JEE Main & Advanced Physics Kinetic Theory of Gases Question Bank

done Topic Test - Kinetic Theory Of Gases-2 Total Questions - 40

• question_answer1)
  The volume of a gas at \[20{}^\circ C\] is \[200ml.\] If the temperature is reduced to \[20{}^\circ C\]at constant pressure, its volume will be
  A)
  \[172.6ml\] done clear
  B)
  \[17.26ml\] done clear
  C)
  \[192.7ml\] done clear
  D)
  \[19.27ml\]         done clear
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• question_answer2)
  Volume of gas become four times if 
  A)
  Temperature become four times at constant pressure done clear
  B)
  Temperature become one fourth at constant pressure done clear
  C)
  Temperature becomes two times at constant pressure done clear
  D)
  Temperature becomes half at constant pressure done clear
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• question_answer3)
  For ideal gas, which statement is not true
  A)
  It obeys Boyle's law done clear
  B)
  It follows \[PV=RT\]        done clear
  C)
  Internal energy depends on temperature only done clear
  D)
  It follows Vander-Waal's equation done clear
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• question_answer4)
  Two thermally insulated vessels 1 and 2 are filled with air at temperatures \[({{T}_{1}},\,\,{{T}_{2}}),\] volume \[({{V}_{1}},\,\,{{V}_{2}})\] and pressure \[({{P}_{1}},\,\,{{P}_{2}})\] respectively. If the valve joining the two vessels is opened, the temperature inside the vessel at equilibrium will be         
  A)
  \[{{T}_{1}}+{{T}_{2}}\] done clear
  B)
  \[({{T}_{1}}+{{T}_{2}})/2\] done clear
  C)
  \[\frac{{{T}_{1}}{{T}_{2}}({{P}_{1}}{{V}_{1}}+{{P}_{2}}{{V}_{2}})}{{{P}_{1}}{{V}_{1}}{{T}_{2}}+{{P}_{2}}{{V}_{2}}{{T}_{1}}}\] done clear
  D)
  \[\frac{{{T}_{1}}{{T}_{2}}({{P}_{1}}{{V}_{1}}+{{P}_{2}}{{V}_{2}})}{{{P}_{1}}{{V}_{1}}{{T}_{1}}+{{P}_{2}}{{V}_{2}}{{T}_{2}}}\] done clear
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• question_answer5)
  Equation of gas in terms of pressure (P), absolute temperature (T) and density is         
  A)
  \[\frac{{{P}_{1}}}{{{T}_{1}}{{d}_{1}}}=\frac{{{P}_{2}}}{{{T}_{2}}{{d}_{2}}}\] done clear
  B)
  \[\frac{{{P}_{1}}{{T}_{1}}}{{{d}_{1}}}=\frac{{{P}_{2}}{{T}_{2}}}{{{d}_{2}}}\] done clear
  C)
  \[\frac{{{P}_{1}}{{d}_{2}}}{{{T}_{1}}}=\frac{{{P}_{2}}{{d}_{1}}}{{{T}_{1}}}\] done clear
  D)
  \[\frac{{{P}_{1}}{{d}_{1}}}{{{T}_{1}}}=\frac{{{P}_{2}}{{d}_{2}}}{{{T}_{2}}}\] done clear
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• question_answer6)
  In thermal equilibrium, the average velocity of gas molecules is                                
  A)
  Proportional to \[\sqrt{T}\] done clear
  B)
  Proportional to \[{{T}^{2}}\] done clear
  C)
  Proportional to \[{{T}^{3}}\] done clear
  D)
  Zero done clear
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• question_answer7)
  The molecules of a given mass of a gas have a r.m.s. velocity of 200 m/sec at \[27{}^\circ C\] and \[1.0\times {{10}^{5}}\,N/{{m}^{2}}\] pressure. When the temperature is \[127{}^\circ C\]and pressure is  \[0.5\times {{10}^{5}}\,N/{{m}^{2}}\], the r.m.s. velocity in  m/sec will be
  A)
  \[\frac{100\sqrt{2}}{3}\] done clear
  B)
  \[100\sqrt{2}\] done clear
  C)
  \[\frac{400}{\sqrt{3}}\]  done clear
  D)
  None of the above done clear
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• question_answer8)
  On any planet, the presence of atmosphere implies (\[{{C}_{rms}}\]= root mean square velocity of molecules and \[{{V}_{e}}\]= escape velocity)
