Practice Questions

Q10.A 15 g mass of nitrogen gas is enclosed in a vessel at a temperature, 27oC. The amount of heat transferred to the gas, so that R. M. S. velocity of molecules is doubled, is about. = 8 .3 J (K [R mole)−1] (1) 14 kJ (2) 10 kJ (3) 6 kJ (4) 0 .9 kJ

Q10.A soap bubble, blown by a mechanical pump at the mouth of a tube increases in volume with time at a constant rate. The graph that correctly depicts the time dependence of pressure inside the bubble is given by: JEE Main 2019 (12 Jan Shift 2) JEE Main Previous Year Paper (1) (2) (3) (4)

Q10.A sample of an ideal gas is taken through the cyclic process abca as shown in the figure. The change in the internal energy of the gas along the path ca is -180 J . The gas absorbs 250 J of heat along the path ab and 60 J along the path bc . The work done by the gas along the path abc is: (1) 130 J (2) 100 J (3) 120 J (4) 140 J JEE Main 2019 (12 Apr Shift 1) JEE Main Previous Year Paper

Q10.In a process, temperature and volume of one mole of an ideal monoatomic gas are varied according to the relation VT = K, where K is a constant. In this process the temperature of the gas is increased by ΔT . The amount of heat absorbed by gas is (R is gas constant): (1) 1 2 RΔT (2) 21 KRΔT (3) 2 3 RΔT (4) 2 3K ΔT

Q10.Following figure shows two processes A and B for a gas. If ΔQA and ΔQB are the amount of heat absorbed by the system in two cases, and ΔUA and ΔUB are changes in internal energies, respectively, then: (1) ΔQA < Δ QB; Δ UA < Δ UB (2) ΔQA = Δ QB; Δ UA = Δ UB (3) ΔQA > Δ QB; Δ UA = Δ UB (4) ΔQA > Δ QB; Δ UA > Δ UB

Q10.A rigid diatomic ideal gas undergoes an adiabatic process at room temperature. The relation between temperature and volume for this process is TVx = constant, then x is: (1) 3 (2) 2 5 5 (3) 2 (4) 5 3 3

Q10.In an experiment, brass and steel wires of length 1 m each with areas of cross section 1 mm2 are used. The wires are connected in series and one end of the combined wire is connected to a rigid support and other end is subjected to elongation. The stress required to produce a net elongation of 0.2 mm is, [Given, the Young's Modulus for steel and brass are, respectively, 120 × 109 N / m2 and 60 × 109 N / m2 ] (1) 8.0 × 106 N / m2 (2) 1.2 × 106 N / m2 (3) 0.2 × 106 N / m2 (4) 1.8 × 106 N / m2

Q10.Two materials having coefficients of thermal conductivity 3K and K and thickness d and 3d respectively, are joined to form a slab as shown in the figure. The temperatures of the outer surfaces are θ2 and θ1 respectively, (θ2 > θ1). The temperature at the interface is 5θ2 (1) θ2+θ1 (2) θ1 2 6 + 6 θ1 2θ2 θ1 9θ2 (3) 3 + 3 (4) 10 + 10

Q10.Young's moduli of two wires A and B are in the ratio 7: 4 . Wire A is 2 m long and has radius R . Wire B is 1.5 m long and has radius 2 mm . If the two wires stretch by the same length for a given load, the value of R is close to: (1) 1.3 mm (2) 1.9 mm (3) 1.5 mm (4) 1.7 mm

Q11.Temperature difference of 120𝑜𝐶 is maintained between two ends of a uniform rod 𝐴𝐵 of length 2𝐿. Another 3𝐿 bent rod 𝑃𝑄, of same cross-section as 𝐴𝐵 and length , is connected across 𝐴𝐵 (See figure). In steady state, 2 temperature difference between 𝑃 and 𝑄 will be close to: (1) 45𝑜𝐶 (2) 35𝑜𝐶 (3) 60𝑜𝐶 (4) 75𝑜𝐶

Q11.A 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 is (1) 15RT (2) 12RT (3) 4RT (4) 20RT

Q11.Three Carnot engines operate in series between a heat source at a temperature T1 and a heat sink at temperature T4 (see figure). There are two other reservoirs at temperature T2 and T3, as shown, with JEE Main 2019 (10 Jan Shift 1) JEE Main Previous Year Paper T1 > T2 > T3 > T4. The three engines are equally efficient if: (1) 1 1 1 1 T2 = (T1T 42 ) 3 ; T3 = (T 12 T4) 3 (2) T2 = (T1T4) 2 ; T3 = (T 12 T4) 3 (3) 1 1 1 1 T2 = (T 12 T4) 3 ; T3 = (T1T 42 ) 3 (4) T2 = (T 13 T4) 4 ; T3 = (T1T 43 ) 3

