STD 11 - Kinetic theory of gases PYQs: JEE Mains Physics

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1. 1. \(5\) moles of unknown gas is heated at constant volume from \(10 \, °C\) to \(20 \, °C\). The molar specific heat of this gas at constant pressure \(c_p = 8\) cal/mol.°C and \(R = 8.36\) J/mol.°C. The change in the internal energy of the gas is _______ calorie. 2026 Medium
2. 2. A gas of certain mass filled in a closed cylinder at a pressure of 3.23 kPa has temperature \(50^{\circ} C\). The gas is now heated to double its temperature. The modified pressure is _________ Pa . 2026 Hard
3. 3. A mixture of carbon dioxide and oxygen has volume \(8310\) cm\(^3\), temperature \(300\) K, pressure \(100\) kPa and mass \(13.2\) 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) \([R = 8.31\) J/mol.K\(]\) 2026 Hard
4. 4. An air bubble of volume \(2.9 cm^3\) rises from the bottom of a swimming pool of 5 m deep. At the bottom of the pool water temperature is \(17^{\circ} C\). The volume of the bubble when it reaches the surface, where the water temperature is \(27^{\circ} C\), is ___________ \(cm ^3\). ( \(g =10 m / s ^2\), density of water \(=10^3 kg / m ^3\), and 1 atm pressure is \(10^5 Pa\) ) 2026 Hard
5. 5. An insulated cylinder of volume \( 60\,cm^{3} \) is filled with a gas at \( 27^{\circ}C \) and 2 atmospheric pressure. Then the gas is compressed making the final volume as \( 20\,cm^{3} \) while allowing the temperature to rise to \( 77^{\circ}C \). The final pressure is __________atmospheric pressure. 2026 Medium
6. 6. Consider two boxes containing ideal gases A and B such that their temperatures, pressures and number densities are same. The molecular size of A is half of that of B and mass of molecule A is four times that of B. If the collision frequency in gas B is \( 32\times10^{18}/s \) then collision frequency in gas A is__________/s. 2026 Easy
7. 7. Given 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 \(H_2\) and \(O_2\) molecules, kept in two different sized containers are same, then their temperatures will be same.
   
   Reason R: The r.m.s. speed of \(H_2\) and \(O_2\) molecules are same at same temperature.
   
   Choose the correct answer from the options given below 2026 Medium
8. 8. If \(2\) mole of an ideal monoatomic gas at temperature \(T\), is mixed with \(6\) mole of another ideal monoatomic gas at temperature \(2T\) then the temperature of mixture is : 2026 Medium
9. 9. One gas of \(n_1\) mole of molecules at temperature \(T_1\), volume \(V_1\), and pressure \(P_1\), and another gas of \(n_2\) mole of molecules at temperature \(T_2\), volume \(V_2\), and pressure \(P_2\), are mixed resulting in pressure \(P\) and volume \(V\) of the mixture. The temperature of the mixture is _____. 2026 Medium
10. 10. The mean free path of a molecule of diameter \(5\times10^{-10}\) m at the temperature \(41^{\circ}C\) and pressure \(1.38\times10^{5}Pa\), is given as ___________ m.
    (Given \(k_{B}=1.38\times10^{-23}J/K\)). 2026 Medium
11. 11. The r.m.s speed of oxygen molecules at \(47^{\circ} C\) is equal to that of the hydrogen molecules kept at _________ \({ }^{\circ} C\). (Mass of oxygen molecule/mass of hydrogen molecule \(=32 / 2\) ) 2026 Medium
12. 12. Two closed vessels of same volume are joined through a narrow tube and both vessels are filled with air of pressure \(90\) kPa and temperature \(400\) K. Keeping the temperature of one vessel constant at \(400\) K the second vessel temperature is raised to \(500\) K. The final pressure in the vessels is _______ kPa. 2026 Medium
13. 13. When 300 J of heat given to an ideal gas with \(C _{ p }=\frac{7}{2} R\) its temperature raises from \(20{ }^{\circ} C\) to \(50^{\circ} C\) keeping its volume constant. The mass of the gas is (approximately) _________ g. \(( R =8.314 J / mol . K )\). 2026 Hard
14. 14. A container of fixed volume contains a gas at \(27^{\circ} \mathrm{C}\). To double the pressure of the gas, the temperature of gas should be raised to ______ \({ }^{\circ} \mathrm{C}\). 2025 Easy
15. 15. \(\gamma_{\mathrm{A}}\) is the specific heat ratio of monoatomic gas A having 3 translational degrees of freedom. \(\gamma_B\) is the specific heat ratio of polyatomic gas B having 3 translational, 3 rotational degrees of freedom and 1 vibrational mode. If \(\frac{\gamma_{\mathrm{A}}}{\gamma_{\mathrm{B}}}=\left(1+\frac{1}{\mathrm{n}}\right)\), then the value of \(n\) is _______. 2025 Easy
16. 16. For a diatomic gas, if \(\gamma_1=\left(\frac{C p}{C v}\right)\) for rigid molecules and \(\gamma_2=\left(\frac{C p}{C v}\right)\) for another diatomic molecules, but also having vibrational modes. Then, which one of the following options is correct ? (Cp and Cv are specific heats of the gas at constant pressure and volume) 2025 Medium
17. 17. Match the List-I with List-II
    