  A)
  \[{{C}_{rms}}<<{{V}_{e}}\] done clear
  B)
  \[{{C}_{rms}}>{{V}_{e}}\] done clear
  C)
  \[{{C}_{rms}}={{V}_{e}}\] done clear
  D)
  \[{{C}_{rms}}=0\] done clear
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• question_answer9)
  If \[{{V}_{H}},\,\,{{V}_{N}}\] and \[{{V}_{O}}\] denote the root-mean square velocities of molecules of hydrogen, nitrogen and oxygen respectively at a given temperature, then 
  A)
  \[{{V}_{N}}>{{V}_{O}}>{{V}_{H}}\] done clear
  B)
  \[{{V}_{H}}>{{V}_{N}}>{{V}_{O}}\] done clear
  C)
  \[{{V}_{O}}={{V}_{N}}={{V}_{H}}\] done clear
  D)
  \[{{V}_{O}}>{{V}_{H}}>{{V}_{N}}\] done clear
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• question_answer10)
  A cubical box with porous walls containing an equal number of \[{{O}_{2}}\] and \[{{H}_{2}}\] molecules is placed in a large evacuated chamber. The entire system is maintained at constant temperature T. The ratio of \[{{v}_{rms}}\]of \[{{O}_{2}}\]molecules to that of the \[{{v}_{rms}}\]of \[{{H}_{2}}\]molecules, found in the chamber outside the box after a short interval is                                   
  A)
   \[\frac{1}{2\sqrt{2}}\] done clear
  B)
  \[\frac{1}{4}\] done clear
  C)
  \[\frac{1}{\sqrt{2}}\] done clear
  D)
  \[\sqrt{2}\] done clear
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• question_answer11)
  For a gas \[\frac{R}{{{C}_{V}}}=0.67\]. This gas is made up of molecules which are
  A)
  Diatomic done clear
  B)
  Mixture of diatomic and polyatomic molecules done clear
  C)
  Monoatomic done clear
  D)
  Polyatomic done clear
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• question_answer12)
  The specific heat of a gas            
  A)
  Has only two values \[{{C}_{p}}\] and \[{{C}_{v}}\] done clear
  B)
  Has a unique value at a given temperature done clear
  C)
  Can have any value between 0 and \[\infty \] done clear
  D)
  Depends upon the mass of the gas done clear
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• question_answer13)
  A gaseous mixture contains equal number of hydrogen and nitrogen molecules. Specific heat measurements on this mixture at temperatures below 100 K would indicate that the value of \[\gamma \] (ratio of specific heats) for this mixture is
  A)
  3/2 done clear
  B)
  4/3 done clear
  C)
  5/3 done clear
  D)
  7/5 done clear
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• question_answer14)
  The degrees of freedom of a stationary rigid body about its axis will be                      
  A)
  One done clear
  B)
  Two done clear
  C)
  Three done clear
  D)
  Four done clear
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• question_answer15)
  The relation between the gas  pressure P and average kinetic energy per unit volume E is
  A)
  \[P=\frac{1}{2}E\] done clear
  B)
  P = E done clear
  C)
  \[P=\frac{3}{2}E\] done clear
  D)
  \[P=\frac{2}{3}E\] done clear
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• question_answer16)
  The average kinetic energy of a gas at \[23{}^\circ C\] and 75 cm pressure is \[5\times {{10}^{-14}}\,erg\] for \[{{H}_{2}}\]. The mean kinetic energy of the \[{{O}_{2}}\]  at \[227{}^\circ C\] and 150 cm pressure will be
  A)
  \[80\times {{10}^{-14}}\,erg\]    done clear
  B)
  \[20\times {{10}^{-14}}\,erg\] done clear
  C)
  \[40\times {{10}^{-14}}\,erg\] done clear
  D)
  \[10\times {{10}^{-14}}\,erg\] done clear
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• question_answer17)

