The mean free path for a gas, with molecular diameter \(d\) and number density \(n,\) can be expressed as:
1. \( \frac{1}{\sqrt{2} n \pi \mathrm{d}^2} \)
2. \( \frac{1}{\sqrt{2} n^2 \pi \mathrm{d}^2} \)
3. \(\frac{1}{\sqrt{2} n^2 \pi^2 d^2} \)
4. \( \frac{1}{\sqrt{2} n \pi \mathrm{d}}\)

Subtopic:  Mean Free Path |
 81%
From NCERT
NEET - 2020
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A cylinder contains hydrogen gas at a pressure of \(249~\text{kPa}\) and temperature \(27^\circ~\mathrm{C}.\) Its density is: (\(R=8.3~\text{J mol}^{-1} \text {K}^{-1}\))
1. \(0.2~\text{kg/m}^{3}\)
2. \(0.1~\text{kg/m}^{3}\)
3. \(0.02~\text{kg/m}^{3}\)
4. \(0.5~\text{kg/m}^{3}\)

Subtopic:  Ideal Gas Equation |
 61%
From NCERT
NEET - 2020
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The average thermal energy for a mono-atomic gas is:
(\(k_B\) is Boltzmann constant and T absolute temperature)
1. \(\frac{3}{2}k_BT\)
2. \(\frac{5}{2}k_BT\)
3. \(\frac{7}{2}k_BT\)
4. \(\frac{1}{2}k_BT\)

Subtopic:  Kinetic Energy of an Ideal Gas |
 87%
From NCERT
NEET - 2020
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The mean free path \(l\) for a gas molecule depends upon the diameter, \(d\) of the molecule as:
1. \(l\propto \frac{1}{d^2}\)
2. \(l\propto d\)
3. \(l\propto d^2 \)
4. \(l\propto \frac{1}{d}\)

Subtopic:  Mean Free Path |
 83%
From NCERT
NEET - 2020
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An ideal gas equation can be written as P=ρRTM0 where ρ and M0 are respectively:

1. mass density, the mass of the gas 
2. number density, molar mass 
3. mass density, molar mass 
4. number density, the mass of the gas 
Subtopic:  Ideal Gas Equation |
 77%
From NCERT
NEET - 2020
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The value \(\gamma = \frac{C_P}{C_V}\) for hydrogen, helium, and another ideal diatomic gas \(X\) (whose molecules are not rigid but have an additional vibrational mode), are respectively equal to:
1. \(\frac{7}{5}, \frac{5}{3}, \frac{9}{7}\)
2. \(\frac{5}{3}, \frac{7}{5}, \frac{9}{7}\)
3. \(\frac{5}{3}, \frac{7}{5}, \frac{7}{5}\)
4. \(\frac{7}{5}, \frac{5}{3}, \frac{7}{5}\)

Subtopic:  Law of Equipartition of Energy |
 56%
From NCERT
NEET - 2019
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If \(C_p\) and \(C_v\) denote the specific heats (per unit mass) of an ideal gas of molecular weight \(M\) (where \(R\) is the molar gas constant), the correct relation is:
1. \(C_p-C_v=R\)
2. \(C_p-C_v=\frac{R}{M}\)
3. \(C_p-C_v=MR\)
4. \(C_p-C_v=\frac{R}{M^2}\)

Subtopic:  Specific Heat |
 64%
From NCERT
AIPMT - 2010
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To find out the degree of freedom, the correct expression is:

1. f=2γ-1

2. f=γ+12

3. f=2γ+1

4. f=1γ+1

Subtopic:  Law of Equipartition of Energy |
 82%
From NCERT
AIPMT - 2000
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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%
From NCERT
AIPMT - 2004
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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) \(\frac13nm\bar v^2\)
(B) the pressure exerted by an ideal gas (Q) \( \sqrt{\frac{3 R T}{M}} \)
(C) the average kinetic energy of a molecule (R) \( \frac{5}{2} R T \)
(D) the total internal energy of 1 mole of a diatomic gas (S) \(\frac32k_BT\)
 
(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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