    List - I	List - II
    (A) Triatomic rigid gas	(I) \(\frac{C_P}{C_V} = \frac{5}{3}\)
    (B) Diatomic non-rigid gas	(II) \(\frac{C_P}{C_V} = \frac{7}{5}\)
    (C) Monoatomic gas	(III) \(\frac{C_P}{C_V} = \frac{4}{3}\)
    (D) Diatomic rigid ga	(IV) \(\frac{C_P}{C_V} = \frac{9}{7}\)

    
    Choose the correct answer from the options given below : 2025 Medium
18. 18. Pressure of an ideal gas, contained in a closed vessel, is increased by \(0.4 \%\) when heated by \(1^{\circ} \mathrm{C}\). Its initial temperature must be : 2025 Easy
19. 19. The 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 \(=4 \mathrm{~g} / \mathrm{mol}\), Molar mass of argon \(=40 \mathrm{~g} / \mathrm{mol}\)) 2025 Easy
20. 20. The internal energy of air in \(4 \mathrm{~m} \times 4 \mathrm{~m} \times 3 \mathrm{~m}\) sized room at 1 atmospheric pressure will be _______ \(\times 10^6 \mathrm{~J}\). (Consider air as diatomic molecule) 2025 Easy
21. 21. The kinetic energy of translation of the molecules in 50 g of \(\mathrm{CO}_2\) gas at \(17^{\circ} \mathrm{C}\) is 2025 Easy
22. 22. The mean free path and the average speed of oxygen molecules at 300 K and 1 atm are \(3 \times 10^{-7} \mathrm{~m}\) and \(600 \mathrm{~m} / \mathrm{s}\) respectively. Find the frequency of its collisions. 2025 Easy
23. 23. The ratio of vapour densities of two gases at the same temperature is \(\frac{4}{25}\), then the ratio of r.m.s. velocities will be: 2025 Easy
24. 24. There are two vessels filled with an ideal gas where volume of one is double the volume of other. The large vessel contains the gas at 8 kPa at 1000 K while the smaller vessel contains the gas at 7 kPa at 500 K. If the vessels are connected to each other by a thin tube allowing the gas to flow and the temperature of both vessels is maintained at 600 K , at steady state the pressure in the vessels will be (in kPa). 2025 Medium
25. 25. A diatomic gas \((\gamma=1.4)\) does \(100 \mathrm{~J}\) of work in an isobaric expansion. The heat given to the gas is _______. 2024 Hard
26. 26. A mixture of one mole of monoatomic gas and one mole of a diatomic gas (rigid) are kept at room temperature \(\left(27^{\circ} \mathrm{C}\right)\). The ratio of specific heat of gases at constant volume respectively is _______. 2024 Hard
27. 27. A sample contains mixture of helium and oxygen gas. The ratio of root mean square speed of helium and oxygen in the sample is _______. 2024 Hard
28. 28. An object is placed in a medium of refractive index \(3\). An electromagnetic wave of intensity \(6 \times 10^8 \mathrm{~W} / \mathrm{m}^2\) falls normally on the object and it is absorbed completely. The radiation pressure on the object would be (speed of light in free space \(=3 \times 10^8 \mathrm{~m} / \mathrm{s}\) ): 2024 Hard
29. 29. At which temperature the r.m.s. velocity of a hydrogen molecule equal to that of an oxygen molecule at \(47^{\circ} \mathrm{C}\) ? 2024 Hard
30. 30. During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio of \(\frac{C_p}{C_v}\) for the gas is: 2024 Hard
31. 31. Energy of \(10\) non rigid diatomic molecules at temperature \(\mathrm{T}\) is _______. 2024 Hard
32. 32. Given 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 option given below: 2024 Hard
33. 33. If \(\mathrm{n}\) is the number density and \(\mathrm{d}\) 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 _______. 2024 Hard
34. 34. If the collision frequency of hydrogen molecules in a closed chamber at \(27^{\circ} \mathrm{C}\) is \(\mathrm{Z}\), then the collision frequency of the same system at \(127^{\circ} \mathrm{C}\) is _______. 2024 Hard
