Physics · JEE Main

Kinetic Theory

168 practice questions with a worked solution for each. Tap an option to see instantly if you are right.

156MCQ12Numerical4With diagram
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  1. 1The ratio of specific heats γ=Cp/Cv\gamma = C_p/C_v for a rigid diatomic gas molecule is:JEE Main/MCQ/Medium
  2. 2The RMS speed of gas molecules at absolute temperature TT is vrmsv_{rms}. If the temperature is increased to 4T4T, the new RMS speed is:JEE Main/MCQ/Medium
  3. 3One gas of n1n_1 mole of molecules at temperature T1T_1, volume V1V_1, and pressure P1P_1, and another gas of n2n_2 mole of molecules at temperature T2T_2, volume V2V_2, and pressure P2P_2, are mixed resulting in pressure PP and volume VV of the mixture. The temperature of the mixture is _____.JEE Main/MCQ/Medium/Gas Laws
  4. 4A mixture of carbon dioxide and oxygen has volume 83108310 cm3^3, temperature 300300 K, pressure 100100 kPa and mass 13.213.2 g. The number of moles of carbon dioxide and oxygen gases in the mixture respectively are _______.
    (Assume both carbon dioxide and oxygen gases behave like ideal gases)     [R=8.31[R = 8.31 J/mol.K]]    JEE Main/MCQ/Medium/Gas Laws
  5. 5The mean free path of a molecule of diameter 5×10−10 m5 \times 10^{-10} \mathrm{~m} at the temperature 41∘C41^{\circ} \mathrm{C} and pressure 1.38×105 Pa1.38 \times 10^{5} \mathrm{~Pa}, is given as ____\_\_\_\_ m.
    (Given     kB=1.38×10−23 J/Kk_{B}=1.38 \times 10^{-23} \mathrm{~J} / \mathrm{K}).    JEE Main/MCQ/Medium/Gas Laws
  6. 6A gas of certain mass filled in a closed cylinder at a pressure of 3.23 kPa has temperature 50∘C50^{\circ} \mathrm{C}. The gas is now heated to double its temperature. The modified pressure is ____\_\_\_\_ Pa. Note: Volume is constant.JEE Main/Numerical/Medium/Gas Laws
  7. 7Consider two boxes containing ideal gases AA and BB such that their temperatures, pressures and number densities are same. The molecular size of AA is half of that of BB and mass of molecule AA is four times that of BB. If the collision frequency in gas BB is 32×1018/s32 \times 10^{18} / \mathrm{s} then collision frequency in gas AA is ____\_\_\_\_ /s/ \mathrm{s}.JEE Main/MCQ/Medium/Gas Laws
  8. 8If the collision frequency of hydrogen molecules in a closed chamber at 27∘C27^{\circ} \mathrm{C} is Z\mathrm{Z}, then the collision frequency of the same system at 127∘C127^{\circ} \mathrm{C} is :JEE Main/MCQ/Medium/Gas Laws
  9. 9The parameter that remains the same for molecules of all gases at a given temperature is :JEE Main/MCQ/Medium/Gas Laws
  10. 10The temperature of a gas having 2.0×10252.0\times {10}^{25} molecules per cubic meter at 1.38atm1.38atm (Given, k=1.38×10−23JK−1)k=1.38\times {10}^{-23}J{K}^{-1}) is :JEE Main/MCQ/Medium/Gas Laws
  11. 11The number of air molecules per cm3{cm}^{3} is increased from 3×10193\times {10}^{19} to 12×1019.12\times {10}^{19}. The ratio of collision frequency of air molecules before and after the increase in number respectively is :JEE Main/MCQ/Medium/Gas Laws
  12. 12The pressure (P)(P) and temperature (T)(T) relationship of an ideal gas obeys the equation PT2=P{T}^{2}= constant. The volume expansion coefficient of the gas will be :JEE Main/MCQ/Medium/Gas Laws
  13. 13A vessel contains 16g16g of hydrogen and 128g128g of oxygen at standard temperature and pressure. The volume of the vessel in cm3{cm}^{3} is :JEE Main/MCQ/Medium/Gas Laws
  14. 14A mixture of hydrogen and oxygen has volume 2000cm32000{cm}^{3}, temperature 300K300K, pressure 100kPa100kPa and mass 0.76g0.76g. The ratio of number of moles of hydrogen to number of moles of oxygen in the mixture will be
    [Take gas constant     R=8.3JK−1mol−1R=8.3J{K}^{-1}{mol}^{-1}]    JEE Main/MCQ/Medium/Gas Laws
  15. 15When a gas filled in a closed vessel is heated by raising the temperature by 1∘C1^{\circ}C, its pressure increases by 0.40.4% The initial temperature of the gas is _____ KK.JEE Main/Numerical/Medium/Gas Laws
  16. 16A balloon carries a total load of 185kg185kg at normal pressure and temperature of 27∘C.27^{\circ}C. What load will the balloon carry on rising to a height at which the barometric pressure is 45cm45cm of HgHg and the temperature is −7∘C.-7^{\circ}C. Assuming the volume constant?JEE Main/MCQ/Medium/Gas Laws
  17. 17The temperature of an open room of volume 30m330{m}^{3} increases from 17∘C17^{\circ}C to 27∘C27^{\circ}C due to the sunshine. The atmospheric pressure in the room remains 1×105Pa1\times {10}^{5}Pa. If ni{n}_{i} and nf{n}_{f} are the number of molecules in the room before and after heating, then nf−ni{n}_{f}-{n}_{i} will be:JEE Main/MCQ/Medium/Gas Laws
  18. 18Modern vacuum pumps can evacuate a vessel down to a pressure of 4.0×10−15\text{4.0}\times 1{0}^{-15} atm. at room temperature (300 K). Taking R = 8.3 JK-1 mole-1, 1 atm = 105 Pa and NAvogadro=6×1023mole−1{\text{N}}_{\text{Avogadro}}=6\times 1{0}^{23}{mole}^{-1}, the mean distance between molecules of gas in an evacuated vessel will be of the order of :JEE Main/MCQ/Medium/Gas Laws
  19. 19This question has Statement-1 and Statement-2. Of the four choices given after the Statements, choose the one that best describes the two Statements.
    Statement 1: The internal energy of a perfect gas is entirely kinetic and depends only on absolute temperature of the gas and not on its pressure or volume.