Q11.An ideal gas is enclosed in a cylinder at pressure of 2 atm and temperature, 300 K. The mean time between two successive collisions is 6 × 10−8s. If the pressure is doubled and temperature is increased to 500 K, the mean time between two successive collisions will be close to: (1) 2 x 10−7s (2) 3 x 10−6s (3) 0. 5 x 10−8s (4) 4 x 10−8s

Q11.A cubical block of side 0.5 m floats on water with 30% of its volume under water. What is the maximum weight that can be put on the block without fully submerging it under water? [Take, density of water = 103 kg / m3 ] JEE Main 2019 (10 Apr Shift 2) JEE Main Previous Year Paper (1) 87.5 kg (2) 65.4 kg (3) 30.1 kg (4) 46.3 kg

Q11.A thermally insulated vessel contains 150 g of water at 0°C . Then the air from the vessel is pumped out adiabatically. A fraction of water turns into ice and the rest evaporates at 0°C itself. The mass of evaporated water will be closest to: (Latent heat of vaporization of water = 2.10 × 106 J kg-1 and Latent heat of Fusion of water = 3.36 × 105 J kg-1 ) (1) 35 g (2) 20 g (3) 130 g (4) 150 g

Q11.Two 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 = 8.3 J / mol K (1) 17.4 J / mol K (2) 19.7 J / mol K (3) 15.7 J / mol K (4) 21.6 J / mol K

Q11.When 100 g of a liquid A at 100∘C is added to 50 g of a liquid B at temperature 75∘C , the temperature of the mixture becomes 90∘C . The temperature of the mixture, if 100 g of liquid A at 100∘C is added to 50 g of liquid B at 50∘C , will be: (1) 85∘C (2) 60∘C (3) 80∘C (4) 70∘C

Q12.A diatomic gas with rigid molecules does 10 J of work when expanded at constant pressure. What would be the heat energy absorbed by the gas, in this process? (1) 40 J (2) 35 J (3) 25 J (4) 30 J

Q12.A massless spring (k = 800 N/m), attached with a mass (500 g) is completely immersed in 1 kg of water. The spring is stretched by 2 cm 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 = 400 J/kg K, specific heat of water = 4184 J/kg K ) (1) 10−5 K (2) 10−1 K (3) 10−3 K (4) 10−4 K

Q12.A hoop and a solid cylinder of same mass and radius are made of a permanent magnetic material with their respective axes. But the magnetic moment of hoop is twice of solid cylinder. They are placed in a uniform magnetic field in such a manner that their magnetic moments make a small angle with the field. If the oscillation periods of hoop and cylinder are Th and Tc respectively, then: (1) Th = 2Tc (2) Th = Tc (3) Th = 0.5Tc (4) Th = 1.5Tc

Q12.A stationary source emits sound waves of frequency 500 Hz . Two observers moving along a line passing through the source detect sound to be of frequencies 480 Hz and 530 Hz . Their respective speeds are, in m s−1 , (Given speed of sound = 300 m/s ) (1) 16, 14 (2) 12, 16 (3) 12, 18 (4) 8, 18

Q12.A train moves towards a stationary observer with speed 34 m/s. The train sounds a whistle and its frequency registered by the observer is f1. If the speed of the train is reduced to 17 m/s, the frequency registered is f2. If speed of sound is 340 m/s, then the ratio f1/f2 is: (1) 21/20 (2) 20/19 (3) 19/18 (4) 18/17

Q12.Two identical beakers A and B contain equal volumes of two different liquids at 60°C each and left to cool down. Liquid in A has density of 8 × 102 kg m-3 and specific heat of 2000 J kg-1K-1 while the liquid in B has density 103 kg m-3 and specific heat of 4000 J kg-1K-1. Which of the following best describes their temperature versus time graph schematically? (assume the emissivity of both the beakers to be the same) (1) (2) (3) (4)

Q12.A metal ball of mass 0.1 kg is heated upto 500∘C and dropped into a vessel of heat capacity 800JK−1 and containing 0.5 kg water. The initial temperature of water and vessel is 30∘C . What is the approximate percentage increment in the temperature of the water? [Specific Heat Capacities of water and metal are, respectively, 4200Jkg−1 K−1 and 400Jkg−1 K−1 ] (1) 15% (2) 30% (3) 25% (4) 20%

Q12.A simple harmonic motion is represented by: cm y = 3πt + √3 cos 3πt) 5(sin The amplitude and time period of the motion are: (1) 5 cm, 23 s (2) 10 cm, 23 s (3) 5 cm, 23 s (4) 10 cm, 32 s