done 11th Physics Behaviour of Perfect Gas and Kinetic Theory

• question_answer1)
  Estimate the fraction of molecular volume to the actual volume occupied by oxygen gas at STP. Take the diameter of an oxygen molecule to be .  
  View Answer play_arrow

• question_answer2)
  Molar volume is the volume occupied by 1 mole of any (ideal) gas at standard temperature and pressure (STP : 1 atmospheric pressure, 0°C). Show that it is 22-4 litres. 
  View Answer play_arrow

• question_answer3)
  Fig. 9(NCT).l shows plot of PV/T versus P for                kg of oxygen gas at two different temperatures.                                        (a) What does the dotted plot signify?                                                   (b) Which is true : or ? (c) What is the value of PV/T where the curves meet on the Y-axis?                                  (d) H we obtained similar plots for of hydrogen, would we get the same value of PV/Tat the point where the curves meet on the y-axis ?If not. What mass of hydrogen yields the same value of PV/T (for low pressure high temperature region of the plot) ? (Molecular mass of H =  u, of u,J             
  View Answer play_arrow

• question_answer4)
                  An oxygen cylinder of volume 30 litres has an initial gauge pressure of 15 atm. and a temperature of27°C. After some oxygen is withdrawn from the cylinder, the gauge pressure drops to 11 atm. and its temperature drops to . Estimate the mass of oxygen taken out of the cylinder. (R = J molecular mass of  = 32 u).  
  View Answer play_arrow

• question_answer5)
  An air bubble of volume rises from the bottom of a lake 40 m deep at a temperature of 12°C.To what volume does it grow when it reaches the surface, which is at a temperature of ? Given1atm.                  
  View Answer play_arrow

• question_answer6)
  Estimate the total number of air molecules (inclusive of oxygen, nitrogen, water vapour and other constituents) in a room of capacity 25-0 m3 at a temperature of 27°C and 1 atm pressure. (Boltzmann constant ).  
  View Answer play_arrow

• question_answer7)
  Estimate the average thermal energy of a helium atom at (i) room temperature (27°C) (ii) the temperature on the surface of the Sun (6000K), (in) the temperature of 10 million kelvin (the typical core temperature in the case of a star). 
  View Answer play_arrow

• question_answer8)
                  Three vessels of equal capacity have gases at the same temperature and pressure. The first vessel contains neon (monatomic), the second contains chlorine (diatomic), and the third contains uranium hexafluoride (polyatomic). Do the vessels contain equal number of respective molecules ? Is the root mean square speed of molecules the same in the three cases ? If not, in which case is  the largest  
  View Answer play_arrow

• question_answer9)
                  At what temperature is the root mean square speed of an atom in an argon gas cylinder equal to the r.m.s. speed of a helium gas atom at - 20°C ? (Atomic mass of Ar =  u, of He = u).         
  View Answer play_arrow

• question_answer10)
                  Estimate the mean free path and collision frequency of a nitrogen molecule in a cylinder containing nitrogen at 2 atm. and temperature 17°C. Take the radius of a nitrogen molecule to be roughly  Compare the collision time with the time the molecule moves freely between two successive collisions, (Molecular mass of nitrogen  
  View Answer play_arrow

• question_answer11)
  A meter long narrow bore held horizontally (and closed at one end) contains a 76 cm long mercury thread which traps a 15 cm column of air. What happens if the tube is held vertically with the open end at the bottom ?                                    
  View Answer play_arrow

• question_answer12)
  From a certain apparatus, the diffusion rate of hydrogen has an average value of The diffusion of another gas under the same conditions is measured to have an average rate of  Identify the gas.  
  View Answer play_arrow

• question_answer13)
  A gas in equilibrium has uniform density and pressure throughout its volume. This is strictly true  only if there are no external influences. A gas column under gravity, for example, does not have uniform density (and pressure). As you might expect, its density decreases with height The precise  dependence is given by the so called 'law of atmospheres': where, refer to number density at heights h-^ and h^ respectively. Use this relation to derive the       equation for sedimentation equilibrium of a suspension in a liquid column :               where, p is the density of the suspended particle, and p' that of surrounding medium. [is Avogadro's number, and R is the universal gas constant].  
  View Answer play_arrow