    Statement 2: A perfect gas is heated keeping pressure constant and later at constant volume. For the same amount of heat the temperature of the gas at constant pressure is lower than that at constant volume.    JEE Main/MCQ/Medium/Gas Laws
  20. 20Three perfect gases at absolute temperatures T1,T2T_1, T_2 and T3T_3 are mixed. The masses of molecules are m1m_1, m2m_2 and m3m_3 and the number of molecules are n1,n2n_1, n_2 and n3n_3 respectively. Assuming no loss of energy, the final temperature of the mixture is :JEE Main/MCQ/Medium/Gas Laws
  21. 21Two thermally insulated vessels 1 and 2 are filled with air at temperatures (T1,T2)\left(T_1, T_2\right), volume (V1,V2)\left(V_1, V_2\right) and pressure (P1,P2)\left(P_1, P_2\right) respectively. If the valve joining two vessels is opened, the temperature inside the vessel at equilibrium will beJEE Main/MCQ/Medium/Gas Laws
  22. 22The r.m.s. speed of oxygen molecules at 47∘C47^{\circ} \mathrm{C} is equal to that of the hydrogen molecules kept at ____\_\_\_\_ ∘C{ }^{\circ} \mathrm{C}. (Mass of oxygen molecule/mass of hydrogen molecule =32/2=32 / 2)JEE Main/MCQ/Medium/Speed of Gas
  23. 23The mean free path and the average speed of oxygen molecules at 300 K and 1 atm are 3×10−7 m3 \times 10^{-7} \mathrm{~m} and 600 m/s600 \mathrm{~m} / \mathrm{s} respectively. Find the frequency of its collisions.JEE Main/MCQ/Medium/Speed of Gas
  24. 24The ratio of vapour densities of two gases at the same temperature is 425\frac{4}{25}, then the ratio of r.m.s. velocities will be:JEE Main/MCQ/Medium/Speed of Gas
  25. 25For a particular ideal gas which of the following graphs represents the variation of mean squared velocity of the gas molecules with temperature?JEE Main/MCQ/Medium/Speed of Gas
  26. 26A sample contains mixture of helium and oxygen gas. The ratio of root mean square speed of helium and oxygen in the sample, is:JEE Main/MCQ/Medium/Speed of Gas
  27. 27If n\mathrm{n} is the number density and d\mathrm{d} is the diameter of the molecule, then the average distance covered by a molecule between two successive collisions (i.e. mean free path) is represented by :JEE Main/MCQ/Medium/Speed of Gas
  28. 28If the root mean square velocity of hydrogen molecule at a given temperature and pressure is 2kms−1,2km{s}^{-1}, the root mean square velocity of oxygen at the same condition in kms−1km{s}^{-1} is:JEE Main/MCQ/Medium/Speed of Gas
  29. 29At which temperature the r.m.s. velocity of a hydrogen molecule equal to that of an oxygen molecule at 47∘C47^{\circ}C ?JEE Main/MCQ/Medium/Speed of Gas
  30. 30The mean free path of molecules of a certain gas at STP is 1500d1500d, where ddis the diameter of the gas molecules. While maintaining the standard pressure, the mean free path of the molecules at 373K373K is approximately:JEE Main/MCQ/Medium/Speed of Gas
  31. 31The rmsrms speed of oxygen molecule in a vessel at particular temperature is (1+5x)12v,{\left(1+\dfrac{5}{x}\right)}^{\dfrac{1}{2}}v, when vv is the average speed of the molecule. The value of xx will be:
    (take     π=227\pi =\dfrac{22}{7})    JEE Main/MCQ/Medium/Speed of Gas
  32. 32If the r.m.s speed of chlorine molecule is 490ms−1490m{s}^{-1} at 27oC{27}^{o}C, the r.m.s speed of argon molecules at the same temperature will be (Atomic mass of argon =39.9u=39.9u, molecular mass of chlorine =70.9u=70.9u)JEE Main/MCQ/Medium/Speed of Gas
  33. 33The root mean square speed of molecules of nitrogen gas at 27∘C27^{\circ}C is approximately: (Given mass of a nitrogen molecule =4.6×10−26kg=4.6\times {10}^{-26}kg and take Boltzmann constant kB=1.4×10−23JK−1{k}_{B}=1.4\times {10}^{-23}J{K}^{-1} )JEE Main/MCQ/Medium/Speed of Gas
  34. 34Three vessels of equal volume contain gases at the same temperature and pressure. The first vessel contains neon (monoatomic), the second contains chlorine (diatomic) and third contains uranium hexafluoride (polyatomic). Arrange these on the basis of their root mean square speed (vrms)\left({v}_{rms}\right) and choose the correct answer from the options given below:JEE Main/MCQ/Medium/Speed of Gas
  35. 35The temperature of an ideal gas is increased from 200K200K to 800K800K. If r.m.s. speed of gas at 200K200K is v0{v}_{0}. Then, r.m.s. speed of the gas at 800K800K will be:JEE Main/MCQ/Medium/Speed of Gas
  36. 36A flask contains hydrogen and oxygen in the ratio of 2:12:1 by mass at temperature 27∘C27^{\circ}C. The ratio of average kinetic energy per molecule of hydrogen and oxygen respectively is :JEE Main/MCQ/Medium/Speed of Gas
  37. 37At 300K300K, the rms speed of oxygen molecules is α+5α\sqrt{\dfrac{\alpha +5}{\alpha }} times to that of its average speed in the gas. Then, the value of α\alpha will be (use π=227\pi =\dfrac{22}{7})JEE Main/MCQ/Medium/Speed of Gas
  38. 38The root mean square velocity of molecules of gas isJEE Main/MCQ/Medium/Speed of Gas
  39. 39Given below are two statements:
    Statement I: The temperature of a gas is     −73∘C-73^{\circ}C. When the gas is heated to 527∘C527^{\circ}C, the root mean square speed of the molecules is doubled.
    Statement II : The product of pressure and volume of an ideal gas will be equal to translational kinetic energy of the molecules.
    In the light of the above statements, choose the correct answer from the options given below:    JEE Main/MCQ/Medium/Speed of Gas
  40. 40The root mean square speed of smoke particles of mass 5×10−17kg5\times {10}^{-17}kg in their Brownian motion in air at NTP is approximately.
    [Given     k=1.38×10−23JK−1k=1.38\times {10}^{-23}J{K}^{-1}]    JEE Main/MCQ/Medium/Speed of Gas
  41. 41A vessel contains 14g14g of nitrogen gas at a temperature of 27∘C27^{\circ}C. The amount of heat to be transferred to the gas to double the r.m.s. speed of its molecules will be : (Take R=8.32Jmol−1k−1R=8.32J{mol}^{-1}{k}^{-1})JEE Main/MCQ/Medium/Speed of Gas
  42. 42Given below are two statements:
    Statement I :The average momentum of a molecule in a sample of an ideal gas depends on temperature.
    Statement II : The rms speed of oxygen molecules in a gas is     vv. If the temperature is doubled and the oxygen molecules dissociate into oxygen atoms, the rms speed will become 2v2v.
    In the light of the above statements, choose the correct answer from the options given below :    JEE Main/MCQ/Medium/Speed of Gas
  43. 43Same gas is filled in two vessels of the same volume at the same temperature. If the ratio of the number of molecules is 1:41:4, then
    AA. The r.m.s. velocity of gas molecules in two vessels will be the same.
    BB. The ratio of pressure in these vessels will be 1:41:4.
    CC. The ratio of pressure will be 1:11:1.
    DD. The r.m.s. velocity of gas molecules in two vessels will be in the ratio of 1:41:4.    JEE Main/MCQ/Medium/Speed of Gas
  44. 44What will be the effect on the root mean square velocity of oxygen molecules if the temperature is doubled and oxygen molecule dissociates into atomic oxygen?JEE Main/MCQ/Medium/Speed of Gas
  45. 45The relation between root mean square speed (vrms)\left({v}_{rms}\right) and most probable speed (vp)\left({v}_{p}\right) for the molar mass MM of oxygen gas molecule at the temperature of 300K300K will beJEE Main/MCQ/Medium/Speed of Gas
  46. 460.056kg0.056kg of Nitrogen is enclosed in a vessel at a temperature of 127∘C127^{\circ}C. The amount of heat required to double the speed of its molecules is_____ kcalkcal.
