A gas mixture consists of \(2\) moles of \(O_2\) 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 |
 77%
From NCERT
NEET - 2017
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At what temperature will the \(\text{rms}\) speed of oxygen molecules become just sufficient for escaping from the earth's atmosphere? 
(Given: Mass of oxygen molecule \((m)= 2.76\times 10^{-26}~\text{kg}\), Boltzmann's constant \(k_B= 1.38\times10^{-23}~\text{J K}^{-1}\))
1. \(2.508\times 10^{4}~\text{K}\)
2. \(8.360\times 10^{4}~\text{K}\)
3. \(5.016\times 10^{4}~\text{K}\)
4. \(1.254\times 10^{4}~\text{K}\)

Subtopic:  Types of Velocities |
 64%
From NCERT
NEET - 2018
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The molecules of a given mass of gas have rms velocity of \(200~\mathrm{ms^{-1}}\) at \(27^\circ \text{C}\) and \(1.0\times 10^{5}~\mathrm{Nm^{-2}}\) pressure. When the temperature and the pressure of the gas are respectively, \(127^\circ \text{C}\) and \(0.05\times10^{5}~\mathrm{Nm^{-2}}\), the RMS velocity of its molecules in \(\mathrm{ms^{-1}}\) is:
1. \(\frac{400}{\sqrt{3}}\)
2. \(\frac{100\sqrt{2}}{3}\)
3. \(\frac{100}{3}\)
4. \(100\sqrt{2}\)
Subtopic:  Types of Velocities |
 83%
From NCERT
NEET - 2016
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Two vessels separately contain two ideal gases \(\mathrm{A}\) and \(\mathrm{B}\) at the same temperature, the pressure of \(\mathrm{A}\) being twice that of \(\mathrm{B}\). Under such conditions, the density of \(\mathrm{A}\) is found to be \(1.5\) times the density of \(\mathrm{B}\). The ratio of molecular weight of \(\mathrm{A}\) and \(\mathrm{B}\) is:

1. \(\frac{2}{3}\) 2. \(\frac{3}{4}\)
3. \(2\) 4. \(\frac{1}{2}\)
Subtopic:  Ideal Gas Equation |
 86%
From NCERT
NEET - 2015
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One mole of an ideal diatomic gas undergoes a transition from \(A\) to \(B\) along a path \(AB\) as shown in the figure. 
         
The change in internal energy of the gas during the transition is:

1. \(20\) kJ 2. \(-20\) kJ
3. \(20\) J 4. \(-12\) kJ

Subtopic:  Law of Equipartition of Energy |
 68%
From NCERT
NEET - 2015
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The ratio of the specific heats \(\frac{{C}_{{P}}}{{C}_{{V}}}=\gamma\)  in terms of degrees of freedom(\(n\)) is given by:

1. \(\left(1+\frac{1}{n}\right )\) 2. \(\left(1+\frac{n}{3}\right)\)
3. \(\left(1+\frac{2}{n}\right)\) 4. \(\left(1+\frac{n}{2}\right)\)

Subtopic:  Specific Heat |
 77%
From NCERT
NEET - 2015
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The mean free path of molecules of a gas (radius \(r\)) is inversely proportional to:
1. \(r^3\)
2. \(r^2\) 
3. \(r\) 
4. \(\sqrt{r}\)

Subtopic:  Mean Free Path |
 84%
From NCERT
AIPMT - 2014
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In the given \({(V\text{-}T)}\) diagram, what is the relation between pressure \({P_1}\) and \({P_2}\)
              

1. \(P_2>P_1\) 2. \(P_2<P_1\)
3. cannot be predicted 4. \(P_2=P_1\)

Subtopic:  Ideal Gas Equation |
 83%
From NCERT
AIPMT - 2013
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The amount of heat energy required to raise the temperature of \(1\) g of Helium at NTP, from \({T_1}\) K to \({T_2}\) K is:
1. \(\frac{3}{2}N_ak_B(T_2-T_1)\)
2. \(\frac{3}{4}N_ak_B(T_2-T_1)\)
3. \(\frac{3}{4}N_ak_B\frac{T_2}{T_1}\)
4. \(\frac{3}{8}N_ak_B(T_2-T_1)\)

Subtopic:  Specific Heat |
 51%
From NCERT
AIPMT - 2013
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At \(10^{\circ}\mathrm{C}\) the value of the density of a fixed mass of an ideal gas divided by its pressure is \(x\). At \(110^{\circ}\mathrm{C}\) this ratio is:
1. \(x\)
2. \(\frac{383}{283}x\)
3. \(\frac{10}{110}x\)
4. \(\frac{283}{383}x\)

Subtopic:  Ideal Gas Equation |
 69%
From NCERT
AIPMT - 2008
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