JEE Main & Advanced Physics Kinetic Theory of Gases Question Bank

done Mock Test - Kinetic Theory of Gases and Laws of Thermodynamics Total Questions - 25

• question_answer1)
  One mole of an ideal monatomic gas requires 210 J heat to raise the temperature by 10 K, when heated at constant temperature. If the same gas is heated at constant volume to raise the temperature by 10 K then heat required is
  A)
  238 J done clear
  B)
  126 J done clear
  C)
  210 J   done clear
  D)
  350 J done clear
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• question_answer2)
  Energy of all molecules of a monatomic gas having a volume \[F\] and pressure \[p\] is 3/2\[P\]\[V\]. The total translational kinetic energy of all molecules of a diatomic gas at the same volume and pressure is
  A)
  \[1/2\,PV\]         done clear
  B)
  \[3/2\,PV\] done clear
  C)
  \[5/2\,PV\]        done clear
  D)
  \[3\,PV\] done clear
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• question_answer3)
  Certain amount of an ideal gas is contained in a closed vessel. The vessel is moving with a constant velocity\[v\]. The molecular mass of gas is\[M\]. The rise in temperature of the gas when the vessel is suddenly stopped is \[(\gamma ={{C}_{P}}/{{C}_{V}})\]
  A)
  \[\frac{M{{v}^{2}}(\gamma -1)}{2R(\gamma +1)}\]      done clear
  B)
  \[\frac{M{{v}^{2}}(\gamma -1)}{2R}\] done clear
  C)
  \[\frac{M{{v}^{2}}}{2R(\gamma +1)}\]           done clear
  D)
  \[\frac{M{{v}^{2}}}{2R(\gamma -1)}\] done clear
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• question_answer4)
  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 root mean square speeds of the molecules of the gas at \[127{}^\circ C\] and 2.0 atmospheric pressure?
  A)
  \[\frac{150}{\sqrt{3}}m/s\]        done clear
  B)
  \[\frac{125}{\sqrt{3}}m/s\] done clear
  C)
  \[\frac{200}{\sqrt{3}}m/s\]        done clear
  D)
  \[100\sqrt{3}m/s\] done clear
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• question_answer5)
  A closed vessel contains 8 g of oxygen and 7 g of nitrogen. The total pressure is 10 atm at a given temperature. If now oxygen is absorbed by introducing a suitable absorbent, the pressure of the remaining gas in atm will be
  A)
  2                      done clear
  B)
  10      done clear
  C)
  4                     done clear
  D)
  5 done clear
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• question_answer6)
  The specific heat at constant volume for the monatomic argon is 0.075 kcal/kg-K, whereas its gram molecular specific heat is\[{{C}_{v}}=2.98\,cal/mol/k\]. The mass of the argon atom is (Avogadro's number \[=6.02\times {{10}^{23}}\] molecules/mol)
  A)
  \[6.60\times {{10}^{-23}}g\]    done clear
  B)
  \[3.30\times {{10}^{-23}}g\] done clear
  C)
  \[2.20\times {{10}^{-23}}g\] done clear
  D)
  \[13.20\times {{10}^{-23}}g\] done clear
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• question_answer7)
  A cyclic process ABCD is shown in the following P-V diagram. Which of the following curves represents the same process?
  A)
  done clear
  B)
    done clear
  C)
    done clear
  D)
    done clear
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• question_answer8)
  A thermodynamic process is shown in figure. The pressures and volumes corresponding to some points in the figure are:\[{{P}_{A}}=3\times {{10}^{4}}Pa,\,\,{{P}_{B}}=8\times {{10}^{4}}Pa\]\[and\,{{V}_{A}}=2\times {{10}^{-3}}{{m}^{3}},\,{{V}_{D}}=5\times {{10}^{-3}}m\] In process\[AB\], 600 J of heat is added to the system and in process\[BC\], 200 J of heat is added to the system. The change in internal energy of the system in process AC would be
  A)
  560 J    done clear
  B)
  800 J done clear
  C)
  600 J   done clear
  D)
  640 J done clear
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• question_answer9)
  Heat energy absorbed by a system in going through a cyclic process shown in figure is
  A)
  \[{{10}^{7}}\pi J\]      done clear
  B)
  \[{{10}^{4}}\pi J\] done clear
  C)
  \[{{10}^{2}}\pi J\]      done clear
  D)
  \[{{10}^{-3}}\pi J\] done clear
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• question_answer10)
  In a mechanical refrigerator, the low temperature coils are at a temperature of \[-23{}^\circ C\] and the compressed gas in the condenser has a temperature of\[27{}^\circ C\]. The theoretical coefficient of performance is
  A)
  5                      done clear
  B)
  8       done clear
  C)
  6                     done clear
  D)
  6.5 done clear
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• question_answer11)
  A reversible engine converts one-sixth of the heat input into work. When the temperature of the sink is reduced by\[62{}^\circ C\], the efficiency of the engine is doubled. The temperatures of the source and sink are
  A)
  \[80{}^\circ C\], \[37{}^\circ C\]           done clear
  B)
  \[95{}^\circ C\], \[98{}^\circ C\] done clear
  C)
  \[90{}^\circ C\], \[37{}^\circ C\]           done clear
  D)
  \[99{}^\circ C\], \[37{}^\circ C\] done clear
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• question_answer12)
  Carbon monoxide is carried around a closed cyclic process\[abc\], in which be is an isothermal process, as shown in figure. The gas absorbs 7000 J of heat as its temperature is increased from 300 K to 1000 K in going from a to b. The quantity of heat ejected by the gas during the process ca is
  A)
  4200 J   done clear
  B)
  500 J done clear
  C)
  9000J   done clear
  D)
  9800J done clear
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• question_answer13)
  The relation between internal energy \[U\], pressure \[P\] and volume \[V\] of a gas in an adiabatic process is \[U=a+bPV\] where a and b are constants. What is the effective value of adiabatic constant\[\gamma \]?
