Given below are two statements: 
Assertion (A): The ratio \(C_p\over C_v\) is more for helium gas than for hydrogen gas.
Reason (R): Atomic mass of helium is more than that of hydrogen.
1. Both (A) and (R) are True and (R) is the correct explanation of (A).
2. Both (A) and (R) are True but (R) is not the correct explanation of (A).
3. (A) is True but (R) is False.
4. Both (A) and (R) are False.

Subtopic:  Specific Heat |
 71%
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Which statements are correct about degrees of freedom?
(A) A molecule with \(n\) degrees of freedom has \(n^2\) different ways of storing energy.
(B) Each degree of freedom is associated with \(\dfrac{1}{2} R T\) average energy per mole.
(C) A monoatomic gas molecule has \(1\) rotational degree of freedom whereas a diatomic molecule has \(2\) rotational degrees of freedom.
(D) \(CH_4\) has a total to \(6\) degrees of freedom.

Choose the correct answer from the option given below:
 
1. (B) and (C) only
2. (B) and (D) only
3. (A) and (B) only
4. (C) and (D) only
Subtopic:  Law of Equipartition of Energy |
 66%
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The Earth’s atmosphere contains oxygen and nitrogen. The mass of an oxygen molecule is greater than the mass of a nitrogen molecule. The temperature of the air in a room on a particular day is \(300~\mathrm{K}\). Below are four statements about the motion of the two types of molecules in this room.
A. They have an equal mean square velocity \((\overline{v^2})\).
B. A nitrogen molecule has a greater mean square velocity \((\overline{v^2})\) than an oxygen molecule.
C. A nitrogen molecule has a greater mean kinetic energy than an oxygen molecule.
D. An oxygen molecule has a greater mean kinetic energy than a nitrogen molecule.

Which of the statements is/are correct?
1. Statement A only
2. Statement A and C only
3. Statement B and D only
4. Statement B only
Subtopic:  Types of Velocities |
 71%
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According to the kinetic theory of gases,
(A)  the motion of the gas molecules freezes at \(0^\circ\text C.\)
(B) the mean free path of gas molecules decreases if the density of molecules is increased.
(C) the mean free path of gas molecules increases if the temperature is increased keeping the pressure constant.
(D) average kinetic energy per molecule per degree of freedom is \(\dfrac32k_B T\) (for monoatomic gases).
Choose the most appropriate answer from the options given below:
1. (A) and (C) only
2. (B) and (C) only
3. (A) and (B) only
4. (C) and (D) only
Subtopic:  Mean Free Path |
 53%
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Given below are two statements: 
Assertion (A): If a gas container in motion is suddenly stopped, the temperature of the gas rises.
Reason (R): The kinetic energy of ordered mechanical motion is converted into the kinetic energy of random motion of gas molecules.
  
1. Both (A) and (R) are true and (R) is the correct explanation of (A).
2. Both (A) and (R) are true but (R) is not the correct explanation of (A).
3. (A) is true but (R) is false.
4. Both (A) and (R) are false.
Subtopic:  Kinetic Energy of an Ideal Gas |
 61%
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An increase in the temperature of a gas-filled in a container would lead to:

1.  decrease in the intermolecular distance.
2.  increase in its mass.
3.  increase in its kinetic energy.
4.  decrease in its pressure.

Subtopic:  Kinetic Energy of an Ideal Gas |
 91%
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Match Column I and Column II and choose the correct match from the given choices.

Column I Column II
(A) root mean square speed of gas molecules (P) \(\dfrac13nm\bar v^2\)
(B) the pressure exerted by an ideal gas (Q) \( \sqrt{\dfrac{3 R T}{M}} \)
(C) the average kinetic energy of a molecule (R) \( \dfrac{5}{2} R T \)
(D) the total internal energy of \(1\) mole of a diatomic gas (S) \(\dfrac32k_BT\)
 
(A) (B) (C) (D)
1. (Q) (P) (S) (R)
2. (R) (Q) (P) (S)
3. (R) (P) (S) (Q)
4. (Q) (R) (S) (P)
Subtopic:  Kinetic Energy of an Ideal Gas |
 76%
From NCERT
NEET - 2021
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A cylinder of fixed capacity \(44.8\) litres contains helium gas at standard temperature and pressure. What is the amount of heat needed to raise the temperature of the gas in the cylinder by \(15.0^\circ~\mathrm{C}?\) (\(R=8.31\) J mol–1 K–1)

1. \(379\) J 2. \(357\) J
3. \(457\) J 4. \(374\) J

Subtopic:  Specific Heat |
 51%
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Uranium has two isotopes of masses  \(235 \) and \(238\) units. If both are present in Uranium hexafluoride gas, which would have the larger average speed?
1. \({ }_{235} \mathrm{UF}_6\)
2. \({ }_{238} \mathrm{UF}_6\)
3. Both will have the same average speed.
4. Data insufficient

Subtopic:  Types of Velocities |
 74%
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The equation of state for 5g of oxygen at a pressure P and temperature T, when occupying a volume V, will be: (where R is the gas constant)
1. PV = 5 RT
2. PV = (5/2) RT
3. PV = (5/16) RT
4. PV = (5/32) RT

Subtopic:  Ideal Gas Equation |
 83%
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AIPMT - 2004
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