Pressure and Energy PYQs: JEE Mains Physics

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1. 1. 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
2. 2. 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
3. 3. The kinetic energy of translation of the molecules in 50 g of \(\mathrm{CO}_2\) gas at \(17^{\circ} \mathrm{C}\) is 2025 Easy
4. 4. 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
5. 5. Energy of \(10\) non rigid diatomic molecules at temperature \(\mathrm{T}\) is _______. 2024 Hard
6. 6. 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
7. 7. The parameter that remains the same for molecules of all gases at a given temperature is _______. 2024 Hard
8. 8. 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
9. 9. 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
10. 10. 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
11. 11. 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
12. 12. 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
13. 13. Given below are two statements: Statements \(I:\) The temperature of a gas is \(-73^{\circ}\,C\). When the gas is heated to \(527^{\circ}\,C\), 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 : 2023 Medium
14. 14. The average kinetic energy of a molecule of the gas is 2023 Easy
15. 15. The temperature at which the kinetic energy of oxygen molecules becomes double than its value at \(27^{\circ}\,C\) is \(............^{\circ}\,C\) 2023 Easy
16. 16. \(0.056 \,kg\) of Nitrogen is enclosed in a vessel at a temperature of \(127\,^{\circ} C\). The amount of heat required to double the speed of its molecules is k cal. (Take \(R =2\) \(cal \,mole\) \(^{-1} K ^{-1}\) ) 2022 Medium
17. 17. \(7\) mole of certain monoatomic ideal gas undergoes a temperature increase of \(40 K\) at constant pressure. The increase in the internal energy of the gas in this process is\(....J\) (Given \(R =8.3 JK ^{-1} mol ^{-1}\) ) 2022 Medium
18. 18. A cylinder of fixed capacity of \(44.8 \,litres\) contains helium gas at standard temperature and pressure. The amount of heat needed to raise the temperature of gas in the cylinder by \(20.0^{\circ} C\) will be ..............  \(J\)(Given gas constant \(R =8.3 \,JK ^{-1}- moI ^{-1}\) ) 2022 Medium
19. 19. A flask contains argon and oxygen in the ratio of \(3: 2\) in mass and the mixture is kept at \(27^{\circ} C\). The ratio of their average kinetic energy per molecule respectively will be ........... 2022 Medium
20. 20. A thermally insulated vessel contains an ideal gas of molecular mass \(M\) and ratio of specific heats \(1.4\). Vessel is moving with speed \(v\) and is suddenly brought to rest. Assuming no heat is lost to the surrounding and vessel temperature of the gas increases by ... ( \(R =\) universal gas constant ) 2022 Medium
21. 21. A vessel contains \(14\,g\) of nitrogen gas at a temperature of \(27^{\circ}\,C\). The amount of heat to be transferred to the gap to double the r.m.s. speed of its molecules will be \(......J\) \(\left(\right.\) Take \(R =8.32\,J\,mol ^{-1} k ^{-1}\) ) 2022 Medium
22. 22. Following 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 pressure. \((5)\) The volume of gas decreases with increase in temperature. Choose the correct answer from the options given below: 2022 Medium
23. 23. The total internal energy of two mole monoatomic ideal gas at temperature \(T=300\,K\) will be ...........\(J\). \(\text { (Given } R =8.31\,J / mol.K )\) 2022 Easy
24. 24. A container is divided into two chambers by a partition. The volume of first chamber is \(4.5\) litre and second chamber is \(5.5\) litre. The first chamber contain \(3.0\) moles of gas at pressure \(2.0\, atm\) and second chamber contain \(4.0\) moles of gas at pressure \(3.0\, atm\) .After the partition is removed and the mixture attains equilibrium, then, the common equilibrium pressure existing in the mixture is \(x \times 10^{-1} atm\). Value of \(x\) is......... 2021 Hard