    (Take     R=2calmoleK−1−1R=2calmole{K-1}^{-1} )    JEE Main/Numerical/Medium/Speed of Gas
  47. 47If the R.M.S. speed of oxygen molecules at 0∘C0^{\circ}C is 160ms−1160m{s}^{-1}. Find the R.M.S. speed of hydrogen molecules at 0∘C0^{\circ}C.JEE Main/MCQ/Medium/Speed of Gas
  48. 48The R.M.S. speeds of the molecules of Hydrogen, Oxygen, and Carbon dioxide at the same temperature are vH,vO{v}_{H},{v}_{O} and vC{v}_{C} respectively, then:JEE Main/MCQ/Medium/Speed of Gas
  49. 49Consider a mixture of gas molecule of types A,BA,B and CC having masses mA<mB<mC.{m}_{A}\lt {m}_{B}\lt {m}_{C}. The ratio of their root mean square speeds at normal temperature and pressure is:JEE Main/MCQ/Medium/Speed of Gas
  50. 50Consider a sample of oxygen behaving like an ideal gas. At 300K300K, the ratio of root-mean-square (RMS) velocity to the average velocity of the gas molecule would be :
    (Molecular weight of oxygen is     32gmol−1;R=8.3JK−1mol−132g{mol}^{-1};R=8.3J{K}^{-1}{mol}^{-1})    JEE Main/MCQ/Medium/Speed of Gas
  51. 51Calculate the value of the mean free path (λ)\left(\lambda \right) for oxygen molecules at temperature 27∘C27^{\circ}C and pressure 1.01×105Pa1.01\times {10}^{5}Pa. Assume the molecular diameter 0.3nm0.3nm and the gas is ideal. (k=1.38×10−23JK−1)\left(k=1.38\times {10}^{-23}J{K}^{-1}\right)JEE Main/MCQ/Medium/Speed of Gas
  52. 52The root-mean-square speed of molecules of a given mass of a gas at 27∘C27^{\circ}C and 11 atmosphere pressure is 200ms−1.200m{s}^{-1}. The root-mean-square speed of molecules of the gas at 127∘C127^{\circ}C and 22 atmosphere pressure is x3ms−1.\dfrac{x}{\sqrt{3}}m{s}^{-1}. The value of xx will be __________.JEE Main/Numerical/Medium/Speed of Gas
  53. 53Assuming the nitrogen molecule is moving with r.m.sr.m.s. velocity at 400K400K, the de-Broglie wave length of nitrogen molecule is close to : (Given : nitrogen molecule weight : 4.64×10−26kg4.64\times {10}^{-26} kg, Boltzman constant : 1.38×10−23JK−11.38\times {10}^{-23} J{K}^{-1}, Planck constant : 6.63×10−34Js6.63\times {10}^{-34} Js)JEE Main/MCQ/Medium/Speed of Gas
  54. 54In a dilute gas at pressure PP and temperature 'tt', the time between successive collision of a molecule varies with TT as :JEE Main/MCQ/Medium/Speed of Gas
  55. 55Nitrogen gas is at 300∘C300^{\circ}C temperature. The temperature (in KK ) at which the rms speed of a H2{H}_{2} molecule would be equal to the rms speed of a nitrogen molecule, is ……….\ldots \ldots \ldots . (Molar mass of N2{N}_{2} gas 28g28g ).JEE Main/Numerical/Medium/Speed of Gas
  56. 56An ideal gas in a closed container is slowly heated. As its temperature increases, which of the following statements are true ?
    (A) the mean free path of the molecules decreases
    (B) the mean collision time between the molecules decreases.
    (C) the mean free path remains unchanged.
    (D) the mean collision time relations unchanged.    JEE Main/MCQ/Medium/Speed of Gas
  57. 57Two gases - argon (atomic radius 0.07nm,0.07nm, atomic weight 4040 ) and xenon (atomic radius 0.1nm,0.1nm, atomic weight 140140 ) have the same number density and are at the same temperature. The ratio of their respective mean free times is closest to:JEE Main/MCQ/Medium/Speed of Gas
  58. 58The plot that depicts the behavior of the mean free time τ\tau (time between two successive collisions) for the molecules of an ideal gas, as a function of temperature (T),\left(T\right), qualitatively, is: (Graphs are schematic and not drawn to scale)JEE Main/MCQ/Medium/Speed of Gas
  59. 59A 25×10−3m325\times {10}^{-3}{m}^{3} volume cylinder is filled with 11 mol of O2{O}_{2} gas at room temperature (300K)(300K) . The molecular diameter of O2{O}_{2} , and its root mean square speed, are found to be 0.3nm0.3nm and 200m/s200m/s , respectively. What is the average collision rate (per second) for an O2{O}_{2} molecule?JEE Main/MCQ/Medium/Speed of Gas
  60. 60For given gas at 1atm1atm pressure, rmsrms speed of the molecules is 200m/s200m/s at 127∘C.127^{\circ}C. At 2atm2atm pressure and at 227∘C,227^{\circ}C, the rmsrms speed of the molecules will be:JEE Main/MCQ/Medium/Speed of Gas
  61. 61The temperature, at which the root mean square velocity of hydrogen molecules equals their escape their escape velocity from the earth, is closest to:
    [[ Boltzmann Constant kB=1.38×10−23J/K{k}_{B}=1.38\times {10}^{-23}J/K
    Avogadro number     NA=6.02×1026/kg{N}_{A}=6.02\times {10}^{26}/kg
    Radius of Earth:     6.4×106m6.4\times {10}^{6}m
    Gravitational acceleration on Earth     =10ms−2]=10m{s}^{-2}]    JEE Main/MCQ/Medium/Speed of Gas
  62. 62An ideal gas is enclosed in a cylinder at pressure of 22 atm and temperature, 300K.300K. The mean time between two successive collisions is 6×10−8s.6\times {10}^{-8}s. If the pressure is doubled and temperature is increased to 500K,500K, the mean time between two successive collisions will be close to:JEE Main/MCQ/Medium/Speed of Gas
  63. 63A mixture of 2 moles of helium gas (atomic mass = 4u) ,, and 1 mole of argon gas (atomic mass = 40 u) is kept at 300K300K in a container. The ratio of their rms speeds [Vrms(helium)Vrms(argon)],\left[\dfrac{{V}_{rms}\left(helium\right)}{{V}_{rms}(argon)}\right], is close to:JEE Main/MCQ/Medium/Speed of Gas
  64. 64At room temperature a diatomic gas is found to have an r.m.s. speed of 1930 ms−11930 \mathrm{~ms}^{-1}. The gas is:JEE Main/MCQ/Medium/Speed of Gas
  65. 65In the isothermal expansion of 10 g10 \mathrm{~g} of gas from volume V\mathrm{V} to 2 V2 \mathrm{~V} the work done by the gas is 575 J575 \mathrm{~J}.
    What is the root mean square speed of the molecules of the gas at that temperature?    JEE Main/MCQ/Medium/Speed of Gas
  66. 66At what temperature is the r.m.s. velocity of a hydrogen molecule equal to that of an oxygen molecule at 47∘C47^{\circ} \mathrm{C} ?JEE Main/MCQ/Medium/Speed of Gas
  67. 67Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
    Statement I: Change in internal energy of a system containing     nn mole of ideal gas can be written as ΔU=nCv(Tf−Ti)=nRγ−1(Tf−Ti)\Delta U = n C_v (T_f - T_i) = \dfrac{nR}{\gamma - 1}(T_f - T_i), where γ=CpCv\gamma = \dfrac{C_p}{C_v}, Ti=T_i = initial temperature, Tf=T_f = final temperature.
