Title 14. Transmission of Heat Hard.pdf ✅

1. There are three thermometers – one in contact with the skin of the man, other in between the vest and the shirt and third in between the shirt and coat. The readings of the thermometers are 300C, 250C and 220C respectively. If the vest and shirt are of the same thickness, the ratio of their thermal conductivities is (a) 9 : 25 (b) 25 : 9 (c) 5 : 3 (d) 3 : 5 2. Two rods of same length and material transfer a given amount of heat in 12 seconds, when they are joined end to end. But when they are joined lengthwise, then they will transfer same heat in same conditions in (a) 24 s (b) 3 s (c) 1.5 s (d) 48 s 3. Three rods made of the same material and having the same cross section have been joined as shown in the figure. Each rod is of the same length. The left and right ends are kept at 00C and o 90 respectively. The temperature of the junction of the three rods will be (a) 45o C (b) 60o C (c) 30o C (d) 20o C 4. Three rods of same dimensions are arranged as shown in figure they have thermal conductivities K1, K2 and K3. The points P and Q are maintained at different temperatures for the heat to flow at the same rate along PRQ and PQ then which of the following option is correct (a) ( ) 2 1 K3 = K1 + K2 (b) K3 = K1 + K2 (c) 1 2 1 2 3 K K K K K + = (d) 2( ) K3 = K1 + K2 5. The coefficient of thermal conductivity of copper is nine times that of steel. In the composite cylindrical bar shown in the figure. What will be the temperature at the junction of copper and steel (a) 750C (b) 670C (c) 330C (d) 250C 6. A cylinder of radius R made of a material of thermal conductivity K1 is surrounded by a cylindrical shell of inner radius R and outer radius 2R made of material of thermal conductivity K2. The two ends of the combined system are maintained at two different temperatures. There is no loss of heat across the cylindrical surface and the system is in steady state. The effective thermal conductivity of the system is (a) K1 + K2 (b) 1 2 1 2 K K K K + (c) 4 K1 + 3K2 (d) 4 3K1 + K2 7. If the ratio of coefficient of thermal conductivity of silver and copper is 10 : 9, then the ratio of the lengths upto which wax will melt in IngenHausz experiment will be (a) 6 : 10 (b) 10 : 3 (c) 100 : 81 (d) 81 : 100 8. An ice box used for keeping eatables cool has a total wall area of 1 metre2 and a wall thickness of 5.0 cm. The thermal conductivity of the ice box is K= 0.01 J/m0C. It is filled with ice at 00C along with eatables on a day when the temperature is 300C. The latent heat of fusion of ice is 334×103 J/kg. The amount of ice melted in one day is (1 day = 86,400 seconds) (a) 776 g (b) 7760 g (c) 11520 g (d) 1552 g 9. Ice starts forming in lake with water at 00C and when the atmospheric temperature is – 100C. If the time taken for 1 cm of ice be 7 hr, then the time taken for the thickness of ice to change from 1 cm to 2 cm is (a) 7 hrs (b) 14 hrs (c) Less than 7 hrs (d) More than 7 hrs 10. The only possibility of heat flow in a thermos flask is through its cork which is 75 cm2 in area and 5 cm thick. Its thermal conductivity is 0.0075 cal/cm sec0C. The outside temperature is 400C and latent heat of ice is 80 cal g–1 . Time taken by 500 g of ice at 00C in the flask to melt into water at 00C is (a) 2.47 hr (b) 4.27 hr (c) 7.42 hr (d) 4.72 hr. 11. 2There is ice formation in a tank of water of thickness 10 cm. How much time it will take to have a layer of 0.1 cm below it ? The outer temperature is – 5 0C, the thermal conductivity of ice K = 0.005 cal/cm-sec0C, the latent heat of ice is 80 cal/gm and the density of ice is 0.91 gm/cc (a) 46.39 minutes (b) 47.63 minutes (c) 48.77 minutes (d) 49.31 minutes 12. The graph. Shown in the adjacent diagram, represents the variation of temperature (T) of two bodies, x and y having same surface area, with time (t) due to the emission of radiation. Find the correct relation between the emissivity (e) and absorptivity (a) of the two bodies (a) ex > ey&ax < ay (b) ex < ey&ax > ay (c) ex > ey&ax > ay (d) ex < ey&ax < ay t T y x Copper Steel 0 100oC oC 18 cm 6 cm R P Q K1 K2 K3 0 oC 90oC 90oC A B C
