Practice Questions

Q8. At which temperature the r.m.s. velocity of a hydrogen molecule equal to that of an oxygen molecule at 47°C ? (1) 80 K (2) −73 K (3) 4 K (4) 20 K

Q9. Energy of 10 non rigid diatomic molecules at temperature T is : (1) 70 KBT (2) 35 KBT (3) 7 2 RT (4) 35RT

Q9. The volume of an ideal gas (γ = 1.5) is changed adiabatically from 5 litres to 4 litres. The ratio of initial pressure to final pressure is: JEE Main 2024 (09 Apr Shift 1) JEE Main Previous Year Paper (1) 16 (2) 4 25 5 (3) 8 (4) 2 5√5 √5

Q9. 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 options given below : (1) Statement I is true but Statement II is false (2) Both Statement I and Statement II are false (3) Both Statement I and Statement II are true (4) Statement I is false but Statement II is true

Q9. The total kinetic energy of 1 mole of oxygen at 27°C is : [Use universal gas constant (R) = 8 . 31 J mol-1 K-1 ] (1) 6845 . 5 J (2) 5942 . 0 J (3) 6232 . 5 J (4) 5670 . 5 J

Q9. The pressure and volume of an ideal gas are related as 𝑃𝑉 32 = 𝐾 (Constant). The work done when the gas is taken from state 𝐴𝑃1, 𝑉1, 𝑇1 to state 𝐵𝑃2, 𝑉2, 𝑇2 is : (1) 2 ( 𝑃1𝑉1 - 𝑃2𝑉2 ) (2) 2 ( 𝑃2𝑉2 - 𝑃1𝑉1 ) (3) 2√𝑃1𝑉1 −√𝑃2𝑉2 (4) 2𝑃2√𝑉2 −𝑃1√𝑉1

Q9. If n is the number density and 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 : (1) √2nπd2 (2) 1 √2nπd2 (3) 1 (4) 1 √2nπd2 √2n2π2d2

Q9. If the root mean square velocity of hydrogen molecule at a given temperature and pressure is 2 km s-1, the root mean square velocity of oxygen at the same condition in km s-1 is: (1) 2 . 0 (2) 0 . 5 (3) 1 . 5 (4) 1 . 0 Q10.𝐶1 and 𝐶2 are two hollow concentric cubes enclosing charges 2𝑄 and 3𝑄 respectively as shown in figure. The ratio of electric flux passing through 𝐶1 and 𝐶2 is: (1) 2 : 5 (2) 5 : 2 (3) 2 : 3 (4) 3 : 2

Q9. Two conductors have the same resistances at 0 °C but their temperature coefficients of resistance are 𝛼1 and 𝛼2 . The respective temperature coefficients for their series and parallel combinations are : (1) 𝛼1 + 𝛼2, 𝛼1 + 𝛼2 (2) 𝛼1 + 𝛼2 , 𝛼1 + 𝛼2 2 2 2 𝛼1 𝛼2 𝛼1 + 𝛼2 (4) (3) 𝛼1 + 𝛼2, , 𝛼1 + 𝛼2 2 𝛼1 + 𝛼2

Q9. The temperature of a gas having 2. 0 × 1025 molecules per cubic meter at 1. 38 atm (Given, k = 1. 38 × 10−23J K−1) is : (1) 500 K (2) 200 K (3) 100 K (4) 300 K

Q9. The translational degrees of freedom (ft) and rotational degrees of freedom (fr) of CH4 molecule are: (1) ft = 2 and fr = 2 (2) ft = 3 and fr = 3 (3) ft = 3 and fr = 2 (4) ft = 2 and fr = 3

Q9. Two different adiabatic paths for the same gas intersect two isothermal curves as shown in P-V diagram. The relation between the ratio Va and the ratio Vb is: Vd Vc (1) Va ≠Vb (2) Va = Vb Vd Vc Vd Vc (3) Va Vb −1 (4) Va Vb 2 = = Vd ( Vc ) Vd ( Vc )

Q9. Five charges +q, +5q, −2q, +3q and −4q are situated as shown in the figure. The electric flux due to this configuration through the surface S is : (1) 4q (2) 5q ϵ0 ϵ0 (3) q (4) 3q ϵ0 ϵ0

Q9. The average kinetic energy of a monatomic molecule is 0. 414 eV at temperature: JEE Main 2024 (27 Jan Shift 1) JEE Main Previous Year Paper (Use KB = 1. 38 × 10−23 J mol−1 K−1 ) (1) 3000 K (2) 3200 K (3) 1600 K (4) 1500 K

Q9. The resistances of the platinum wire of a platinum resistance thermometer at the ice point and steam point are 8Ω and 10Ω respectively. After inserting in a hot bath of temperature 400∘C , the resistance of platinum wire is : (1) 10Ω (2) 8Ω (3) 16Ω (4) 2Ω

Q9. Two thermodynamical process are shown in the figure. The molar heat capacity for process A and B are CA and CB . The molar heat capacity at constant pressure and constant volume are represented by CP and CV , respectively. Choose the correct statement. (1) CP > CB > CV (2) CA = 0 and CB = ∞ (3) CP > CV > CA = CB (4) CA > CP > CV

Q9. A sample contains mixture of helium and oxygen gas. The ratio of root mean square speed of helium and oxygen in the sample, is: (1) 1 (2) 2√2 32 1 (3) 1 (4) 1 2√2 4

Q9.Match List I with List II : (1) (A)-(III), (B)-(IV), (C)-(I), (D)-(II) (2) (A)-(II), (B)-(I), (C)-(IV), (D)-(III) (3) (A)-(I), (B)-(II), (C)-(III), (D)-(IV) (4) (A)-(I), (B)-(IV), (C)-(II), (D)-(III)

Q9. If three moles of monoatomic gas 𝛾= 5 is mixed with two moles of a diatomic gas 𝛾= 7 the value of adiabatic 3 5, exponent 𝛾 for the mixture is: (1) 1 . 75 (2) 1 . 40 (3) 1 . 52 (4) 1 . 35

Q9. Two vessels A and B are of the same size and are at same temperature. A contains 1 g of hydrogen and B contains 1 g of oxygen. PA and PB are the pressures of the gases in A and B respectively, then PA is : PB (1) 16 (2) 8 (3) 4 (4) 32

Q9. The speed of sound in oxygen at S.T.P. will be approximately: (Given, 𝑅= 8 . 3 J K-1, 𝛾= 1 . 4) (1) 310 m s-1 (2) 333 m s-1 (3) 341 m s-1 (4) 325 m s-1

Q10.The vehicles carrying inflammable fluids usually have metallic chains touching the ground : (1) To protect tyres from catching dirt from ground (2) To alert other vehicles (3) It is a custom (4) To conduct excess charge due to air friction to ground and prevent sparking

Q10.A plane progressive wave is given by y = 2 cos 2π(330t −x)m . The frequency of the wave is : (1) 330 Hz (2) 660 Hz (3) 340 Hz (4) 165 Hz

Q10.A bulb and a capacitor are connected in series across an ac supply. A dielectric is then placed between the plates of the capacitor. The glow of the bulb: (1) increases (2) decreases (3) remains same (4) becomes zero

Q10.Two 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 : 9 7 (1) 4𝑅 (2) 4𝑅 (3) 3 (4) 5 2𝑅 2𝑅