    Statement II: Relation between degree of freedom     ff and γ(=Cp/Cv)\gamma (= C_p/C_v) is (γ=1+2f)\left(\gamma = 1 + \dfrac{2}{f}\right)
    Choose the correct answer from the options given below    JEE Main/MCQ/Medium/Degree of Freedom and Specific Heat
  68. 68The volume of an ideal gas increases 8 times and temperature becomes (1/4)th (1 / 4)^{\text {th }} of initial temperature during a reversible change. If there is no exchange of heat in this process (ΔQ=0)(\Delta \mathrm{Q}=0) then identify the gas from the following options (Assuming the gases given in the options are ideal gases):JEE Main/MCQ/Medium/Degree of Freedom and Specific Heat
  69. 69Match the List−I\mathrm {List-I} with List−II\mathrm {List-II}
    List-IList-IIA.Triatomic rigid gasI.CPCV=53B.Diatomic non-rigidgasII.CPCV=75C.Monoatomic gasIII.CPCV=43D.Diatomic rigid gasIV CPCV=97\begin{array}{|l|l|l|l|}\hline & \text{List-I} & & \text{List-II} \\ \hline \text{A.} & \text{Triatomic rigid gas} & \text{I.} & \frac{\mathrm{C}_{\mathrm{P}}}{\mathrm{C}_{\mathrm{V}}}=\frac{5}{3} \\ \hline \text{B.} & \begin{array}{l} \text{Diatomic non-rigid} \\ \text{gas} \end{array} & \text{II.} & \frac{\mathrm{C}_{\mathrm{P}}}{\mathrm{C}_{\mathrm{V}}}=\frac{7}{5} \\ \hline \text{C.} & \text{Monoatomic gas} & \text{III.} & \frac{\mathrm{C}_{\mathrm{P}}}{\mathrm{C}_{\mathrm{V}}}=\frac{4}{3} \\ \hline \text{D.} & \text{Diatomic rigid gas} & \text{IV }& \frac{\mathrm{C}_{\mathrm{P}}}{\mathrm{C}_{\mathrm{V}}}=\frac{9}{7} \\ \hline\end{array}
    Choose the     correct\mathrm {correct} answer from the options given below :    JEE Main/MCQ/Medium/Degree of Freedom and Specific Heat
  70. 70γA\gamma_{\mathrm{A}} is the specific heat ratio of monoatomic gas A having 3 translational degrees of freedom. γB\gamma_B is the specific heat ratio of polyatomic gas B having 3 translational, 3 rotational degrees of freedom and 1 vibrational mode. If γAγB=(1+1n)\frac{\gamma_{\mathrm{A}}}{\gamma_{\mathrm{B}}}=\left(1+\frac{1}{\mathrm{n}}\right), then the value of nn is _______.JEE Main/Numerical/Medium/Degree of Freedom and Specific Heat
  71. 71A mixture of one mole of monoatomic gas and one mole of a diatomic gas (rigid) are kept at room temperature (27∘C)\left(27^{\circ} \mathrm{C}\right). The ratio of specific heat of gases at constant volume respectively is:JEE Main/MCQ/Medium/Degree of Freedom and Specific Heat
  72. 72The specific heat at constant pressure of a real gas obeying PV2=RTP V^2=R T equation is:JEE Main/MCQ/Medium/Degree of Freedom and Specific Heat
  73. 73During an adiabatic process, if the pressure of a gas is found to be proportional to the cube of its absolute temperature, then the ratio of CPCV\frac{C_{\mathrm{P}}}{\mathrm{C}_{\mathrm{V}}} for the gas is :JEE Main/MCQ/Medium/Degree of Freedom and Specific Heat
  74. 74The translational degrees of freedom (ft)\left(f_t\right) and rotational degrees of freedom (fr)\left(f_r\right) of CH4\mathrm{CH}_4 molecule are:JEE Main/MCQ/Medium/Degree of Freedom and Specific Heat
  75. 75Two moles of a monoatomic gas is mixed with six moles of a diatomic gas. The molar specific heat of the mixture at constant volume is :JEE Main/MCQ/Medium/Degree of Freedom and Specific Heat
  76. 76If three moles of monoatomic gas (γ=53)\left(\gamma =\dfrac{5}{3}\right) is mixed with two moles of a diatomic gas (γ=75)\left(\gamma =\dfrac{7}{5}\right), the value of adiabatic exponent γ\gamma for the mixture is:JEE Main/MCQ/Medium/Degree of Freedom and Specific Heat
  77. 77Two thermodynamical process are shown in the figure. The molar heat capacity for process AA and BB are CA{C}_{A} and CB{C}_{B}. The molar heat capacity at constant pressure and constant volume are represented by CP{C}_{P} and CV{C}_{V}, respectively. Choose the correct statement.JEE Main/MCQ/Medium/Degree of Freedom and Specific Heat/With diagram
  78. 78NN moles of a polyatomic gas(f=6)(f=6) must be mixed with two moles of a monoatomic gas so that the mixture behaves as a diatomic gas. The value of NN is:JEE Main/MCQ/Medium/Degree of Freedom and Specific Heat
  79. 79A gas mixture consists of 22 moles of oxygen and 44 moles of neon at temperature TT. Neglecting all vibrational modes, the total internal energy of the system will be:JEE Main/MCQ/Medium/Degree of Freedom and Specific Heat
  80. 80Match List I with List II: List I List II (A) 33 Translational degrees of freedom (I) Monoatomic gases (B) 33 Translational, 22 rotational degrees of freedoms (II) Polyatomic gases (C) 33 Translational, 22 rotational and 11 vibrational degrees of freedom (III) Rigid diatomic gases (D) 33 Translational, 33 rotational and more than one vibrational degrees of freedom (IV) Nonrigid diatomic gases Choose the correct answer from the options given below:JEE Main/MCQ/Medium/Degree of Freedom and Specific Heat
  81. 81One mole of a monoatomic gas is mixed with three moles of a diatomic gas. The molecular specific heat of mixture at constant volume is α24RJmolK−1\dfrac{{\alpha }^{2}}{4}RJmol{K}^{-1}; then the value of α\alpha will be _____ . (Assume that the given diatomic gas has no vibrational mode.)JEE Main/Numerical/Medium/Degree of Freedom and Specific Heat
  82. 82Which statements are correct about degrees of freedom?
    A. A molecule with     nn degrees of freedom has n2{n}^{2} different ways of storing energy.
    B. Each degree of freedom is associated with     12RT\dfrac{1}{2}RT average energy per mole.
    C. A monoatomic gas molecule has     11 rotational degree of freedom where as diatomic molecule has 22 rotational degrees of freedom
    D.     CH4{CH}_{4} has a total to 66 degrees of freedom.
    Choose the correct answer from the option given below:    JEE Main/MCQ/Medium/Degree of Freedom and Specific Heat
  83. 83A gas has nn degrees of freedom. The ratio of specific heat of gas at constant volume to the specific heat of gas at constant pressure will beJEE Main/MCQ/Medium/Degree of Freedom and Specific Heat
  84. 84According to kinetic theory of gases,
    A. The motion of the gas molecules freezes at     0∘C0^{\circ}C.
    B. The mean free path of gas molecules decreases if the density of molecules is increased.
    C. The mean free path of gas molecules increases if temperature is increased keeping pressure constant.
    D. Average kinetic energy per molecule per degree of freedom is     32kBT\dfrac{3}{2}{k}_{B}T (for monoatomic gases).
    Choose the most appropriate answer from the options given below    JEE Main/MCQ/Medium/Degree of Freedom and Specific Heat
  85. 85The ratio of specific heats (CPCV)\left(\dfrac{{C}_{P}}{{C}_{V}}\right) in terms of degree of freedom (f)\left(f\right) is given by :JEE Main/MCQ/Medium/Degree of Freedom and Specific Heat
  86. 86A monoatomic gas performs a work of Q4\dfrac{Q}{4} where QQ is the heat supplied to it. The molar heat capacity of the gas will be _____ RR during this transformation.