  Read the given statements and decide which is/are correct on the basis of kinetic theory of gases

  (I) Energy of one molecule at absolute temperature is zero

  (II) r.m.s. speeds of different gases are same at same temperature

  (III) For one gram of all ideal gas kinetic energy is same at same temperature

  (IV) For one mole of all ideal gases mean kinetic energy is same at same temperature

  A)
  All are correct done clear
  B)
  I and IV are correct done clear
  C)
  IV is correct done clear
  D)
  None of these done clear
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• question_answer18)
  At the same temperature and pressure and volume of two gases, which of the following quantities is constant
  A)
  Total number of molecules done clear
  B)
  Average kinetic energy done clear
  C)
  Root mean square velocity done clear
  D)
  Mean free path done clear
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• question_answer19)
  Vapour is injected at a uniform rate in a closed vessel which was initially evacuated. The pressure in the vessel
  A)
  Increase continuously done clear
  B)
  Decreases continuously done clear
  C)
  First increases and then decreases done clear
  D)
  First increase and then becomes constant done clear
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• question_answer20)
  The kinetic energy of one mole gas at 300K temperature, is E. At 400K temperature kinetic energy is \[{E}'.\] The value of \[{E}'/E\] is       
  A)
  1.33 done clear
  B)
   \[\sqrt{\left( \frac{4}{3} \right)}\] done clear
  C)
  \[\frac{16}{9}\] done clear
  D)
   2 done clear
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• question_answer21)
  When air is filled in the balloon, the pressure and volume both increases while temperature does not change. Here Boyle's law is not obeyed because
  A)
  Mass of air is negligible done clear
  B)
  Mass of air does not remain constant done clear
  C)
  Air is not perfect gas done clear
  D)
  Pressure inside the balloon is less than that of the atmospheric pressure done clear
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• question_answer22)
  At NTP, sample of equal volume of chlorine and oxygen is taken. Now ratio of No. of molecules
  A)
  1 : 1      done clear
  B)
  32 : 27 done clear
  C)
  2 : 1 done clear
  D)
  16 : 14 done clear
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• question_answer23)
  That gas cannot be liquified
  A)
  Which obeys Vander Waal's equation done clear
  B)
  Which obeys gas equation at every temperature and pressure done clear
  C)
  The molecules of which are having potential energy done clear
  D)
  Which is a inert gas done clear
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• question_answer24)
  A flask is filled with 13 gm of an ideal gas at \[27{}^\circ C\]and its temperature is raised to\[52{}^\circ C\]. The mass of the gas that has to be released to maintain the temperature of the gas in the flask at \[52{}^\circ C\]and the pressure remaining the same is
  A)
  2.5 g     done clear
  B)
  2.0 g done clear
  C)
  1.5 g     done clear
  D)
  1.0 g done clear
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• question_answer25)
  The value of critical temperature in terms of Vander Waal’s constant a and b is          
  A)
  \[{{T}_{c}}=\frac{8a}{27Rb}\] done clear
  B)
  \[{{T}_{c}}=\frac{a}{2Rb}\] done clear
  C)
  \[{{T}_{c}}=\frac{8}{27Rb}\] done clear
  D)
  \[{{T}_{c}}=\frac{27a}{8Rb}\] done clear
