $1.254×{10}^{4}$ $K$

Subtopic:  Types of Velocities |
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A gas mixture consists of $$2$$ moles of O2 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) $R$

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 105 Nm-2 pressure. When the temperature and pressure of the gas are increased to ,respectively, 127°C and 0.05 X 10Nm-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. $$100\sqrt{2}$$
Subtopic:  Types of Velocities |
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To view explanation, please take trial in the course below.
NEET 2023 - Target Batch - Aryan Raj Singh