Thermodynamics PYQs Set 2 (PDF)

Set 2 of 17 · Questions 31-60 of 484

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Mere Teacher · Previous Year Questions JEE Main Physics · Thermodynamics · Set 2 (Q31-60)
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31. $The temperature of 100 g of water is to be raised from 24^{\circ} C to 90^{\circ} C by adding steam at 100^{\circ} C to it. The mass of the steam required in this process is (latent heat of steam is 540 cal g^{- 1})$ (1) $2 g$ (2) $4 g$ (3) $10 g$ (4) $12 g$ 32. $If the volume of a block of metal changes by 0.12 % when heated through 20^{\circ} C, then find its coefficient of linear expansion.$ (1) $4 \times 10^{- 5} ° C^{- 1}$ (2) $4 \times 10^{- 4} ° C^{- 1}$ (3) $2 \times 10^{- 5} ° C^{- 1}$ (4) $2 \times 10^{- 4} ° C^{- 1}$ 33. $A metal ball of mass 1 kg is heated using a 40 W heated in a room at 30^{\circ} C . The temperature of the ball becomes steody at 70^{\circ} C . Assuming Newton's law of cooling the rate of loss of heat to the surrounding when the ball is at 40^{\circ} C is$ (1) $20 W$ (2) $5 W$ (3) $25 W$ (4) $10 W$ 34. $The molecules of a given mass of a gas have r.m.s. velocity of 200 m s^{- 1} at 2 7^{o} C and 1.0 \times 1 0^{5} N m^{- 2} pressure. When the temperature and pressure of the gas are respectively, 12 7^{o} C and 0. 05 \times 1 0^{5} N m^{- 2}, the r.m.s. velocity of its molecules in m s^{- 1} is$ (1) $\frac{100 2}{3}$ (2) $\frac{100}{3}$ (3) $1002$ (4) $\frac{400}{3}$ 35. $A monoatomic ideal gas, initially at temperature T_{1} is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature T_{2} by releasing the piston suddenly. If L_{1} and L_{2} are the lengths of the gas column before and after expansion respectively then T_{1} / T_{2} is given by$ (1) $(\frac{L _{2}}{L _{1}})^{2/3}$ (2) $(\frac{L _{1}}{L _{2}})$ (3) $(\frac{L _{1}}{L _{2}})^{2/3}$ (4) $(\frac{L _{2}}{L _{1}})$ 36. $In a thermodynamic process, there is no exchange of heat between the system and surroundings. Then the thermodynamic process is$ (1) $isothermal$ (2) $isobaric$ (3) $isochoric$ (4) $adiabatic.$ 37. $The amount of heat needed to raise the temperature of 4 moles of a rigid diatomic gas from 0^{0} C to 5 0^{0} C when no work is done is ___ (R is the universal gas constant)$ (1) $250R$ (2) $750R$ (3) $175R$ (4) $500R$ 38. $For a perfect black body, the absorption coefficient is$ (1) $a = 1$ (2) $a < 1$ (3) $a > 1$ (4) $a = 0$ 39. $The temperature of the sink of a Carnot's engine is 300 K and the efficiency of the engine is 0.25. If the temperature of the source of the engine is increased by 100 K, the efficiency of the engine increases by$ (1) $0.50$ (2) $0.25$ (3) $0.15$ (4) $0.40$ 40. $An ideal heat engine exhausting heat at 7 7^{o} C is to have a 30% efficiency. It must take heat at$ (1) $12 7^{o} C$ (2) $22 7^{o} C$ (3) $32 7^{o} C$ (4) $67 3^{o} C$ 41. $The equation of state for 5 g of oxygen at a pressure P and temperature T, when occupying a volume V, will be$ (1) $PV = (5/32) RT$ (2) $PV = 5 RT$ (3) $PV = (5/2) RT$ (4) $PV = (5/16) RT$ 42. $Water falls from a height of 200 m into a pool. Calculate the rise in temperature of the water assuming no heat dissipation from the water in the pool. (Take g = 10 m / s^{2}, specific heat of water = 4200 J/(kg K))$ (1) $0.36 K$ (2) $0.23 K$ (3) $0.48 K$ (4) $0.14 K$ 43. $One mole of an ideal monoatomic gas undergoes a process described by the equation p V^{3} = constant. The heat capacity of the gas during this process is [NEET 2016]$ (1) $3 2 R$ (2) $5 2 R$ (3) $2 R$ (4) $R$ 44. $Match List - I with List - II. List - I (A) Isothermal (B) Adiabatic (C) Isobaric (D) Isochoric List - II (I) Δ W (work done) =0 (II) Δ Q (supplied heat) =0 (III) Δ U (change in internal energy) \neq = 0 (IV) Δ U = 0 Choose the correct answer from the options given below:$ (1) $(A)-(III), (B)-(II), (C)-(I), (D)-(IV)$ (2) $(A)-(II), (B)-(IV), (C)-(I), (D)-(III)$ (3) $(A)-(IV), (B)-(II), (C)-(III), (D)-(I)$ (4) $(A)-(IV), (B)-(I), (C)-(III), (D)-(II)$ 45. $Which of the following processes is reversible?$ (1) $Transfer of heat by conduction$ (2) $Transfer of heat by radiation$ (3) $Isothermal compression$ (4) $Electrical heating of a nichrome wire.