A thermally insulated piston divides a container into two compartments.  Volume, temperature, and pressure in the right compartment are \(2V\), \(T\) and \(2P\), while in the left compartment the respective values are \(V\), \(T\) and \(P\).  If the piston can slide freely, then in the final equilibrium position, the volume of the right-hand compartment will be:

1. \(V\) 2. \(3V \over 5\)
3. \(9V \over 4\) 4. \(12V \over 5\)

Subtopic:  Ideal Gas Equation |
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The curve between absolute temperature and \(\mathrm{v}^2_{rms}\) is:

1. 2.
3. 4.
Subtopic:  Types of Velocities |
 71%
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At constant temperature, on increasing the pressure of a gas by 5% , its volume will decrease by:          

1. 5%       

2. 5.26 %         

3. 4.26 %         

4. 4.76 %

Subtopic:  Ideal Gas Equation |
From NCERT
PMT - 2006
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At what temperature is the root mean square speed of molecules of hydrogen twice as that at STP?
1. \(273\) K
2. \(546\) K
3. \(819\) K
4. \(1092\) K

Subtopic:  Types of Velocities |
 65%
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 Volume, pressure, and temperature of an ideal gas are \(V,\) \(P,\) and \(T\) respectively. If the mass of its molecule is \(m\), then its density is: [\(k\)=Boltzmann's constant]

1. \(mkT\) 2. \(P \over kT\)
3. \(P \over kTV\) 4. \(Pm \over kT\)
Subtopic:  Ideal Gas Equation |
 81%
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Which one of the following graph is correct at constant pressure?

1. 2.
3. 4.
Subtopic:  Ideal Gas Equation |
 62%
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Molecular weight of two gases are \(M_1\) and \(M_2.\) At any temperature, the ratio of root mean square velocities \(v_1\) and \(v_2\) will be:
1. \(\sqrt{\frac{M_1}{M_2}}\)
2. \(\sqrt{\frac{M_2}{M_1}}\)
3. \(\sqrt{\frac{M_1+M_2}{M_1-M_2}}\)
4. \(\sqrt{\frac{M_1-M_2}{M_1+M_2}}\)

Subtopic:  Types of Velocities |
 88%
From NCERT
PMT - 1996
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PV versus T graphs of equal masses of \(H_2\)\(He\) and \(O_2\) are shown in the figure. Choose the correct alternative:          

1. A corresponds to \(H_2\), B to \(He\) and C to \(O_2\) 2. A corresponds to \(He\), B to \(H_2\), and C to \(O_2\)
3. A corresponds to \(He\), B to \(O_2\), and C to \(H_2\) 4. A corresponds to \(O_2\), B to \(He\)  and C to \(H_2\)
Subtopic:  Ideal Gas Equation |
 65%
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Mean kinetic energy per degree of freedom of gas molecules is:

1. 32kT             

2. kT             

3. 12kT             

4. 32RT

Subtopic:  Law of Equipartition of Energy |
 58%
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The pressure and temperature of two different gases are P and T with volume V for each.  If they are mixed, keeping the same volume and temperature, the pressure of the mixture will be:

1. P/2 2. P
3. 2P 4. 4P
Subtopic:  Ideal Gas Equation |
 50%
From NCERT
PMT - 1997
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