25. 25. A monoatomic gas of mass \(4.0\, u\) is kept in an insulated container. Container is moving with velocity \(30 \,m / s\). If container is suddenly stopped then change in temperature of the gas \(\left( R =\right.\) gas constant) is \(\frac{ x }{3 R } .\) Value of \(x\) is .......... 2021 Hard
26. 26. For an ideal gas the instantaneous change in pressure \('{p} '\) with volume \('v'\) is given by the equation \(\frac{{dp}}{{dv}}=-{ap} .\) If \({p}={p}_{0}\) at \({v}=0\) is the given boundary condition, then the maximum temperature one mole of gas can attain is : (Here \({R}\) is the gas constant) 2021 Hard
27. 27. On the basis of kinetic theory of gases, the gas exerts pressure because its molecules: 2021 Medium
28. 28. The average translational kinetic energy of \({N}_{2}\) gas molecules at \(\ldots \ldots \ldots . .{ }^{\circ} {C}\) becomes equal to the \({K} . {E}\). of an electron accelerated from rest through a potential difference of \(0.1\) \(volt.\) \(\left(\right.\) Given \(\left.{k}_{{B}}=1.38 \times 10^{-23} \, {J} / {K}\right)\) (Fill the nearest integer). 2021 Medium
29. 29. The number of molecules in one litre of an ideal gas at \(300 \,{K}\) and \(2\) atmospheric pressure with mean kinetic energy \(2 \times 10^{-9}\, {J}\) per molecules is \(....\, \times 10^{11}\) 2021 Medium
30. 30. The volume \(V\) of an enclosure contains a mixture of three gases, \(16\, g\) of oxygen, \(28\, g\) of nitrogen and \(44\, g\) of carbon dioxide at absolute temperature \(T\). Consider \(R\) as universal gas constant. The pressure of the mixture of gases is 2021 Medium
31. 31. Two ideal polyatomic gases at temperatures \(T _{1}\) and \(T _{2}\) are mixed so that there is no loss of energy. If \(F _{1}\) and \(F _{2}, m _{1}\) and \(m _{2}, n _{1}\) and \(n _{2}\) 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 2021 Hard
32. 32. What will be the average value of energy along one degree of freedom for an ideal gas in thermal equilibrium at a temperature \(T \,?\left( k _{ B }\right.\) is Boltzmann constant) 2021 Medium
33. 33. A gas mixture consists of \(3\) moles of oxygen and \(5\) moles of argon at temperature \(T\). Assuming the gases to be ideal and the oxygen bond to be rigid, the total internal energy (in units of \(RT\) ) of the mixture is 2020 Medium
34. 34. Consider a gas of triatomic molecules. The molecules are assumed to the 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 \(......RT\)
    2020 Medium
35. 35. Initially a gas of diatomic molecules is contained in a cylinder of volume \(V _{1}\) at a pressure \(P_{1}\) and temperature \(250\, K\). Assuming that \(25 \%\) of the molecules get dissociated causing a change in number of moles. The pressure of the resulting gas at temperature \(2000\, K ,\) when contained in a volume \(2 V _{1}\) is given by \(P _{2}\). The ratio \(\frac{P _{2}}{  P _{1}}\) is. 2020 Medium
36. 36. Molecules of an ideal gas are known to have three translational degrees of freedom and two rotational 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 \(\gamma\left(=\frac{ C _{ P }}{ C _{ v }}\right)\) given, respectively, by 2020 Medium
37. 37. Number of molecules in a volume of \(4\, cm ^{3}\) of a perfect monoatomic gas at some temperature \(T\) and at a pressure of \(2\, cm\) of mercury is close to \(?\) (Given, mean kinetic energy of a molecule (at \(T\) ) is \(4 \times 10^{-14}\) erg, \(g=980\, cm / s ^{2}\), density of mercury \(=13.6\, g / cm ^{3}\)) 2020 Medium