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• question_answer26)
  The value of PV/T for one mole of an ideal gas is nearly equal to                             
  A)
  \[2J\text{ }mo{{l}^{1}}{{K}^{1}}\]    done clear
  B)
  \[8.3cal\text{ }mo{{l}^{1}}{{K}^{1}}\] done clear
  C)
  \[4.2J\text{ }mo{{l}^{1}}{{K}^{1}}\] done clear
  D)
  \[2cal\text{ }mo{{l}^{1}}{{K}^{1}}\] done clear
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• question_answer27)
  The root mean  square velocity  of a gas molecule of mass m at a given temperature is proportional to
  A)
  \[{{m}^{0}}\] done clear
  B)
  m done clear
  C)
  \[\sqrt{m}\]        done clear
  D)
  \[\frac{1}{\sqrt{m}}\] done clear
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• question_answer28)
  According to the kinetic theory of gases the r.m.s. velocity of gas molecules is directly proportional to
  A)
  T done clear
  B)
  \[\sqrt{T}\] done clear
  C)
  \[{{T}^{2}}\] done clear
  D)
  \[1/\sqrt{T}\] done clear
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• question_answer29)
  By what factor the r.m.s. velocity will change, if the temperature is raised from \[27{}^\circ C\] to \[327{}^\circ C\]
  A)
  \[\sqrt{2}\] done clear
  B)
  2 done clear
  C)
  \[2\sqrt{2}\] done clear
  D)
  1 done clear
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• question_answer30)
  If the ratio of vapour density for hydrogen and oxygen is \[\frac{1}{16}\], then under constant pressure the ratio of their rms velocities will be
  A)
  \[\frac{4}{1}\] done clear
  B)
  \[\frac{1}{4}\] done clear
  C)
  \[\frac{1}{16}\] done clear
  D)
  \[\frac{16}{1}\] done clear
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• question_answer31)
  A monoatomic gas molecule has  
  A)
  Three degrees of freedom done clear
  B)
  Four degrees of freedom done clear
  C)
  Five degrees of freedom done clear
  D)
  Six degrees of freedom done clear
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• question_answer32)
  The following sets of values for \[{{C}_{V}}\] and \[{{C}_{P}}\] of a gas has been reported by different students. The units are cal/gm-mole-K. Which of these sets is most reliable
  A)
  \[{{C}_{v}}=3,\,{{C}_{p}}=5\] done clear
  B)
  \[{{C}_{V}}=4,\,{{C}_{P}}=6\] done clear
  C)
  \[{{C}_{v}}=3,\,{{C}_{p}}=2\] done clear
  D)
  \[{{C}_{V}}=3,\,{{C}_{P}}=4.2\] done clear
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• question_answer33)
  The specific heat of 1 mole of an ideal gas at constant pressure \[({{C}_{P}})\] and at constant volume \[({{C}_{V}})\] which is correct
  A)
  \[{{C}_{P}}\] of hydrogen gas is \[\frac{5}{2}R\] done clear
  B)
  \[{{C}_{V}}\] of hydrogen gas is \[\frac{7}{2}R\] done clear
  C)
  \[{{H}_{2}}\] has very small values of \[{{C}_{p}}\] and \[{{C}_{V}}\] done clear
  D)
  \[{{C}_{p}}-{{C}_{V}}~=1.99cal/mole-K\]  for \[{{H}_{2}}\] done clear
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• question_answer34)
  The value of the gas constant (R) calculated from the perfect gas equation is 8.32 joules/gm mole K, whereas its value calculated from the knowledge of \[{{C}_{P}}\] and \[{{C}_{V}}\] of the gas is 1.98 cal/gm mole K. From this data, the value of J is           
  A)
  \[4.16\ J/cal\] done clear
  B)
  \[4.18\ J/cal\] done clear
  C)
  \[4.20\ J/cal\] done clear
  D)
  \[4.22\ J/cal\] done clear
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• question_answer35)