13. Certain substance emits only the wavelengths 1 2 3  ,  ,  and 4 when it is at a high temperature. When this substance is at a colder temperature, it will absorb only the following wavelengths (a) 1 (b) 2 (c) 1 and 2 (d) 1 2 3  ,  ,  and 4 14. The following figure shows two air-filled bulbs connected by a U-tube partly filled with alcohol. What happens to the levels of alcohol in the limbs X and Y when an electric bulb placed midway between the bulbs is lighted (a) The level of alcohol in limb X falls while that in limb Y rises (b) The level of alcohol in limb X rises while that in limb Y falls (c) The level of alcohol falls in both limbs (d) There is no change in the levels of alcohol in the two limbs 15. The plots of intensity versus wavelength for three black bodies at temperatures T1, T2 and T3 respectively are as shown. Their temperature are such that (a) T1>T2> T3 (b) T1>T3> T2 (c) T2>T3> T1 (d) T3>T2> T1 16. The adjoining diagram shows the spectral energy density distribution E of a black body at two different temperatures. If the areas under the curves are in the ratio 16 : 1, the value of temperature T is (a) 32,000 K (b) 16,000 K (c) 8,000 K (d) 4,000 K 17. Following graph shows the correct variation in intensity of heat radiations by black body and frequency at a fixed temperature (a) (b) (c) (d) 18. A black body at 200 K is found to emit maximum energy at a wavelength of 14  m . When its temperature is raised to 1000 K, the wavelength at which maximum energy is emitted is (a) 14  m (b) 70  F (c) 2.8  m (d) 2.8 mm 19. The energy spectrum of a black body exhibits a maximum around a wavelength 0 . The temperature of the black body is now changed such that the energy is maximum around a wavelength 4 30 . The power radiated by the black body will now increase by a factor of (a) 256/81 (b) 64/27 (c) 16/9 (d) 4/3 20. The wavelength of maximum energy released during an atomic explosion was m 10 2.93 10 −  . Given that Wien's constant is m 3 2.93 10 −  –K, the maximum temperature attained must be of the order of (a) 10–7 K (b) 107 K (c) 10–13 K (d) K 7 5.86 10 21. A black body is at a temperature of 2880 K. The energy of radiation emitted by this object with wavelength between 499 nm and 500 nm is U1, between 999 nm and 1000 nm is U2 and E  Visible 1500K 2500K 3500K Infra-red Ultra-violet E  Infra-red Visible Ultra-violet 3500K 2500K 1500K 1500K 2500K 3500K E  UV Visible Infra-red UV Visible 3500K 2500K 1500K E  Infra-red  E 2000 K T K T2  I T1 T3 Bulb Black Painted Alcohol X Y
between 1499 nm and 1500 nm is U3. The Wien's constant b nm K 6 = 2.88 10 . Then (a) U1 = 0 (b) U3 = 0 (c) U1 > U2 (d) U2 > U1 22. Which of the following is the vm-T graph for a perfectly black body (a) A (b) B (c) C (d) D 23. Two black metallic spheres of radius 4m, at 2000 K and 1m at 4000 K will have ratio of energy radiation as (a) 1 : 1 (b) 4 : 1 (c) 1 : 4 (d) 2 : 1 24. Two identical metal balls at temperature 2000C and 4000C kept in air at 270C. The ratio of net heat loss by these bodies is (a) 1/ 4 (b) 1/ 2 (c) 1/ 16 (d) 4 4 4 4 673 300 473 300 − − 25. Two spheres made of same material have radii in the ratio 1 : 2. Both are at same temperature. Ratio of heat radiation energy emitted per second by them is (a) 1 : 2 (b) 1 : 8 (c) 1 : 4 (d) 1 : 16 26. Two spherical black bodies of radii 1 r and 2 r and with surface temperature T1 and T2 respectively radiate the same power. Then the ratio of 1 r and 2 r will be (a) 2 1 2         T T (b) 4 1 2         T T (c) 2 2 1         T T (d) 4 2 1         T T 27. The rectangular surface of area 8 cm × 4 cm of a black body at a temperature of 1270C emits energy at the rate of E per second. If the length and breadth of the surface are each reduced to half of the initial value and the