    Where     RR is the gas constant.    JEE Main/Numerical/Medium/Degree of Freedom and Specific Heat
  87. 87For a gas CP−CV=R{C}_{\text{P}}-{C}_{\text{V}}=R in a state PP and CP−CV=1.10R{C}_{\text{P}}-{C}_{\text{V}}=1.10R in a state Q,TPQ,{T}_{\text{P}} and TQ{T}_{\text{Q}} are the temperatures in two different states PP and QQ, respectively. ThenJEE Main/MCQ/Medium/Degree of Freedom and Specific Heat
  88. 88The correct relation between the degrees of freedom ff and the ratio of specific heat γ\gamma is:JEE Main/MCQ/Medium/Degree of Freedom and Specific Heat
  89. 89If one mole of the polyatomic gas is having two vibrational modes and β\beta is the ratio of molar specific heats for polyatomic gas (β=CPCv)\left(\beta =\dfrac{{C}_{P}}{{C}_{v}}\right) then the value of β\beta is :JEE Main/MCQ/Medium/Degree of Freedom and Specific Heat
  90. 90A polyatomic ideal gas has 2424 vibrational modes. What is the value of γ?\gamma ?JEE Main/MCQ/Medium/Degree of Freedom and Specific Heat
  91. 91A monoatomic gas of mass 4.0u4.0u is kept in an insulated container. The container is moving with velocity 30ms−130m{s}^{-1}. If the container is suddenly stopped then a change in temperature of the gas (R=R=gas constant) is x3R\dfrac{x}{3R}. Value of xx is,JEE Main/Numerical/Medium/Degree of Freedom and Specific Heat
  92. 92A diatomic gas, having CP=72R{C}_{P}=\dfrac{7}{2}R and CV=52R,{C}_{V}=\dfrac{5}{2}R, is heated at constant pressure. The ratio dU:dQ:dWdU:dQ:dWJEE Main/MCQ/Medium/Degree of Freedom and Specific Heat
  93. 93Molecules of an ideal gas are known to have three translational degrees of freedom. The gas is maintained at a temperature of T. The total internal energy, U of a mole of this gas, and the value of γ=(CpCv)\gamma =\left(\dfrac{{C}_{p}}{{C}_{v}}\right) are given, respectively, byJEE Main/MCQ/Medium/Degree of Freedom and Specific Heat
  94. 94A bullet of mass 5gram5gram, travelling with a speed of 210ms−1210m{s}^{-1} strikes a fixed wooden target. One half of its kinetic energy is converted into heat in the wood. The rise of temperature of the bullet if the specific heat of its material is 0.030(gram∘C)−1(1calorie=4.2×107ergs)0.030{\left(gram^{\circ}C\right)}^{-1}\left(1calorie=4.2\times {10}^{7}ergs\right) close to :JEE Main/MCQ/Medium/Degree of Freedom and Specific Heat
  95. 95To raise the temperature of a certain mass of gas by 50∘C50^{\circ}C at a constant pressure,160160 calories of heat is required. When the same mass of gas is cooled by 100∘C100^{\circ}C at constant volume,240240 calories of heat is released. How many degrees of freedom does each molecule of this gas have (assume gas to be ideal)?JEE Main/MCQ/Medium/Degree of Freedom and Specific Heat
  96. 96
    Consider a gas of triatomic molecules. The molecules are assumed to be triangular and made of massless rigid rods whose vertices are occupied by atoms. The internal energy of a mole of the gas at temperature T is:    JEE Main/MCQ/Medium/Degree of Freedom and Specific Heat/With diagram
  97. 97Consider two ideal diatomic gases AA and BB at some temperature TT . Molecules of the gas AA are rigid, and have a mass mm . Molecules of the gas BB have an additional vibrational mode and have a mass m4\dfrac{m}{4} . The ratio of the specific heats (CV)Aand(CV)B{\left({C}_{V}^{}\right)}_{A}\text{and}{\left({C}_{V}^{}\right)}_{B} of gas AA and B,B, respectively is:JEE Main/MCQ/Medium/Degree of Freedom and Specific Heat
  98. 98Consider a mixture of nn moles of helium gas and 2n2n moles of oxygen gas (molecules taken to be rigid) as an ideal gas. Its CPCV\dfrac{{C}_{P}}{{C}_{V}} value will be:JEE Main/MCQ/Medium/Degree of Freedom and Specific Heat
  99. 99Two moles of an ideal gas, with CPCV=53\dfrac{{C}_{P}}{{C}_{V}}=\dfrac{5}{3}, are mixed with three moles of another ideal gas CPCV=43\dfrac{{C}_{P}}{{C}_{V}}=\dfrac{4}{3}. The value of CPCV\dfrac{{C}_{P}}{{C}_{V}} for the mixture isJEE Main/MCQ/Medium/Degree of Freedom and Specific Heat
  100. 100A diatomic gas with rigid molecules does 10J10J of work when expanded at constant pressure. What would be the heat energy absorbed by the gas, in this process?JEE Main/MCQ/Medium/Degree of Freedom and Specific Heat
  101. 101Two moles of helium gas is mixed with three moles of hydrogen molecules (taken to be rigid). What is the molar specific heat of mixture at constant volume? (R=8.3J/molK)\left(R=8.3J/molK\right)JEE Main/MCQ/Medium/Degree of Freedom and Specific Heat
  102. 102When heat QQ is supplied to a diatomic gas of rigid molecules, at constant volume its temperature increases by ∆T∆T . The heat required to produce the same change in temperature, at a constant pressure is:JEE Main/MCQ/Medium/Degree of Freedom and Specific Heat
  103. 103A massless spring (k=800N/m),\left(k=800 N/m\right), attached with a mass (500g)\left(500 g\right) is completely immersed in 1kg1kg of water. The spring is stretched by 2cm2cm and released so that it starts vibrating. What would be the order of magnitude of the change in the temperature of water when the vibrations stop completely? (Assume that the water container and spring receive negligible heat and specific heat of mass =400J/kgK,=400J/kgK, specific heat of water =4184J/kgK=4184 J/kg K )JEE Main/MCQ/Medium/Degree of Freedom and Specific Heat
  104. 104The specific heats, Cp{C}_{p} and Cv{C}_{v} of a gas of diatomic molecules, A,A, are given (in units of Jmol−1K−1Jmo{l}^{-1}{K}^{-1} ) by 2929 and 22,22, respectively. Another gas of diatomic molecules, B,B, has the corresponding values 3030 and 21.21. If they are treated as ideal gases, then:JEE Main/MCQ/Medium/Degree of Freedom and Specific Heat