  The pressure exerted by the gas on the walls of the container because
  A)
  It loses kinetic energy done clear
  B)
  It sticks with the walls done clear
  C)
  On collision with the walls there is a change in momentum done clear
  D)
  It is accelerated towards the walls done clear
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• question_answer36)
  Consider a gas with density \[\rho \] and \[\bar{c}\] as the root mean square velocity of its molecules contained in a volume. If the system moves as whole with velocity v, then the pressure exerted by the gas is
  A)
  \[\frac{1}{3}\rho \,{{\bar{c}}^{2}}\] done clear
  B)
  \[\frac{1}{3}\rho {{(c+v)}^{2}}\] done clear
  C)
  \[\frac{1}{3}\rho {{(\bar{c}-v)}^{2}}\] done clear
  D)
  \[\frac{1}{3}\rho {{({{c}^{-2}}-v)}^{2}}\] done clear
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• question_answer37)
  The time average of the kinetic energy of one molecule of a gas taken over a long period of time
  A)
  Is proportional to the square root of the absolute temperature of the gas done clear
  B)
  Is proportional to the absolute temperature of the gas done clear
  C)
  Is proportional to the square of the absolute temperature of the gas done clear
  D)
  Does not depend upon the absolute temperature of the gas done clear
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• question_answer38)
  The average translational energy and the r.m.s. speed of molecules in a sample of oxygen gas at 300 K are \[6.21\times {{10}^{-21}}\,J\] and 484 m/s respectively. The corresponding values at 600 K are nearly (assuming ideal gas behaviour)
  A)
  \[12.42\times {{10}^{21}}\,J,\ 968\,m/s\]           done clear
  B)
  \[8.78\times {{10}^{21}}J,\ 684\,m/s\] done clear
  C)
  \[6.21\times {{10}^{21}}\,J,\,968\,m/s\] done clear
  D)
  \[12.42\times {{10}^{21}}\,J,\ 684\,m/s\] done clear
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• question_answer39)
  A gas mixture consists of molecules of type 1, 2 and 3, with molar masses \[{{m}_{1}}>{{m}_{2}}>{{m}_{3}}.\] \[{{V}_{rms}}\] and \[\overline{K}\] are the r.m.s. speed and average kinetic energy of the gases. Which of the following is true
  A)
  \[{{\left( {{V}_{rms}} \right)}_{1}}<\text{ }{{\left( {{V}_{rms}} \right)}_{2}}<\text{ }{{\left( {{V}_{rms}} \right)}_{3}}\]  and \[{{(\overline{K})}_{1}}={{(\overline{K})}_{2}}=({{\overline{K}}_{3}})\] done clear
  B)
  \[{{\left( {{V}_{rms}} \right)}_{1}}=\text{ }{{\left( {{V}_{rms}} \right)}_{2}}=\text{ }{{\left( {{V}_{rms}} \right)}_{3}}\]  and \[{{(\overline{K})}_{1}}={{(\overline{K})}_{2}}>{{(\overline{K})}_{3}}\] done clear
  C)
  \[{{\left( {{V}_{rms}} \right)}_{1}}>{{\left( {{V}_{rms}} \right)}_{2}}>{{\left( {{V}_{rms}} \right)}_{3}}\]  and \[{{(\overline{K})}_{1}}<{{(\overline{K})}_{2}}>({{\overline{K}}_{3}})\] done clear
  D)
  \[{{\left( {{V}_{rms}} \right)}_{1}}>{{\left( {{V}_{rms}} \right)}_{2}}>{{\left( {{V}_{rms}} \right)}_{3}}\]  and \[{{(\overline{K})}_{1}}<{{(\overline{K})}_{2}}<{{(\overline{K})}_{3}}\] done clear
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• question_answer40)
  The average translational kinetic energy of a hydrogen gas molecules at NTP will be [Boltzmann’s constant \[{{k}_{B}}=1.38\times {{10}^{-23}}J/K]\]          
  A)
  \[0.186\times {{10}^{-20}}\]Joule done clear
  B)
  \[0.372\times {{10}^{-20}}\]Joule done clear
  C)
  \[0.56\times {{10}^{-20}}\] Joule done clear
  D)
  \[5.6\times {{10}^{-20}}\]Joule done clear
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