$ 46. $The volume of an ideal gas (γ = 1.5) is changed adiabatically from 5 liters to 4 liters. The ratio of initial pressure to final pressure is:$ (1) $\frac{16}{25}$ (2) $\frac{4}{5}$ (3) $\frac{8}{5 5}$ (4) $\frac{2}{5}$ 47. $A blacksmith fixes circular iron frame on the wooden wheel of a bullock cart. The diameter of wooden wheel and circular iron frame are 5.012 m and 5 m respectively at 27^{\circ} C . The temperature (in ° C) to which the iron ring must be heated so as to fit the wooden wheel is (Coefficient of linear expansion of iron = 1.2 \times 10^{- 5} ° C^{- 1})$ (1) $200$ (2) $227$ (3) $254$ (4) $300$ 48. $During an isothermal expansion, a confined ideal gas does‐150 J ofwork against its surroundings. This implies that$ (1) $150 J ofheat has been removed from the gas$ (2) $300 J of heat has been added to the gas$ (3) $no heat is transferred because the process is isothermal$ (4) $150 J of heat has been added to the gas$ 49. $A Carnot engine takes 3 \times 1 0^{6} cal of heat from a reservoir at 627ºC and gives it to a sink at 27ºC. The work done by the engine is:$ (1) $4.2 \times 1 0^{6} J$ (2) $8.4 \times 1 0^{6} J$ (3) $16.8 \times 1 0^{6} J$ (4) $zero$ 50. $What is the source temperature of the Carnot engine required to get 70 % efficiency? Given sink temperature = 27^{\circ} C$ (1) $270^{\circ} C$ (2) $1000^{\circ} C$ (3) $727^{\circ} C$ (4) $90^{\circ} C$ 51. $An object cools from 100^{\circ} C to 40^{\circ} C in 10 minutes, when the surrounding temperature is 10^{\circ} C . Then the time taken by the object to cool from 70^{\circ} C to 20^{\circ} C is [Take ln 2 = 0.7, ln 3 = 1.1, ln 6 = 1.8]$ (1) $30 min$ (2) $8.5 min$ (3) $22.4 min$ (4) $16.3 min$ 52. $One mole of nitrogen gas being initially at a temperature of T_{0} = 300 K is adiabatically compressed to increase its pressure 10 times. The final gas temperature after compression is (Assume, nitrogen gas molecules as rigid diatomic and 100^{1/7} = 1.9)$ (1) $120 K$ (2) $750 K$ (3) $650 K$ (4) $570 K$ 53. $Two thin metallic spherical shells of radii 20 cm and 30 cm, respectively are placed with their centers coinciding. A material of thermal conductivity α is filled in the space between the shells. The inner shell is maintained at 300 K and the outer shell at 310 K . If the rate at which heat flows radially through the material is 40 W, find the value of α (in units of Js^{- 1} m^{- 1} K^{- 1}).$ (1) $\frac{3}{π}$ (2) $\frac{4 π}{3}$ (3) $\frac{5}{3 π}$ (4) $\frac{π}{2}$ 54. $A diatomic gas initially at 1 8^{o} C is compressed adiabatically to one eighth ofits original volume. The temperature after compression will be$ (1) $395. 4^{o} C$ (2) $14 4^{o} C$ (3) $1 8^{o} C$ (4) $887. 4^{o} C .$ 55. $In an adiabatic process, which of the following statements is true?$ (1) $The internal energy of the gas decreases as the temperature increases$ (2) $The molar heat capacity is zero$ (3) $Work done by the gas equals the increase in internal energy$ (4) $The molar heat capacity is infinite$ 56. $A monoatomic gas at pressure P and volume V is suddenly compressed to one eighth of its original volume. The final pressure at constant entropy will be:$ (1) $P$ (2) $8P$ (3) $32P$ (4) $64 P$ 57. $The internal energy of a monoatomic gas is 3 nRT . One mole of helium is kept in a cylinder having internal cross section area of 17 cm^{2} and fitted with a light movable frictionless piston. The gas is heated slowly by suppling 126 J heat. If the temperature rises by 4^{\circ} C, then the piston will move____cm . (atmospheric pressure = 10^{5} Pa)$ (1) $1.45$ (2) $15.5$ (3) $1.55$ (4) $14.5$ 58. $A Carnot engine takes 3 \times 10^{6} cal . of heat from a reservoir at 627^{\circ} C, and gives it to a sink at 27^{\circ} C . The work done by the engine is$ (1) $4.2 \times 10^{6} J$ (2) $8.4 \times 10^{6} J$ (3) $16.8 \times 10^{6} J$ (4) $Zero$ 59. $Two containers A and B contain equal volumes of an identical gas at the same pressure and temperature. The gas in container A is compressed to half its original volume isothermally, while the gas in container B is compressed to half its original volume adiabatically. The ratio of the final pressure of gas in container B to that of gas in container A is$ (1) $2^{γ - 1}$ (2) $(\frac{1}{2})^{γ - 1}$ (3) $(\frac{1}{1 - γ})^{2}$ (4) $(\frac{1}{γ - 1})^{2}$ 60. $One mole of an ideal gas is taken through an adiabatic process where the temperature rises from 270C to 370C. If the ideal gas is composed of polyatomic molecule that has 4 vibrational modes, which of the following is true? (R = 8.314 Jmo l^{- 1} k^{- 1})$ (1) $work done by the gas is close to 332J$ (2) $work done on the gas is close to 582J$ (3) $work done by the gas is close to 582J$ (4) $work done on the gas is close to 332J$