  105. 105An ideal gas occupies a volume of 2m32{m}^{3} at a pressure of 3×106Pa.3\times {10}^{6}Pa. The energy of the gas is:JEE Main/MCQ/Medium/Degree of Freedom and Specific Heat
  106. 106A metal ball of mass 0.1 kg0.1 \mathrm{~kg} is heated upto 500∘C500^{\circ} \mathrm{C} and dropped into a vessel of heat capacity 800JK−1800 \mathrm{JK}^{-1} and containing 0.5 kg0.5 \mathrm{~kg} water. The initial temperature of water and vessel is 30∘C30^{\circ} \mathrm{C}. What is the approximate percentage increment in the temperature of the water? [Specific Heat Capacities of water and metal are, respectively, 4200Jkg−4200 \mathrm{Jkg}^{-} 1 K−1{ }^{1} \mathrm{~K}^{-1} and 400Jkg−1 K−1400 \mathrm{Jkg}^{-1} \mathrm{~K}^{-1} ]JEE Main/MCQ/Medium/Degree of Freedom and Specific Heat
  107. 107When 100 g100 \mathrm{~g} of a liquid A\mathrm{A} at 100∘C100^{\circ} \mathrm{C} is added to 50 g50 \mathrm{~g} of a liquid BB at temperature 75∘C75^{\circ} \mathrm{C}, the temperature of the mixture becomes 90∘C90^{\circ} \mathrm{C}. The temperature of the mixture, if 100 g100 \mathrm{~g} of liquid AA at 100∘C100^{\circ} \mathrm{C} is added to 50 g50 \mathrm{~g} of liquid B\mathrm{B} at 50∘C50^{\circ} \mathrm{C}, will be:JEE Main/MCQ/Medium/Degree of Freedom and Specific Heat
  108. 108A gas mixture consists of 3 moles of oxygen and 5 moles of argon at temperature T. Considering only translational and rotational modes, the total internal energy of the system isJEE Main/MCQ/Medium/Degree of Freedom and Specific Heat
  109. 109An unknown metal of mass 192g192 g heated to a temperature of 100∘C100^{\circ}C was immersed into a brass calorimeter of mass 128g128g containing 240g240 g of water at a temperature of 8.4oC.{8.4}^{o}C. Calculate the specific heat of the unknown metal if water temperature stabilizes at 21.5oC.{21.5}^{o}C. (( Specific heat of brass is 394Jkg−1K−1)394J k{g}^{-1}{K}^{-1})JEE Main/MCQ/Medium/Degree of Freedom and Specific Heat
  110. 110A 15g15g mass of nitrogen gas is enclosed in a vessel at a temperature, 27oC{27}^{o}C. The amount of heat transferred to the gas, so that R.M.S.R.M.S. velocity of molecules is doubled, is about.
    [R=8.3J(Kmole)−1]\left[R=8.3J{\left(Kmole\right)}^{-1}\right]    JEE Main/MCQ/Medium/Degree of Freedom and Specific Heat
  111. 111Two moles of helium are mixed with n moles of hydrogen. If CpCv=32\dfrac{{C}_{p}}{{C}_{v}}=\dfrac{3}{2} for the mixture then the value of nn is,JEE Main/MCQ/Medium/Degree of Freedom and Specific Heat
  112. 112The value closest to the thermal velocity of a Helium atom at room temperature (300 K)(300 \mathrm{~K}) in ms−1\mathrm{ms}^{-1} is:
    [kB=1.4×10−23 J/K;mHe=7×10−27 kg]\left[\mathrm{k}_{\mathrm{B}}=1.4 \times 10^{-23} \mathrm{~J} / \mathrm{K} ; \mathrm{m}_{\mathrm{He}}=7 \times 10^{-27} \mathrm{~kg}\right]    JEE Main/MCQ/Medium/Degree of Freedom and Specific Heat
  113. 113An ideal gas has molecules with 55 degrees of freedom. The ratio of specific heats at constant pressure (Cp)\left({C}_{p}\right) and at constant volume (CV)\left({C}_{V}\right) is:JEE Main/MCQ/Medium/Degree of Freedom and Specific Heat
  114. 114Cp−Cv=RM{C}_{p}-{C}_{v}=\dfrac{R}{M} and Cv{C}_{v} are specific heats at constant pressure and constant volume respectively. It is observed that, Cp−Cv=a{C}_{p}-{C}_{v}=a for hydrogen gas and Cp−Cv=b{C}_{p}-{C}_{v}=b for nitrogen gas. The correct relation between aa and bb is:JEE Main/MCQ/Medium/Degree of Freedom and Specific Heat
  115. 115An ideal gas undergoes a quasi-static, reversible process in which its molar heat capacity C remains constant. If during this process the relation of pressure P and volume V is given by PVn=P{V}^{n}= constant, then n is given by (Here CP{C}_{P} and CV{C}_{V} are molar specific heat at constant pressure and constant volume, respectively) :JEE Main/MCQ/Medium/Degree of Freedom and Specific Heat
  116. 116If Cp\mathrm{C}_p and Cv\mathrm{C}_{\mathrm{v}} denote the specific heats of nitrogen per unit mass at constant pressure and constant volume respectively, thenJEE Main/MCQ/Medium/Degree of Freedom and Specific Heat
  117. 117A gaseous mixture consists of 16 g16 \mathrm{~g} of helium and 16 g16 \mathrm{~g} of oxygen. The ratio CpCv\frac{C_p}{C_v} of the mixture isJEE Main/MCQ/Medium/Degree of Freedom and Specific Heat
  118. 118One mole of ideal monoatomic gas (γ=5/30)(\gamma=5 / 30) is mixed with one mole of diatomic gas (γ=7/5)(\gamma=7 / 5). What is γ\gamma for the mixture? γ\gamma denotes the ratio of specific heat at constant pressure, to that at constant volume.JEE Main/MCQ/Medium/Degree of Freedom and Specific Heat
  119. 119During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio Cp/Cv\mathrm{C}_{\mathrm{p}} / \mathrm{C}_{\mathrm{v}} for the gas isJEE Main/MCQ/Medium/Degree of Freedom and Specific Heat
  120. 1201 mole of a gas with γ=7/5\gamma=7 / 5 is mixed with 1 mole of a gas with γ=5/3\gamma=5 / 3, then the value of γ\gamma for the resulting mixture isJEE Main/MCQ/Medium/Degree of Freedom and Specific Heat
  121. 121If 22 mole of an ideal monoatomic gas at temperature TT, is mixed with 66 mole of another ideal monoatomic gas at temperature 2T2T then the temperature of mixture is :JEE Main/MCQ/Medium/Pressure and Energy of gas
  122. 122Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R

    Assertion A: If the average kinetic energy of     H2H_2 and O2O_2 molecules, kept in two different sized containers are same, then their temperatures will be same.

    Reason R: The r.m.s. speed of     H2H_2 and O2O_2 molecules are same at same temperature.