• question_answer14)
  Given below are densities of some solids and liquids. Give rough estimates of the size of their atoms :                

  Substance	Atomic Mass (u)	Density
  Carbon (diamond)
  Gold
  Nitrogen (Liquid)
  Lithium
  Fluorine (liquid)

   
  View Answer play_arrow

• question_answer15)                 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 \[500\,m\,{{s}^{-1}}\] in vertical direction. The pressure of the gas inside the vessel as observed by us on the ground                 (a) remains the same because \[500\,m\,{{s}^{-1}}\] is very much smaller than \[{{\upsilon }_{rms}}\] of the gas.                 (b) remains the same because motion of the vessel as a whole does not affect the relative motion of the gas molecules and the walls.                 (c) will increase by a factor equal to \[{{\upsilon }^{2}}_{rms}+{{(500)}^{2}})/{{\upsilon }^{2}}\,rms,\] where \[{{\upsilon }_{rms}}\] was the original mean square velocity of the gas.                 (d) will be different on the top wall and bottom wall of the vessel.

  View Answer play_arrow

• question_answer16)                   1 mole of an ideal gas is contained in a cubical volume V, AQBCDEFGH at 300 K fig. 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.                 (a) the pressure oil EFGH would be zero.                 (b) the pressure on all die faces will the equal.                 (c) the pressure of EFGH would be double the pressure, on ABCD.                 (a) die pressure on EFGH would be hall' that on ABCD.

  View Answer play_arrow

• question_answer17)                   Boyle's law is applicable for an                 (a) adiabatic process.                 (b) isothermal process.                 (c) isobaric process.                 (d) isochoric process. Exp. Boyle's law stats that

  View Answer play_arrow

• question_answer18)                   A cylinder containing an ideal gas is in vertical position and has a piston of mass M that is able to move up or down without friction (Fig.). If the temperature is increased,                 (a) both  p and V of the gas will change.                 (b) only  p will increase according to Charle's law.                 (c) V will change but not p.                 (d) p will change but not V.

  View Answer play_arrow

• question_answer19)                   Volume versus temperature graphs for a given mass of an ideal gas are shown in Fig. at two different values of constant pressure. What can be inferred about relation between \[{{P}_{1}}\And {{P}_{2}}\]?                 (a) \[{{P}_{1}}>{{P}_{2}}\]                     (b) \[{{P}_{1}}={{P}_{2}}\]                 (c) \[{{P}_{1}}<{{P}_{2}}\]                     (d) data is insufficient.

  View Answer play_arrow

• question_answer20)                   1 mole of \[{{H}_{2}}\], gas is contained in a box of volume \[V=1.00\,{{m}^{3}}\] at \[T=300\,K\]. The gas is heated to a temperature of \[T=3000\,K\] and die gas gets converted to a gas of hydrogen atoms. The final pressure would be (considering all gases to be ideal)                 (a) same as the pressure initially.                 (b) 2 times the pressure initially.                 (c) 10 times die pressure initially.                 (d) 20 times the pressure initially.

  View Answer play_arrow

• question_answer21)                   A vessel of volume V contains a mixture 1 mole of Hydrogen and 1 mole of Oxygen (both considered as ideal). Let \[{{f}_{1}}(\upsilon )d\upsilon ,\] denote die fraction of molecules with speed between \[\upsilon \] and \[(\upsilon +d\upsilon )\] with \[{{f}_{2}}(\upsilon )d\upsilon ,\] similarly for oxygen. Then                 (a) \[{{f}_{1}}(\upsilon )+{{f}_{2}}(\upsilon )\] obeys the Maxwell?s distribution law.                 (b) \[{{f}_{1}}(\upsilon ),\,\,{{f}_{2}}(\upsilon )\] will obey the Maxwell?s distribution law separately.                 (c) Neither \[{{f}_{1}}(\upsilon ),\] nor \[{{f}_{2}}(\upsilon )\] will obey the Maxwell's distribution law.                 (d) \[{{f}_{2}}(\upsilon )\] and \[{{f}_{1}}(\upsilon )\] will be the same.