temperature is raised to 3270C, the rate of emission of energy will become (a) E 8 3 (b) E 16 81 (c) E 16 9 (d) E 64 81 28. A solid copper cube of edges 1 cm is suspended in an evacuated enclosure. Its temperature is found to fall from 1000C to 990C in 100s. Another solid copper cube of edges 2 cm, with similar surface nature, is suspended in a similar manner. The time required for this cube to cool from 1000C to 990C will be approximately (a) 25 s (b) 50 s (c) 200 s (d) 400 s 29. Two metallic spheres S1 and S2 are made of the same material and have identical surface finish. The mass of S1 is three times that of S2. Both the spheres are heated to the same high temperature and placed in the same room having lower temperature but are thermally insulated from each other. The ratio of the initial rate of cooling of S1 to that of S2 is (a) 1/ 3 (b) (1/ 3)1/ 3 (c) 1 / 3 (d) 3 / 1 30. A sphere, a cube and a thin circular plate, all made of same substance and all have same mass. These are heated to 2000C and then placed in a room, then the (a) Temperature of sphere drops to room temperature at last (b) Temperature of cube drops to room temperature at last (c) Temperature of thin circular plate drops to room temperature at last (d) Temperature of all the three drops to room temperature at the same time 31. A solid copper sphere (density  and specific heat capacity c ) of radius r at an initial temperature 200K is suspended inside a chamber whose walls are at almost 0K. The time required (in  s) for the temperature of the sphere to drop to 100 K is (a)  rc 7 72 (b)  rc 72 7 (c)  rc 7 27 (d)  rc 27 7 32. A sphere and a cube of same material and same volume are heated up to same temperature and allowed to cool in the same surroundings. The ratio of the amounts of radiations emitted will be (a) 1 : 1 (b) 4π 3 : 1 (c) ( π 6 ) 1/3 : 1 (d) 1 2 ( 4π 3 ) 2/3 : 1 33. A bucket full of hot water cools from 750C to 700C in time T1, from 700C to 650C in time T2 and from 650C to 600C in time T3, then (a) T1 = T2 = T3 (b) T1  T2  T3 (c) T1  T2  T3 (d) T1  T2  T3 34. A cup of tea cools from 800C to 600C in one minute. The ambient temperature is 300C. In cooling from 600C to 500C it will take (a) 30 Seconds (b) 60 Seconds (c) 90 Seconds (d) 50 Seconds 35. A body takes T minutes to cool from 620C to 610C when the surrounding temperature is 300C. The time taken by the body to cool from 460C to 45.50C is (a) Greater than T minutes (b) Equal to T minutes (c) Less than T minutes (d) Equal to T/2 minutes 36. The rates of cooling of two different liquids put in exactly similar calorimeters and kept in identical surroundings are the same if (a) The masses of the liquids are equal (b) Equal masses of the liquids at the same temperature are taken (c) Different volumes of the liquids at the same temperature are taken (d) Equal volumes of the liquids at the same temperature are taken B C  D m A T
37. Hot water cools from 600C to 500C in the first 10 minutes and to 420C in the next 10 minutes. The temperature of the surrounding (a) 50C (b) 100C (c) 150C (d) 200C 38. In a room where the temperature is 300C, a body cools from 610C to 590C is 4 minutes. The time taken by the body to cool from 510C to 490C will be: (a) 4 minutes (b) 6 minutes (c) 5 minutes (d) 8 minutes 39. A compound slab consists of two parallel plates of different material of same thickness and having thermal conductivities k1 and k2. What is the equivalent thermal conductivity of the slab ? (a) k1 + k2 (b) k1k2 (c) k1+k2 k1k2 (d) 2k1k2 k1+k2 40. A black body is at a temperature of 2880K. The energy of radiation emitted by this object with wave length between 499 nm and 500 nm is U1, between 999 nm and 1000 nm is U2 and between 1499 nm and 1500 nm is U3. Wein constant b=2.88 x 106 nmK. Then (a) U1 = 0 (b) U3 = 0 (c) U1 = U2 (d) U2> U1 41. The dimensional formula of thermal resistance is (a) [M−1L −2T 3K] (b) [ML 2T −2K −1 ] (c) [ML 2T −3K] (d) [ML 2T −2K −2 ]