    Choose the correct answer from the options given below    JEE Main/MCQ/Medium/Pressure and Energy of gas
  123. 123A cylindrical tube ABA B of length ll, closed at both ends contains an ideal gas of 1 mol having molecular weight MM. The tube is rotated in a horizontal plane with constant angular velocity ω\omega about an axis perpendicular to ABA B and passing through the edge at end AA, as shown in the figure. If PAP_{A} and PBP_{B} are the pressures at AA and BB respectively, then (Consider the temperature is same at all points in the tube)
    JEE Main/MCQ/Medium/Pressure and Energy of gas/With diagram
  124. 124The helium and argon are put in the flask at the same room temperature ( 300 K). The ratio of average kinetic energies (per molecule) of helium and argon is :
    (Give : Molar mass of helium     =4 g/mol=4 \mathrm{~g} / \mathrm{mol}, Molar mass of argon =40 g/mol=40 \mathrm{~g} / \mathrm{mol})    JEE Main/MCQ/Medium/Pressure and Energy of gas
  125. 125The kinetic energy of translation of the molecules in 50 g of CO2\mathrm{CO}_2 gas at 17∘C17^{\circ} \mathrm{C} isJEE Main/MCQ/Medium/Pressure and Energy of gas
  126. 126The temperature of a gas is −78∘C-78^{\circ} \mathrm{C} and the average translational kinetic energy of its molecules is K\mathrm{K}. The temperature at which the average translational kinetic energy of the molecules of the same gas becomes 2 K2 \mathrm{~K} is :JEE Main/MCQ/Medium/Pressure and Energy of gas
  127. 127Given below are two statements :
    Statement (I) : The mean free path of gas molecules is inversely proportional to square of molecular diameter.
    Statement (II) : Average kinetic energy of gas molecules is directly proportional to absolute temperature of gas.
    In the light of the above statements, choose the correct answer from the options given below :    JEE Main/MCQ/Medium/Pressure and Energy of gas
  128. 128Energy of 10 non rigid diatomic molecules at temperature TT is :JEE Main/MCQ/Medium/Pressure and Energy of gas
  129. 129A gas mixture consists of 88 moles of argon and 66 moles of oxygen at temperature TT. Neglecting all vibrational modes, the total internal energy of the system isJEE Main/MCQ/Medium/Pressure and Energy of gas
  130. 130Two vessels AA and BB are of the same size and are at same temperature. AA contains 1g1g of hydrogen and BB contains 1g1g of oxygen. PA{P}_{A} and PB{P}_{B} are the pressures of the gases in AA and BB respectively, then PAPB\dfrac{{P}_{A}}{{P}_{B}} is :JEE Main/MCQ/Medium/Pressure and Energy of gas
  131. 131The total kinetic energy of 11 mole of oxygen at 27∘C27^{\circ}C is :
    [Use universal gas constant     (R)=8.31Jmol−1K−1(R)=8.31J{mol}^{-1}{K}^{-1} ]    JEE Main/MCQ/Medium/Pressure and Energy of gas
  132. 132The average kinetic energy of a monatomic molecule is 0.414eV0.414eV at temperature:
    (Use     KB=1.38×10−23Jmol−1K−1{K}_{B}=1.38\times {10}^{-23}J{mol}^{-1}{K}^{-1})    JEE Main/MCQ/Medium/Pressure and Energy of gas
  133. 133A flask contains Hydrogen and Argon in the ratio 2:12:1 by mass. The temperature of the mixture is 30∘C30^{\circ}C. The ratio of average kinetic energy per molecule of the two gases (KargonKhydrogen)\left(\dfrac{{K}_{argon}}{{K}_{hydrogen}}\right) is: (Given : Atomic Weight of Ar=39.9Ar=39.9)JEE Main/MCQ/Medium/Pressure and Energy of gas
  134. 134The temperature at which the kinetic energy of oxygen molecules becomes double than its value at 27∘C27^{\circ}C isJEE Main/MCQ/Medium/Pressure and Energy of gas
  135. 135The average kinetic energy of a molecule of the gas isJEE Main/MCQ/Medium/Pressure and Energy of gas
  136. 136Following statements are given
    (1) The average kinetic energy of a gas molecule decreases when the temperature is reduced.
    (2) The average kinetic energy of a gas molecule increases with increase in pressure at constant temperature.
    (3) The average kinetic energy of a gas molecule decreases with increases in volume.
    (4) Pressure of a gas increases with increase in temperature at constant volume.
    (5) The volume of gas decreases with increase in temperature.
    Choose the correct answer from the options given below :    JEE Main/MCQ/Medium/Pressure and Energy of gas
  137. 137A flask contains argon and oxygen in the ratio of 3:23:2 in mass and the mixture is kept at 27∘C27^{\circ}C. The ratio of their average kinetic energy per molecule respectivelyJEE Main/MCQ/Medium/Pressure and Energy of gas
  138. 138A uniform heating wire of resistance 36Ω36\Omega is connected across a potential difference of 240V.240V. The wire is then cut into half and a potential difference of 240V240V is applied across each half separately. The ratio of power dissipation in first case to the total power dissipation in the second case would be 1:x,1:x, where xx isJEE Main/Numerical/Medium/Pressure and Energy of gas
  139. 139A mixture of hydrogen and oxygen has volume 500cm3,500{cm}^{3}, temperature 300K,300K, pressure 400kPa400kPa and mass 0.76g.0.76g. The ratio of masses of oxygen to hydrogen will be:JEE Main/MCQ/Medium/Pressure and Energy of gas
  140. 140For an ideal gas the instantaneous change in pressure PP with volume VV is given by the equation dPdV=−aP.\dfrac{dP}{dV}=-aP. If P=P0P={P}_{0} at V=0V=0 is the given boundary condition, then the maximum temperature one mole of gas can attain is: (Here RR is the gas constant)JEE Main/MCQ/Medium/Pressure and Energy of gas
  141. 141A cylindrical container of volume 4.0×10−3m34.0\times {10}^{-3}{m}^{3} contains one mole of hydrogen and two moles of carbon dioxide. Assume the temperature of the mixture is 400K400K. The pressure of the mixture of gases is :
    [Take gas constant as     8.3Jmol−1K−1]\left.8.3J{mol}^{-1}{K}^{-1}\right]    JEE Main/MCQ/Medium/Pressure and Energy of gas
  142. 142The number of molecules in one litre of an ideal gas at 300K300K and 22 atmospheric pressure with mean kinetic energy 2×10−9J2\times {10}^{-9}J per molecule is:JEE Main/MCQ/Medium/Pressure and Energy of gas
  143. 143A system consists of two types of gas molecules AA and BB having the same number density 2×1025m−32\times {10}^{25}{m}^{-3}. The diameter of AA and BB are 10A10A and 5A5A respectively. They suffer collisions at room temperature. The ratio of average distance covered by the molecule AA to that of BB between two successive collisions is ___________×10−2\times {10}^{-2}JEE Main/Numerical/Medium/Pressure and Energy of gas
  144. 144Two spherical soap bubbles of radii r1{r}_{1} and r2{r}_{2} in vacuum combine under isothermal conditions. The resulting bubble has a radius equal to:JEE Main/MCQ/Medium/Pressure and Energy of gas
  145. 145What will be the average value of energy for a monoatomic gas in thermal equilibrium at temperature T?T?JEE Main/MCQ/Medium/Pressure and Energy of gas
  146. 146What will be the average value of energy along one degree of freedom for an ideal gas in thermal equilibrium at a temperature T?T? (kB{k}_{B} is Boltzmann constant)JEE Main/MCQ/Medium/Pressure and Energy of gas
  147. 147Two ideal polyatomic gases at temperatures T1{T}_{1} and T2{T}_{2} are mixed so that there is no loss of energy. If F1{F}_{1} and F2,m1{F}_{2},{m}_{1} and m2,n1{m}_{2},{n}_{1} and n2{n}_{2} be the degrees of freedom, masses, number of molecules of the first and second gas respectively, the temperature of mixture of these two gases is:JEE Main/MCQ/Medium/Pressure and Energy of gas
  148. 148The volume VV of an enclosure contains a mixture of three gases, 16g16g of oxygen, 28g28g of nitrogen and 44g44g of carbon dioxide at absolute temperature TT. Consider RR as universal gas constant. The pressure of the mixture of gases is :JEE Main/MCQ/Medium/Pressure and Energy of gas
  149. 149Given below are two statements:
    Statement I: In a diatomic molecule, the rotational energy at a given temperature obeys Maxwell's distribution.