  A)
  \[\frac{a}{b}\]              done clear
  B)
  \[\frac{b+1}{b}\] done clear
  C)
  \[\frac{a+1}{a}\]          done clear
  D)
  \[\frac{b}{a}\] done clear
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• question_answer14)
  A diatomic ideal gas is heated at constant volume until the pressure is doubled and again heated at constant pressure until the volume is doubled. The average molar heat capacity for the whole process is
  A)
  \[\frac{13R}{6}\]           done clear
  B)
  \[\frac{19R}{6}\] done clear
  C)
  \[\frac{23R}{6}\]           done clear
  D)
  \[\frac{17R}{6}\] done clear
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• question_answer15)
  A diatomic ideal gas undergoes a thermodynamic change according to the \[P\]-\[V\] diagram shown in figure. The total heat given to the gas is nearly
  A)
  \[2.5{{P}_{0}}{{V}_{0}}\] done clear
  B)
  \[1.4{{P}_{0}}{{V}_{0}}\] done clear
  C)
  \[3.9{{P}_{0}}{{V}_{0}}\]      done clear
  D)
  \[1.1{{P}_{0}}{{V}_{0}}\] done clear
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• question_answer16)
  Three closed vessels\[A\], \[B\] and \[C\] are at the same temperature \[T\] and contain gases which obey the Maxwellian distribution of velocities. Vessel contains only\[{{O}_{2}}\], \[B\] only \[{{N}_{2}}\] and \[C\] a mixture of equal quantities of \[{{O}_{2}}\] and \[{{N}_{2}}\]. If the average speed of the \[{{O}_{2}}\] molecules in vessel A is \[{{V}_{2}}\] that of the \[{{N}_{3}}\] molecules in vessel B is \[{{V}_{2}}\], the average speed of the \[{{O}_{2}}\] molecules in vessel C is (where \[M\] is the mass of an oxygen molecule)
  A)
  \[({{V}_{2}}+{{V}_{2}})/2\]   done clear
  B)
  \[{{V}_{1}}\] done clear
  C)
  \[{{({{V}_{1}}{{V}_{2}})}^{1/2}}\]  done clear
  D)
  \[\sqrt{3kT/M}\] done clear
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• question_answer17)
  A light container having a diatomic gas enclosed within is moving with velocity\[v\]. Mass of the gas is \[M\] and number of    mass of moles is n. The kinetic energy of gas w.r.t. ground is
  A)
  \[\frac{1}{2}M{{V}^{2}}+\frac{3}{2}nRT\] done clear
  B)
  \[\frac{1}{2}M{{V}^{2}}\] done clear
  C)
  \[\frac{1}{2}M{{V}^{2}}+\frac{5}{2}nRT\] done clear
  D)
  \[\frac{5}{2}nRT\] done clear
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• question_answer18)
  The air tight and smooth pistons of a cylindrical vessel are connected with a string, as shown. Initially,, pressure and temperature of the gas are \[{{p}_{0}}\] and \[{{T}_{0}}\]. The atmospheric pressure is also\[{{p}_{0}}\]. At a later time, tension in the string is \[\frac{3}{8}{{p}_{0}}A\] where A is the cross-sectional are of the cylinder. At this time, the temperature of the gas has become:
  A)
  \[\frac{3}{8}{{T}_{0}}\]                      done clear
  B)
  \[\frac{3}{4}{{T}_{0}}\] done clear
  C)
  \[\frac{11}{8}{{T}_{0}}\]         done clear
  D)
  \[\frac{13}{8}{{T}_{0}}\] done clear
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• question_answer19)
  The given curve represents the variation of temperature as a function of volume for one mole of an ideal gas. Which of the following curves best represents the variation of pressure as a function of volume?
  A)
    done clear
  B)
    done clear
  C)
    done clear
  D)
    done clear
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• question_answer20)
  A certain mass of an ideal diatomic gas contained in a closed vessel is heated; it is observed that the temperature remains constant; however, half the amount of gas gets dissociated; the ratio of the heat supplied to the gas initial internal energy of the gas will be
  A)
  1:2                    done clear
  B)
  1 : 4 done clear
  C)
  1 :5                  done clear
  D)
  1 : 10 done clear
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• question_answer21)
  A cylinder of fixed capacity 44.8 litre contains a monatomic gas at standard temperature and pressure. The amount of heat required to cylinder by \[10{}^\circ C\]is NR. Find the value of N. (R= universal gas constant)
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• question_answer22)
  A Carnot engine absorbs an amount Q of heat from a reservoir at an abosolute temperature Tand rejects heat to a sink at a temperature of\[T/3\]. The amount of heat rejected is\[Q/M\]. Find the value of \[M\]
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• question_answer23)
  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 is ______.
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• question_answer24)
  Find the amount of work done (in J) to increase the temperature of 1 mol of an ideal gas by \[30{}^\circ C\] if it is expanding under the condition\[V\propto {{T}^{2/3}}\].
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• question_answer25)
  A spherical balloon of volume \[4.00\times {{10}^{3}}c{{m}^{3}}\] contains helium at a pressure of \[1.20\times {{10}^{5}}\] Pa. How many moles of helium are in the balloon if the average kinetic energy of the helium atoms is \[3.60\times {{10}^{-22}}\]J?
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