Q. No.An inflated rubber balloon contains one mole of an ideal gas, has a pressure \(P,\) volume \(V\) and temperature \(T.\) If the temperature rises to \(1.1T,\) and the volume is increased to \(1.05V,\) the final pressure will be:
1.
\(1.1P\)
2.
\(P\)
3.
less than \(P\)
4.
between \(P\) and \(1.1P\)
ABCDEFGH is a hollow cube made of an insulator (figure). Face ABCD has a positive charge on it. Inside the cube, we have ionised hydrogen. The usual kinetic theory expression for pressure:
| (a) | will be valid. |
| (b) | will not be valid, since the ions would experience forces other than due to collisions with the walls. |
| (c) | will not be valid, since collisions with walls would not be elastic. |
| (d) | will not be valid because isotropy is lost. |
Choose the correct alternatives:
1. only (a)
2. (b), (c)
3. (b), (d)
4. (c), (d)
A vessel of volume V contains a mixture of 1 mole of hydrogen and 1 mole of oxygen (both considered ideal). Let denotes the fraction of molecules with a speed between v and (v+dv) with (v)dv similarly for oxygen. Then,
1. (v) = f(v) obeys the Maxwell's distribution law.
2. will obey Maxwell’s distribution law separately.
3. neither nor will obey Maxwell’s distribution law.
4. and will be the same.
(considering all gases to be ideal)
| 1. | same as the pressure initially. |
| 2. | \(2\) times the pressure initially. |
| 3. | \(10\) times the pressure initially. |
| 4. | \(20\) times the pressure initially. |
The volume versus temperature graphs for a given mass of an ideal gas are shown in the figure at two different values of constant pressure. What can be inferred about relation between \(\mathrm{P_1}\) and \(\mathrm{P_2}\)?
1. \(\mathrm{P_1}>\mathrm{P_2} \)
2. \(\mathrm{P_1}=\mathrm{P_2} \)
3. \(\mathrm{P_1}<\mathrm{P_2} \)
4. data is insufficient
A cylinder containing an ideal gas is in a vertical position and has a piston of mass \(M\) that is able to move up or down without friction (figure). If the temperature is increased,
| 1. | both \(P\) and \(V\) of the gas will change. |
| 2. | only \(P\) will increase according to Charles' law. |
| 3. | \(V\) will change but not \(P.\) |
| 4. | \(P\) will change but not \(V.\) |
Boyle's law is applicable for an:
| 1. | adiabatic process | 2. | isothermal process |
| 3. | isobaric process | 4. | isochoric process |
\(1\) mole of an ideal gas is contained in a cubical volume V, ABCDEFGH at \(300\) K (figure). One face of the cube (EFGH) is made up of a material which totally absorbs any gas molecule incident on it. At any given time:
| 1. | the pressure on EFGH would be zero. |
| 2. | the pressure on all the faces will be equal. |
| 3. | the pressure on EFGH would be double the pressure on ABCD. |
| 4. | the pressure on EFGH would be half that on ABCD. |
A cubic vessel (with faces horizontal \(+\) vertical) contains an ideal gas at NTP. The vessel is being carried by a rocket which is moving at a speed of \(500~\text{ms}^{-1}\) in the vertical direction. The pressure of the gas inside the vessel as observed by us on the ground:
| 1. | remains the same because \(500~\text{ms}^{-1}\) is very much smaller than \(v_\text{rms}\) of the gas. |
| 2. | remains the same because the motion of the vessel as a whole does not affect the relative motion of the gas molecules and the walls. |
| 3. | will increase by a factor equal to \(\left(\dfrac{v_\text{rms}^2+(500)^2}{v_\text{rms}^2}\right) \) where \(v_\text{rms}^2\) was the original mean square velocity of the gas. |
| 4. | will be different on the top wall and bottom wall of the vessel. |
Which of the following diagrams (figure) depicts ideal gas behaviour?
| 1. | (a), (c) | 2. | (a), (d) |
| 3. | (c), (d) | 4. | (a), (b) |
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