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Q. No.

The following graph represents the \(T\text -V\) curves of an ideal gas (where \(T\) is the temperature and \(V\) the volume) at three pressures \(P_1, P_2\) and \(P_3\) compared with those of Charles's law represented as dotted lines.
                      
Then the correct relation is :
1. \(P_1>P_3>P_2 \) 2. \(P_2>P_1>P_3 \)
3. \( P_1>P_2>P_3\) 4. \(P_3 > P_2>P_1\)
Q1:
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Subtopic:  Ideal Gas Equation |
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An ideal gas at \(0^{\circ}\text{C}\) and atmospheric pressure \(P\) has volume \(V.\) The percentage increase in its temperature needed to expand it to \(3V\) at constant pressure is:
1. \(100\%\) 2. \(200\%\)
3. \(300\%\) 4. \(50\%\)
Q2:
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Subtopic:  Ideal Gas Equation |
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The equilibrium state of a thermodynamic system is described by:
\(A.\) Pressure
\(B.\) Total heat
\(C.\) Temperature
\(D.\) Volume
\(E.\) Work done
 
Choose the most appropriate answer from the options given below:
1. \(A,B\) and \(E\) only
2. \(B,C\) and \(D\) only
3. \(A,B\) and \(C\) only
4.  \(A,C\) and \(D\) only
Q3:
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Subtopic:  Ideal Gas Equation |
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According to the law of equipartition of energy, the number of vibrational modes of a polyatomic gas of constant \(\gamma=\dfrac{C_{\mathrm{p}}}{C_{\mathrm{v}}}\) is (where \(C_p\) and \(C_v\) are the specific heat capacities of the gas at constant pressure and constant volume, respectively):
1. \(\dfrac{4+3\gamma}{\gamma-1}\) 2. \(\dfrac{3+4\gamma}{\gamma-1}\)
3. \(\dfrac{4-3\gamma}{\gamma-1}\) 4. \(\dfrac{3-4\gamma}{\gamma-1}\)
Q4:
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Subtopic:  Law of Equipartition of Energy |
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The temperature of a gas is \(-50^\circ \text{C}.\) To what temperature the gas should be heated so that the RMS speed is increased by \(3\) times?
1. \(223~\text{K}\) 2. \(669^\circ \text{C}\)
3. \(3295^\circ \text{C}\) 4. \(3097~\text{K}\)
Q5:
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Subtopic:  Types of Velocities |
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A container of volume \(200\) cm3 contains \(0.2\) mole of hydrogen gas and \(0.3\) mole of argon gas. The pressure of the system at temperature \(200\) K (\(R=8.3\) JK–1 mol–1) will be:
1. \( 6.15 \times 10^5 ~\text{Pa} \)
2. \( 6.15 \times 10^4 ~\text{Pa} \)
3. \( 4.15 \times 10^5 ~\text{Pa} \)
4. \( 4.15 \times 10^6 ~\text{Pa}\)
Q6:
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Subtopic:  Ideal Gas Equation |
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The volume occupied by the molecules contained in \(4.5~\text{kg}\) water at STP, if the molecular forces vanish away, is:
1. \(5.6~\text{m}^3\) 
2. \(5.6\times10^{6}~\text{m}^3\)
3. \(5.6\times10^{3}~\text{m}^3\) 
4. \(5.6\times10^{-3}~\text{m}^3\)
Q7:
From NCERT NEET - 2022
Subtopic:  Ideal Gas Equation |
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The temperature at which the RMS speed of atoms in neon gas is equal to the RMS speed of hydrogen molecules at \(15^{\circ} \mathrm{C}\) is:
(Atomic mass of neon \(=20.2~\text u,\) molecular mass of hydrogen \(=2~\text u\) )

1. \(2.9\times10^{3}~\text K\)  2. \(2.9~\text K\) 
3. \(0.15\times10^{3}~\text K\)  4. \(0.29\times10^{3}~\text K\) 
Q8:
 74% From NCERT NEET - 2022
Subtopic:  Types of Velocities |
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Three vessels of equal capacity have gases at the same temperature and pressure. The first vessel contains helium (monoatomic), the second contains fluorine (diatomic) and the third contains sulfur hexafluoride (polyatomic). The correct statement, among the following, is:
1.  all vessels contain an unequal number of respective molecules.
2.  the root mean square speed of molecules is the same in all three cases.
3.  the root mean square speed of helium is the largest.
4.  the root mean square speed of sulfur hexafluoride is the largest.
Q9:
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Subtopic:  Types of Velocities |
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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 a 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)
Q10:
 77% From NCERT NEET - 2021
Subtopic:  Kinetic Energy of an Ideal Gas |
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