  View Answer play_arrow

• question_answer22)                   An inflated rubber balloon contains one mole of an ideal gas, has pressure p, volume V and temperature T. If the temperature rises to 1.1 T and the volume is increased to 1.05 V, the final pressure will be                 (a) 1.1 p                                (b) p                 (c) less than p                    (d) between p and 1.1.

  View Answer play_arrow

• question_answer23)                   ABCDEFGH is a hollow cube made of an insulator (fig.) Face ABCD has positive charge on it. Inside the cube, we have ionizied 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.

  View Answer play_arrow

• question_answer24)                   Diatomic molecules like hydrogen have energies due to both translational as well as rotational motion. From the equation in kinetic theory \[pV=\,\frac{2}{3}\,E,\,E\] is                 (a) the total energy per unit volume.                 (b) only the translational part of energy because rotational energy is very small compared to the translational energy.                 (c) only the translational part of the energy because during collisions with the wall pressure relates to change in linear momentum.                 (d) the translational part of the energy because rotational energies of molecules can be of either sign and its average over all the molecules is zero.

  View Answer play_arrow

• question_answer25)                   In a diatomic molecule, the rotational energy at a given temperature                 (a) obeys Maxwell s distribution.                 (b) have die same value for all molecules.                 (c) equals the translational kinetic energy for each molecule.                 (a) is (2/3)rd the translational kinetic energy for each molecule.

  View Answer play_arrow

• question_answer26)                   Which of die following diagrams Fig, depicts ideal gas behaviour?                       (a)      (b)                 (c)       (d)

  View Answer play_arrow

• question_answer27)                   When an ideal gas is compressed adiabatically, its temperature rises: the molecules on the average have more kinetic energy than before. The kinetic energy increase.                 (a) because of collisions with moving parts of the wall only.                 (b) because of collisions with the entire wall.                 (c) because the molecules gets accelerated in their motion inside the volume.                 (d) because of redistribution of energy amongst the molecules.

  View Answer play_arrow

• question_answer28)                   Calculate the number of atoms in 39.4 g gold. Molar mass of gold is 197 g \[mol{{e}^{-1}}\].

  View Answer play_arrow

• question_answer29)                   The volume of a given mass of a gas at \[{{27}^{o}}C\], 1 atm is 100 cc. What will be its volume at \[{{327}^{o}}C\]?

  View Answer play_arrow

• question_answer30)                   The molecules of a given mass of a gas have root mean square speeds of \[100\,m\,{{s}^{-1}}\]at \[27{}^\circ C\] and 1.00 atmospheric pressure. What will be the roots means square speeds of the molecules of the gas at \[127{}^\circ C\] and 2.0 atmospheric pressure?

  View Answer play_arrow

• question_answer31)                   Two molecules of a gas have speed of \[9\times {{10}^{6}}\,m\,{{s}^{-1}}\] and \[1\times {{10}^{6}}\,m\,{{s}^{-1}}\], respectively. What is the root mean square speed of these molecules?

  View Answer play_arrow

• question_answer32)                   A gas mixture consists of 2.0 moles of oxygen and 4.0 moles of neon at temperature T. Neglecting all vibrational modes, calculate the total internal energy of the system (Oxygen has two rotational modes.)    

  View Answer play_arrow

• question_answer33)                   Calculate the ratio of the mean free paths of the molecules of two gases having molecular diameters \[1\overset{\text{o}}{\mathop{\text{A}}}\,\] and \[2\overset{\text{o}}{\mathop{\text{A}}}\,\]. The gases may be considered under identical conditions of temperature, pressure and volume.