38. 38. The change in the magnitude of the volume of an ideal gas when a small additional pressure \(\Delta P\) is applied at a constant temperature, is the same as the change when the temperature is reduced by a small quantity \(\Delta T\) at constant pressure. The initial temperature and pressure of the gas were \(300\, K\) and \(2\; atm\) respectively. If \(|\Delta T|=C|\Delta P|\) then value of \(C\) in \((K / a t m)\) is...... 2020 Hard
39. 39. \(2\, kg\) of a monoatomic gas is at a pressure of \(4\times10^4\, N/m^2\). The density of the gas is \(8\, kg/m^3\). What is the order of energy of the gas due to its thermal motion ? 2019 Medium
40. 40. A \(15\,g\) mass of nitrogen gas is enclosed in a vessel at a temperature \(27\,^oC.\) Amount of heat transferred to the gas, so that rms velocity of molecules is doubled, is about ...... \(kJ\) [Take \(R = 8.3\,J/K\,mole\) ] 2019 Medium
41. 41. A cylinder with fixed capacity of \(67.2\, lit\) contains helium gas at \(STP\). The amount of heat needed to raise the temperature of the gas by \(20\,^oC\) is ..... \(J\) [Given that \(R = 8.31\, J\, mol^{-1}\, K^{-1}\)] 2019 Medium
42. 42. A gas mixture consists of \(3\,moles\) of oxygen and \(5\,moles\) or argon at temperature \(T.\) Considering only translational and rotational modes, the total internal  energy of the system is 2019 Medium
43. 43. A vertical closed cylinder is separated into two parts by a frictionless piston of mass \(m\) and of negligible thickness. The piston is free to move along the length of the cylinder .The length of the cylinder above the piston is \(l_1,\) and that below the piston is \(l_2,\) such that \(l_1 > l_2.\) Each part of the cylinder contains \(n\) moles of an ideal gas at equal temperature \(T.\) If the piston is stationary, its mass, \(m,\) will be given by: ( \(R\) is universal gas constant and \(g\) is the acceleration due to gravity) 2019 Hard
44. 44. An \(HCl\) molecule has rotational, translational and vibrational motions. If the \(rms\) velocity of \(HCl\) molecules in its gaseous phase is \(\bar v ,\,m\) is its mass and \(k_B\) is Boltzmann constant, then its temperature will be 2019 Medium
45. 45. An ideal gas occupies a volume of \(2\, m^3\) at a pressure of \(3\times10^6\, Pa\). The energy of  the gas is 2019 Medium
46. 46. If \(10^{22}\) gas molecules each of mass \(10^{-26}\, kg\) collide with a surface (perpendicular to it)elastically per second over an area \(1\, m^2\) with a speed \(10^4\,m/s\), the pressure exerted by the gas molecules will be of the order of 2019 Medium
47. 47. One mole of an ideal gas passes through a process where pressure and volume obey the relation \(P\, = {P_0}\,\left[ {1 - \frac{1}{2}{{\left( {\frac{{{V_0}}}{V}} \right)}^2}} \right]\).  Here \(P_0\) and \(V_0\) are constants. Calculate the change in the temperature of the gas if its volume change from \(V_0\) to \(2V_0\) 2019 Hard
48. 48. When heat \(Q\) is supplied to a diatomic gas of rigid molecules at constant volume its temperature increases by \(\Delta T.\) The heat required to produce the same change in temperature, at constant pressure is 2019 Medium
49. 49. \(N\,moles\) of a diatomic gas in a cylinder are at a temperature \(T\). Heat is supplied to the cylinder such that the temperature remains constant but \(n\,moles\) of the diatomic gas get converted into monoatomic gas. What is the change in the total kinetic energy of the gas ? 2017 Medium
50. 50. Using equipartition of energy, the specific heat (in \(J\, kg^{-1}\, K^{-1}\) ) of aluminium at room temperature can be estimated to be ( atomic weight of aluminium \(= 27\)) 2015 Hard

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