    Statement II : In a diatomic molecule, the rotational energy at a given temperature equals the translational kinetic energy for each molecule.
    In the light of the above statements, choose the correct answer from the options given below:    JEE Main/MCQ/Medium/Pressure and Energy of gas
  150. 150On the basis of kinetic theory of gases, the gas exerts pressure because its molecules:JEE Main/MCQ/Medium/Pressure and Energy of gas
  151. 151Number of molecules in a volume of 4cm34{cm}^{3} of a perfect monoatomic gas at some temperature T and at a pressure of 2cm2cm of mercury is close to? (Given, mean kinetic energy of a molecule (at T) is 4×10−14erg,g=980cms−24\times {10}^{-14}erg,g=980cm{s}^{-2} density of mercury =13.6gcm−3=13.6g{cm}^{-3})JEE Main/MCQ/Medium/Pressure and Energy of gas
  152. 152A closed vessel contains 0.10.1 mole of a monoatomic ideal gas at 200K200\text{K}. If 0.050.05 mole of the same gas at 400K400K is added to it, the final equilibrium temperature (in K\text{K}) of the gas in the vessel will be close to ______JEE Main/Numerical/Medium/Pressure and Energy of gas
  153. 153A gas mixture consists of 33 moles of oxygen and 55 moles of argon at temperature TT. Assuming the gases to be ideal and the oxygen bond to be rigid, the total internal energy (in units of RTRT) of the mixutre is :JEE Main/MCQ/Medium/Pressure and Energy of gas
  154. 154The number density of molecules of a gas depends on their distance r from the origin as, n(r)=n0e−αr4.n\left(r\right)={n}_{0}{e}^{-\alpha {r}^{4}}. Then the numer of molecules is proportional to:JEE Main/MCQ/Medium/Pressure and Energy of gas
  155. 155An HClHCl molecule has rotational, translational and vibrational motions. If the rms velocity of HClHCl molecules in its gaseous phase is ν−\nu ^{-} , m is its mass and kB{k}_{B} is Boltzmann's constant, then its temperature will be:JEE Main/MCQ/Medium/Pressure and Energy of gas
  156. 1562kg2kg of a monoatomic gas is at a pressure of 4×104Nm−24\times {10}^{4}N{m}^{-2}. The density of the gas is 8kgm−38 kg{m}^{-3}. What is the order of energy of the gas due to its thermal motion?JEE Main/MCQ/Medium/Pressure and Energy of gas
  157. 157NN moles of diatomic gas in a cylinder is at a temperature TT. Heat is supplied to the cylinder such that the temperature remains constant but nn moles of the diatomic gas get converted into monoatomic gas. The change in the total kinetic energy of the gas isJEE Main/MCQ/Medium/Pressure and Energy of gas
  158. 158Which of the following shows the correct relationship between the pressure ′P′'P' and density ρ\rho of an ideal gas at constant temperature ?JEE Main/MCQ/Medium/Pressure and Energy of gas
  159. 159Using equipartition of energy, the specific heat (in Jkg−1K−1J{kg}^{-1}{K}^{-1} ) of Aluminium at high temperature can be estimated to be (atomic weight of Aluminium =27=27)JEE Main/MCQ/Medium/Pressure and Energy of gas
  160. 160In an ideal gas at temperature T, the average force that a molecule applies on the walls of a closed container depends on TasTqTas{T}^{q} . A good estimate for q is:JEE Main/MCQ/Medium/Pressure and Energy of gas
  161. 161A gas molecule of mass MM at the surface of the earth has kinetic energy equivalent to 0∘C0^{\circ}C. If it were to go up straight without colliding with any other molecules, how high it would rise? Assume that the height attained is much less than the radius of the earth. (kB{k}_{B} is Boltzmann constant)JEE Main/MCQ/Medium/Pressure and Energy of gas
  162. 162

    There are two identical chambers, completely thermally insulated from surroundings. Both chambers have a partition wall dividing the chambers in two compartments. Compartment     11 is filled with an ideal gas and Compartment 33 is filled with a real gas. Compartments 22 and 44 are vacuum. A small hole (orifice) is made in the partition walls and the gases are allowed to expand in vacuum.
    Statement−1:\mathrm{Statement-1:} No change in the temperature of the gas takes place when ideal gas expands in vacuum. However, the temperature of real gas goes down (cooling) when it expands in vacuum.
    Statement−2:\mathrm{Statement-2:} The internal energy of an ideal gas is only kinetic. The internal energy of a real gas is kinetic as well as potential.    JEE Main/MCQ/Medium/Pressure and Energy of gas/With diagram
  163. 163A thermally insulated vessel contains an ideal gas of molecular mass MM and ratio of specific heats γ\gamma. It is moving with speed vv and is suddenly brought to rest. Assuming no heat is lost to the surroundings, its temperature increases by :JEE Main/MCQ/Medium/Pressure and Energy of gas
  164. 164One kg of a diatomic gas is at a pressure of 8×104 N/m28 \times 10^4 \mathrm{~N} / \mathrm{m}^2. The density of the gas is 4 kg/m−34 \mathrm{~kg} / \mathrm{m}^{-3}. What is the energy of the gas due to its thermal motion?JEE Main/MCQ/Medium/Pressure and Energy of gas
  165. 165An insulated container of gas has two chambers separated by an insulating partition. One of the chambers has volume V1V_1 and contains ideal gas at pressure P1P_1 and temperature T1T_1. The other chamber has volume V2V_2 and contains ideal gas at pressure P2P_2 and temperature T2T_2. If the partition is removed without doing any work on the gas, the final equilibrium temperature of the gas in the container will beJEE Main/MCQ/Medium/Pressure and Energy of gas
  166. 166Two rigid boxes containing different ideal gases are placed on a table. Box A contains one mole of nitrogen at temperature T0T_0, while Box BB contains one mole of helium at temperature (7/3)T0(7 / 3) T_0. The boxes are then put into thermal contact with each other and heat flows between them until the gases reach a common final temperature. (Ignore the heat capacity of boxes). Then, the final temperature of the gases, TfT_f, in terms of T0T_0 isJEE Main/MCQ/Medium/Pressure and Energy of gas
  167. 167In the nuclear fusion reaction 12H+13H→24He+n{ }_1^2 \mathrm{H}+{ }_1^3 \mathrm{H} \rightarrow{ }_2^4 \mathrm{He}+\mathrm{n} given that the repulsive potential energy between the two nuclei is ∼7.7×10−14 J\sim 7.7 \times 10^{-14} \mathrm{~J}, the temperature at which the gases must be heated to initiate the reaction is nearly [Boltzmann's Constant k=1.38×10−23 J/K\mathrm{k}=1.38 \times 10^{-23} \mathrm{~J} / \mathrm{K} ]JEE Main/MCQ/Medium/Pressure and Energy of gas
  168. 168Cooking gas containers are kept in a lorry moving with uniform speed. The temperature of the gas molecules inside willJEE Main/MCQ/Medium/Pressure and Energy of gas

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