35. 35. If the root mean square velocity of hydrogen molecule at a given temperature and pressure is \(2 \mathrm{~km} / \mathrm{s}\), the root mean square velocity of oxygen at the same condition in \(\mathrm{km} / \mathrm{s}\) is _______. 2024 Hard
36. 36. If three moles of monoatomic gas \(\left(\gamma=\frac{5}{3}\right)\) is mixed with two moles of a diatomic gas \(\left(\gamma=\frac{7}{5}\right)\), the value of adiabatic exponent \(\gamma\) for the mixture is _______. 2024 Hard
37. 37. \(\mathrm{N}\) moles of a polyatomic gas \((f=6)\) must be mixed with two moles of a monoatomic gas so that the mixture behaves as a diatomic gas. The value of \(\mathrm{N}\) is _______. 2024 Hard
38. 38. \(P-T\) diagram of an ideal gas having three different densities \(\rho_1, \rho_2, \rho_3\) (in three different cases) is shown in the figure. Which of the following is correct?
    2024 Hard
39. 39. The average kinetic energy of a monatomic molecule is \(0.414 \mathrm{eV}\) at temperature : (Use \(\mathrm{K}_{\mathrm{B}}=1.38 \times 10^{-23} \mathrm{~J} / \mathrm{mol}-\mathrm{K}\) ) 2024 Hard
40. 40. The parameter that remains the same for molecules of all gases at a given temperature is _______. 2024 Hard
41. 41. The temperature of a gas having \(2.0 \times 10^{25}\) molecules per cubic meter at \(1.38 \mathrm{~atm}\) (Given, \(\mathrm{k}=\) \(\left.1.38 \times 10^{-23} \mathrm{JK}^{-1}\right)\) is _______. 2024 Hard
42. 42. The temperature of a gas is \(-78^{\circ} \mathrm{C}\) and the average translational kinetic energy of its molecules is \(\mathrm{K}\). The temperature at which the average translational kinetic energy of the molecules of the same gas becomes \(2 \mathrm{~K}\) is _______. 2024 Hard
43. 43. The total kinetic energy of \(1\) mole of oxygen at \(27^{\circ} \mathrm{C}\) is : [Use universal gas constant \((R)=8.31 \mathrm{~J} / \mathrm{mole} \mathrm{K}\) ] 2024 Hard
44. 44. The translational degrees of freedom \((f)\) and rotational degrees of freedom \((f)\) of \(\mathrm{CH}_4\) molecule are _______. 2024 Hard
45. 45. Two moles a monoatomic gas is mixed with six moles of a diatomic gas. The molar specific heat of the mixture at constant volume is _______. 2024 Hard
46. 46. Two thermodynamical process are shown in the figure. The molar heat capacity for process \(A\) and \(B\) are \(C_A\) and \(C_B\). The molar heat capacity at constant pressure and constant volume are represented by \(C_P\) and \(C_V\), respectively. Choose the correct statement.
    2024 Hard
47. 47. Two vessels \(A\) and \(B\) are of the same size and are at same temperature. A contains \(1 \mathrm{~g}\) of hydrogen and \(B\) contains \(1 \mathrm{~g}\) of oxygen. \(\mathrm{P}_{\mathrm{A}}\) and \(\mathrm{P}_{\mathrm{B}}\) are the pressures of the gases in \(A\) and \(\mathrm{B}\) respectively, then \(\frac{\mathrm{P}_{\mathrm{A}}}{\mathrm{P}_{\mathrm{B}}}\) is _______. 2024 Hard
48. 48. A flask contains Hydrogen and Argon in the ratio \(2: 1\) by mass. The temperature of the mixture is \(30^{\circ} C\). The ratio of average kinetic energy per molecule of the two gases ( \(K\) argon/ \(K\) hydrogen) is: (Given: Atomic Weight of \(Ar = 39.9\)) 2023 Medium
49. 49. A flask contains hydrogen and oxygen in the ratio of \(2: 1\) by mass at temperature \(27^{\circ} C\). The ratio of average kinetic energy per molecule of hydrogen and oxygen respectively is : 2023 Easy
50. 50. A gas mixture consists of \(2\) moles of oxygen and 4 moles of neon at temperature \(T\). Neglecting all vibrational modes, the total internal energy of the system will be \(...........\,RT\)  2023 Medium

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