  View Answer play_arrow

• question_answer34)                   The container shown in Fig. has two chambers, separated by a partition, of volumes \[{{V}_{1}}=2.0\] litre and \[{{V}_{1}}=3.0\] litre. The chambers contain \[{{\mu }_{1}}=4.0\] and \[{{\mu }_{2}}=\ 5.0\] moles of a gas at pressures \[{{p}_{1}}=1.00\] atm and \[{{p}_{2}}=2.00\] atm. Calculate the pressure after the partition is removed and the mixture attains equilibrium.

  View Answer play_arrow

• question_answer35)                   A gas mixture consists of molecules of types A, B and C with masses \[{{m}_{A}}>{{m}_{B}}>{{m}_{C}}\]. Rank the three types of molecules in decreasing order of (a) average K.E., (b) rms speeds.

  View Answer play_arrow

• question_answer36)                   We have 0.5 g of hydrogen gas in a cubic chamber of size 3 cm kept at NTP. The gas in the chamber is compressed keeping the temperature constant till a final pressure of 100 atm. Is one justified in assuming the ideal gas law, in the final state?                 (Hydrogen molecules can be consider as spheres of radius \[1\,\overset{\text{o}}{\mathop{\text{A}}}\,\]).

  View Answer play_arrow

• question_answer37)                   When air is pumped into a cycle tyre the volume and pressure of the air in the tyre both are increased. What about Boyle's law in this case?

  View Answer play_arrow

• question_answer38)                   A balloon has 5.0 g mole of helium at \[{{7}^{o}}C\]. Calculate                 (a) the number of atoms of helium in the balloon,                 (b) the total internal energy of the system.

  View Answer play_arrow

• question_answer39)                   Calculate the number of degrees of freedom of molecules of hydrogen in 1 cc of hydrogen E gas at NTP.

  View Answer play_arrow

• question_answer40)                   An insulated container containing monoatomic gas of molar mass m is moving with velocity \[{{\upsilon }_{0}}.\] If the container is suddenly stopped, find the change in temperature.

  View Answer play_arrow

• question_answer41)                   Explain why                 (a) there is no atmosphere on moon.                 (b) there is fall in temperature with altitude.

  View Answer play_arrow

• question_answer42)                   Consider an ideal gas with following distribution of speeds.                 Speed (m/s)                       % of molecules                 200                                         10                 400                                         20                 600                                         40                 800                                         20                 1000                                       10                 (i) Calculate \[{{V}_{rms}}\] and hence T. \[(m=3.0\times {{10}^{26}}kg)\]                 (ii)If all the molecules with speed 1000 m/s escape from the system, calculate new \[{{V}_{rms}}\]and hence T.

  View Answer play_arrow

• question_answer43)                   Ten small planes are flying at a speed of 150 km/li in total darkness in an air space that is \[20\times 20\times 1.5\text{ }k{{m}^{3}}\] in volume. You are in one of the planes, flying at random within this space with no way of knowing where the other planes are. On the average about how long a time will elapse between near collision with your plane. Assume for this rough computation that a saftey region around die plane can be approximated by a sphere of radius 10 m.

  View Answer play_arrow

• question_answer44)                   A box of \[1.00\,{{m}^{3}}\] is filled with nitrogen at 1.50 atm at 300 K. The box has a hole of an area \[0.010\,m{{m}^{2}}\]. How much time is required for the pressure to reduce by 0.10 atm, if the pressure outside is 1 atm?

  View Answer play_arrow

• question_answer45)                   Consider a rectangular block of wood moving with a velocity \[{{\upsilon }_{0}}\] in a gas at temperature T and mass density \[\rho \]. Assume the velocity is along x-axis and the area of cross-section of the block perpendicular to \[{{\upsilon }_{0}}\] is A. Show that the drag force on the block is,  \[4\,\rho \,A{{\upsilon }_{0}}\]\[\sqrt{\frac{kT}{m}},\] where \[m\] is the mass of the gas molecule.

  View Answer play_arrow