On the basis of the kinetic theory of gases, one compares \(1~\text{gm}\) of hydrogen with \(1~\text{gm}\) of argon both at \(0^\circ \text{C}.\) Then:

1. the same temperature implies that the average kinetic energy of the molecules is the same in both cases.
2. the same temperature implies that the average potential energy of the molecules is the same in both cases.
3. the internal energies in both cases are equal.
4. when both the samples are heated by \(1^\circ \text{C},\) the total energy added to both of them is the same.

Subtopic:  Kinetic Energy of an Ideal Gas |
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Consider a mole of a sample of hydrogen gas at NTP. Then:

1. the volume of the gas is exactly \(2.24\times10^{-2}\, \text{m}^3.\)
2. the volume of the gas is approximately \(2.24\times10^{-2}\, \text{m}^3.\)
3. the gas will be in thermal equilibrium with \(1\) mole of oxygen gas at NTP.
4. the gas will be in thermodynamic equilibrium with \(1\) mole of oxygen at NTP.

Subtopic:  Ideal Gas Equation |
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Consider the following statements for air molecules in an airtight container:

I. the average speed of molecules is larger than the root mean square speed.
II. the mean free path of molecules is larger than the mean distance between molecules.
III. the mean free path of molecules increases with temperature.
IV. the RMS speed of a nitrogen molecule is smaller than an oxygen molecule.

The true statements are:

1. only II
2. II and III
3. II and IV
4. I, II, and IV

Subtopic:  Mean Free Path |
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An ideal gas is confined in a closed container and slowly heated. As the temperature rises, which of the following statements are correct?

(A) The mean free path of gas molecules decreases.
(B) The mean collision time between the molecules decreases.
(C) The mean free path remains unchanged.
(D) The mean collision time remains unchanged.

Choose the correct option from the given ones:
1. (C) and (D) only
2. (A) and (B) only
3. (A) and (D) only
4. (B) and (C) only
Subtopic:  Mean Free Path |
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Consider a gas of triatomic molecules. The molecules are assumed to be triangular, composed of massless rigid rods with atoms at the vertices. The internal energy of a mole of the gas at temperature \(T\) is:

               

1. \( 3 R T \) 2. \(\dfrac{5}{2} R T \)
3. \( \dfrac{9}{2} R T \) 4. \( \dfrac{3}{2} R T \)
Subtopic:  Law of Equipartition of Energy |
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Match the \(C_p/C_V\)  ratio for ideal gases with different type of molecules :
 

Column I Column II
(A) Monatomic (I) \(7/5\)
(B) Diatomic rigid molecules (II) \(9/7\)
(C) Diatomic non-rigid molecules (III) \(4/3\)
(D) Triatomic rigid molecules (IV) \(5/3\)
 
1. (A)-(III), (B)-(IV), (C)-(II), (D)-(I)
2. (A)-(II), (B)-(III), (C)-( I), (D)-(IV)
3. (A)-(IV), (B)-(II), (C)-(I), (D)-(III)
4. (A)-(IV), (B)-(I), (C)-(II), (D)-(III)
 

Subtopic:  Law of Equipartition of Energy |
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The pressure of an ideal gas is written as \(p=\dfrac{2E}{3V},\) where \(E\) is the total kinetic energy, and \(V\) is the volume.
This statement is:

1. always true.
2. true for mono-atomic gases.
3. always false.
4. true for diatomic gases.
Subtopic:  Kinetic Energy of an Ideal Gas |
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Suppose that the average kinetic energy (translational & rotational) of random molecular motion of helium \(\mathrm{(He})\) at temperature \(T_\mathrm{He}\) is equal to that of hydrogen \(\mathrm{(H_2})\) at temperature \(T_\mathrm{H_2}.\) Then;
1. \(T_\mathrm {H_{2}}=T_\mathrm{H e}\) 2. \(\dfrac{T_\mathrm{H_2}}{2}=\dfrac{T_\mathrm{He}}{4}\)
3. \(5 T_\mathrm{H_2}=3 T_\mathrm{He}\) 4. \(\dfrac{T_\mathrm{H_{2}}}{5}=\dfrac{T_\mathrm{{He }}}{3}\)
Subtopic:  Kinetic Energy of an Ideal Gas |
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The average momentum of the molecules in a sample of \(H_2\) - gas at temperature 300 K has a magnitude \(p_1\) and that for He-gas at the same temperature has the magnitude \(p_2.\) Then, 
1. \(p_1 > p_2\)
2. \(p_2 > p_1\)
3. \(p_1 = p_2\)
4. the relationship between \(p_1\) and \(p_2\) depends on pressure.
Subtopic:  Types of Velocities |
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Given below are two statements: 
Assertion (A): The translational kinetic energy of every molecule of an ideal gas increases by \(50\%,\) if the absolute temperature is raised by \(50\text{%}.\)
Reason (R): The average translational kinetic energy of the molecules of an ideal gas is directly proportional to its absolute temperature.
 
1. (A) is True but (R) is False.
2. (A) is False but (R) is True.
3. Both (A) and (R) are True and (R) is the correct explanation of (A).
4. Both (A) and (R) are True but (R) is not the correct explanation of (A).
Subtopic:  Kinetic Energy of an Ideal Gas |
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