Thermal Properties & Calorimetry PYQs Set 2 (PDF)

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Set 2 of 5 · Questions 31-60 of 145

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Mere Teacher · Previous Year Questions JEE Main Physics · Thermal Properties & Calorimetry · Set 2 (Q31-60)
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31. $An unknown metal of mass 192 g heated to a temperature of 100°C was immersed into a brass calorimeter of mass 128 g containing 240 g of water at a temperature of 8.4°C. Calculate the specific heat of the unknown metal if water temperature stabilizes at 21.5°C. (Specific heat of brass is 394 J k g^{-1} K^{-1})$ (1) $916 J k g^{-1} K^{-1}$ (2) $458 J k g^{-1} K^{-1}$ (3) $1232 J k g^{-1} K^{-1}$ (4) $654 J k g^{-1} K^{-1}$ 32. $In a process, temperature and volume of one mole of an ideal monoatomic gas are varied according to the relation VT = K where K is a constant. In this process the temperature of the gas is increased by Δ T . The amount of heat absorbed by gas is (R is gas constant):$ (1) $\frac{1}{2} R Δ T$ (2) $\frac{1}{2} KR Δ T$ (3) $\frac{3}{2} R Δ T$ (4) $\frac{2 K}{3} Δ T$ 33. $Four rods with different radii r and length l are used to connect two heat reservoirs at different temperatures. Which one will conduct most heat?$ (1) $r = 1 cm, l = 1 m$ (2) $r = 1 cm, l = \frac{1}{2} m$ (3) $r = 2 cm, l = 2 m$ (4) $r = 2 cm, l = \frac{1}{2} m$ 34. $A copper block of mass 5.0 kg is heated to a temperature of 500°C and is placed on a large ice block. What is the maximum amount of ice that can melt? [Specific heat of copper: 0.39 J g^{- 1} ° C^{- 1} and latent heat of fusion of water: 335 J g^{- 1}]$ (1) $1.5 kg$ (2) $5.8 kg$ (3) $2.9 kg$ (4) $3.8 kg$ 35. $In a photoelectric experiment, the wavelength of the light incident on a metal is changed from 300 nm to 400 nm . The decrease in the stopping potential is close to: (\frac{hc}{e} = 1240 nm - V)$ (1) $0.5 V$ (2) $1.5 V$ (3) $1.0 V$ (4) $2.0 V$ 36. $The temperature of a body in air falls from 40^{\circ} C to 24^{\circ} C in 4 minutes. The temperature of the air is 16^{\circ} C . The temperature of the body in the next 4 minutes will be:$ (1) $\frac{14}{3}^{\circ} C$ (2) $\frac{42}{3}^{\circ} C$ (3) $\frac{28}{3}^{\circ} C$ (4) $\frac{56}{3}^{\circ} C$ 37. $Two rods A and B of identical dimensions are at temperature 30^{\circ} C . If A is heated upto 180^{\circ} C and B upto T^{\circ} C then the new lengths are the same. If the ratio of the coefficients of linear expansion of A and B is 4 : 3, then the value of T is:$ (1) $230^{\circ} C$ (2) $270^{\circ} C$ (3) $200^{\circ} C$ (4) $250^{\circ} C$ 38. $Which of the following best represents the temperature versus heat supplied graph for water, in the range of - 20^{\circ} C to 120^{\circ} C ?$ (1) (2) (3) (4) 39. $A pan filled with hot food cools form 94^{\circ} C to 86^{\circ} C in 2 minutes. When the room temperature is 20^{\circ} C . How long will it cool from 74^{\circ} C to 66^{\circ} C ?$ (1) $2 minutes$ (2) $2.8 minutes$ (3) $2.5 minutes$ (4) $1.8 minutes$ 40. $2 liters water at 27°C is heated by a 1 kW heater in an open container. On an average heat is lost to surroundings at the rate 160 J/s. The time required for the temperature to reach 77°C is$ (1) $8 min 20 sec$ (2) $10 min$ (3) $7 min$ (4) $14 min$ 41. $Time taken by a 836 W heater to heat one liter of water from 10ºC to 40ºC is:$ (1) $50 s$ (2) $100 s$ (3) $150 s$ (4) $200 s$ 42. $A copper rod of 88 cm and an aluminium rod of unknown length have their increase in length independent of increase in temperature. The length of aluminium rod is [NEET 2019]$ (1) $113.9 cm$ (2) $88 cm$ (3) $68 cm$ (4) $6.8 cm$ 43. $An aluminium and steel rods having same lengths and cross-sections are joined to make total length of 120 cm at 30^{\circ} C . The coefficient of linear expansion of aluminium and steel are 24 \times 10^{- 6} /^{\circ} C and 1.2 \times 10^{- 5} /^{\circ} C, respectively. The length of this composite rod when its temperature is raised to 100^{\circ} C, is____cm .$ (1) $120.20$ (2) $120.15$ (3) $120.06$ (4) $120.03$ 44. $A metal ball of mass 0.1 kg is heated upto 500° C and dropped into a vessel of heat capacity 800 J K^{- 1} and containing 0.5 kg water. The initial temperature of water and vessel is 30° C. What is the approximate percentage increment in the temperature of the water? [Specific Heat Capacities of water & metal are, respectively, 4200 Jk g^{- 1} K^{- 1} and 400 JK g^{- 1} K^{- 1}]$ (1) $15%$ (2) $30%$ (3) $25%$ (4) $20%$ 45. $Two conductors have the same resistances at 0^{\circ} C but their temperature coefficients of resistance are α_{1} and α_{2} The respective temperature coefficients for their series and parallel combinations are:$ (1) $α_{1} + α_{2}, \frac{α _{1} + α _{2}}{2}$ (2) $\frac{α _{1} + α _{2}}{2}, \frac{α _{1} + α _{2}}{2}$ (3) $α_{1} + α_{2}, \frac{α _{1} α _{2}}{α _{1} + α _{2}}$ (4) $\frac{α _{1} + α _{2}}{2}, α_{1} + α_{2}$ 46. $Liquid oxygen at 50K is heated to 300 K at constant pressure of 1 atm. The rate of heating is constant. Which one of the following graphs represents the variation of temperature with time$ (1) (2) (3) (4) 47. $The amount of heat energy radiated by a metal at temperature T is E . When the temperature is increased to 3 T, energy radiated is$ (1) $81 E$ (2) $9 E$ (3) $3 E$ (4) $27 E$ 48. $An external pressure P is applied on a cube at 0°C so that it is equally compressed from all sides. K is the bulk modulus of the material of the cube and α is its coefficient of linear expansion. Suppose we want to bring the cube to its original size by heating. The temperature should be raised by:$ (1) $3PKα$ (2) $\frac{P}{3 α K}$ (3) $\frac{P}{α K}$ (4) $\frac{3 α}{P K}$ 49. $At what temperature a gold ring of diameter 6.230 cm be heated so that it can be fitted on a wooden bangle of diameter 6.241 cm? Both the diameters have been measured at room temperature (27°C). (Given: coefficient of linear thermal expansion of gold α_{L} = 1.4 x 10-5 K^{- 1})$ (1) $125.7°C$ (2) $91.7°C$ (3) $425.7°$ (4) $152.7°C$ 50. $The quantities of heat required to raise the temperature of two solid copper spheres of radii r_{1} and r_{2} (r_{1} = 1.5 r_{2}) through 1 K are in the ratio [NEET 2020]$ (1) $\frac{9}{4}$ (2) $\frac{3}{2}$ (3) $\frac{5}{3}$ (4) $\frac{27}{8}$ 51. $Two cylindrical vessels of equal cross sectional area of 2 m^{2} contain water upto heights 10 m and 6 m, respectively. If the vessels are connected at their bottom then the work done by the force of gravity is (Density of water is 10^{3} kg / m^{3} and g = 10 m / s^{2})$ (1) $1 \times 10^{5} J$ (2) $4 \times 10^{4} J$ (3) $8 \times 10^{4} J$ (4) $6 \times 10^{4} J$ 52. $Two Carnot engines A and B are operated in series. The first one, A receives heat at T_{1} (= 600 K) and rejects to a reservoir at temperature T_{2} The second engine B receives heat rejected by the first engine and in turn, rejects to a heat reservoir at T_{3} (= 400 K) . Calculate the temperature T_{2} if the work outputs of the two engines are equal:$ (1) $600 K$ (2) $400 K$ (3) $300 K$ (4) $500 K$ 53. $On a temperature scale 'X' the boiling point of water is 65°X and the freezing point is -15°X. Assuming that the X scale is linear. The equivalent temperature corresponding to -95 °X on the Fahrenheit scale would be$ (1) $-112°F$ (2) $-48 °F$ (3) $-148 F$ (4) $-63°F$ 54. $A piece of ice falls from a height h, so that it melts completely. Only one-quarter of the heat produced is absorbed by the ice and all energy of ice gets converted into heat during its fall. The value of h is [Latent heat of ice is 3.4 \times 10^{5} J / kg and g = 10 N / kg] [NEET 2016]$ (1) $544 km$ (2) $136 km$ (3) $68 km$ (4) $34 km$ 55. $Two plates A and B have thermal conductivities 84 W m^{- 1} K^{- 1} and 126 W m^{- 1} K^{- 1} respectively. They have same surface area and same thickness. They are placed in contact along their surfaces. If the temperatures of the outer surfaces of A and B are kept at 100° C and 0°C respectively, then the temperature of the surface of contact in steady state is_____°C.$ 56. $Steel wire of length ‘L’ at 40°C is suspended from the ceiling and then a mass ‘m’ is hung from its free end. The wire is cooled down from 40°C to 30°C to regain its original length ‘L’. The coefficient of linear thermal expansion of the steel is 1 0^{-5} /°C, Young’s modulus of steel is 1 0^{11} N/ m^{2} and radius of the wire is 1 mm. Assume that L >> diameter of the wire. Then the value of ‘m’ in kg is nearly.$ 57. $The length of a light string is 1.4 m when the tension on it is 5 N. If the tension increases to 7 N, the length of the string is 1.56 m. The original length of the string is m.$ 58. $A water heater of power 2000 W is used to heat water. The specific heat capacity of water is 4200 J k g^{- 1} K^{- 1} . The efficiency of heater is 70%. Time required to heat 2 kg of water from 10°C to 60°C is _________s. (Assume that the specific heat capacity of water remains constant over the temperature range of the water).$ 59. $A steel rod of length 1 m and cross-sectional area 1 0^{- 4} m^{2} is heated from 0°C to 200 °C without being allowed to extend or bend. The compressive tension produced in the rod is_____x 1 0^{4} N. (Given Young's modulus of steel = 2 x 1 0^{11} N m^{- 2}, coefficient of linear expansion = 1 0^{- 5} K^{- 1})$ 60. $A geyser heats water flowing at a rate of 2.0 kg per minute from 30°C to 70°C. If geyser operates on a gas burner, the rate of combustion of fuel will be ____________ g mi n^{- 1} [Heat of combustion = 8 x 1 0^{3} J g^{- 1} Specific heat of water = 4.2 J g^{- 1} ° C^{- 1}]$