Title 5C.TRANSMISSION OF HEAT_Final (118-139).pdf ✅

THERMAL PHYSICS 118 NISHITH Multimedia India (Pvt.) Ltd., JEE ADVANCED - VOL - IV NISHITH Multimedia India (Pvt.) Ltd., LEVEL V SINGLE ANSWER QUESTIONS 1. 0.5 mole of an ideal gas at constant temperature 27°C kept inside a cylinder of length L and cross-section area A closed by a massless piston. The cylinder is attached with a conducting rod of length L, cross-section area (1/9) m2 and thermal conductivity k, whose other end is maintained at 0°C. If piston is moved such that rate of heat flow through the conducing rod is constant then find velocity of piston when it is at height L/2 from the bottom of cylinder. [Neglect any kind of heat loss from system] (A) k 50R (B) k 100R (C) k 110R (D) k 90R 2. Two thin walled spheres of different materials, one with double the radius and one-fourth wall thickness of the other, are filled with ice. If the time taken for complete melting of ice in the sphere of larger radius is 25 minutes and that for smaller one is 16 minutes, the ratio of thermal conductivities of the materials of larger sphere to the smaller sphere is : (A) 4 : 5 (B) 25 : 1 (C) 1 : 25 (D) 8 : 25 3. The power radiated by a black body is P, and it radiates maximum energy around the wavelength 0 . If the temperature of the black body is now changed so that it radi- ates maximum energy around a wavelength 30 /4, the power radiated by it will increase by a factor of (A) 4/3 (B) 16/9 (C) 64/27 (D) 256/81 4. A calorimeter of negligible heat capacity contains 100 cc of water at 0 40 C. The water cools to 0 35 C .in 5 min. The water is now replaced by k-oil A equal volume at 0 40 C ,. Find the time taken for the temp to become 0 35 C (Given densities of water and K-oil are respectively 1000 and 800 3 kg m.  ; and their specific heats are respectively: 420 and 2100 0 J kg C /  ) (A) 1 min (B) 2 min (C) 3 min (D) 4 min O τ 2τ Time t  T T 0 T  0 ΔT  0 0.37 ΔT     2 0 0.37 ΔT 5. A and B are two points on a uniform metal ring whose centre is C. The angle ABC =  . A and B are maintained at two different constant temperatures. When  = 180°, the rate of total heat flow from A to B is 1.2 W. When  = 90°, this rate will be (A) 0.6 W (B) 0.9 W (C) 1.6 W (D) 1.8 W 6. Two metallic spheres S1 and S2 are made of the same material and have got identical surface finish. The mass of S1 is thrice 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 S2 is (IIT - 1995) (A) 1 3 (B) 1 3 (C) 3 1 (D) 1 3 1 3           TRANSMISSION OF HEAT
NISHITH Multimedia India (Pvt.) Ltd., 119 JEE MAINS - CW - VOL - I JEE ADVANCED - VOL - IV TRANMISSION OF HEAT NISHITH Multimedia India (Pvt.) Ltd., 7. 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 between 1499 nm and 1500 nm is U3 . The Wein constant, b = 2.88 × 106 nm-K. Then (IIT - 1998) (A) U1 = 0 (B) U3 = 0 (C) U1 > U2 (D) U2 > U1 8. Three discs, A, B and C having radii 2 m, 4 m and 6 m respectively are coated with carbon black on their outer surfaces. The wavelengths corresponding to maximum intensity are 300 nm, 400 nm and 500 nm respectively. The power radiated by them are QA , QB and QC respectively (IIT - 2004) (A) QA is maximum (B) QB is maximum (C) QC is maximum (D) QA = QB = QC 9. In which of the following process, convection does not take place primarily ? (IIT- 2005) (A) Sea and land breeze (B) Boiling of water (C) Warming of glass bulb due to filament (D) heating air around a furnace 10. Variation of radiant energy emitted by sun, filament of tungsten lamp and welding arc as a function of its wavelength is shown in figure. Which of the following option is the correct match? (A) Sun-T1 ,tungsten filament-T2 , welding arc-T3 (B) Sun-T2 ,tungsten filament-T1 , welding arc-T2 (C) Sun-T3 ,tungsten filament-T2 , welding arc-T1 (D) Sun-T1 ,tungsten filament-T3 , welding arc-T2 11. A solid copper sphere ( density  and spe- cific heat C) of radius r at a n initial temeprature 200K is suspended inside a chamber whose walls are at almost 0K. The time required for the temeprature of the sphere to drop to 100K is A) 1.7  rc B) 2.7  rc C) 3.3  rc D) 4.2  rc 12. Three very large plates of same area kept parallel and close to each other. They are considered as ideal black surfaces and have very high thermal conductivity. The first and third plates are maintained at temperature 2T and 3T respectively. The temperature of the middle (i.e. second) plate under steady state condition is (IIT JEE-2012) (a) 1 65 4 2 T       (b) 1 97 4 4 T       (c) 1 97 4 2 T       (d)   1 97 4 T 13. A metal rod A of 25 cm length expands by 0.05 cm when its temperature is raised from 0 0 C to 0 100 C. Another rod B of a different metal of length 40cm expands by 0.04cm for the same rise in temperature.A third rod C of 50 cm length is made up of pices of rods AandB placed end to end expands by 0.03 cm on heating from 0 0 C to 0 50 C . The length of each portion of composite rod C. (A) 20cm, 35cm (B) 12cm, 48cm (C) 10cm, 40cm (D) 15cm, 60cm MULTIPLE ANSWER TYPE 14. Two identical objects A and B are at temperatures TA and TB , respectively. Both objects are placed in a room with perfectly absorbing walls maintained at a temperature T (TA > T > TB ). The objects A and B attain the temperature T eventually. Select the correct statements from the following. (A) A only emits radiation, while B only absorbs it until both attain the temperature T (B) A loses more heat by radiation than it absorbs, while B absorbs more radiation than it emits, until they attain the temperature T (C) Both A and B only absorb radiation, but do not emit it,until they attain the temperature T (D) Each object continuous to emit and absorb radiation even after attaiing the temperature T
THERMAL PHYSICS 120 NISHITH Multimedia India (Pvt.) Ltd., JEE ADVANCED - VOL - IV NISHITH Multimedia India (Pvt.) Ltd., 15. Two solid spheres are heated to the same tempearature and allowed to cool under identical conditions. Compare; (i) initial rates of fall of temperature, and (ii) initial rates of loss of heat. Assume that all the surfaces have the same emissivity and ratios of their radii, specific heats and densities are respectively 1: ,1: ,1: α β γ. (A) α β γ : 1; (B) 2 1 : α (C) β α γ  (D) 3 1 : α 16. Two bodies A and B have thermal emissivities of 0.01 and 0.81 respectively. The outer surface areas of the two bodies are the same. The two bodies emit total radiant power at the same rate. The wavelength B corresponding to maximum spectral radiancy in the radiation from B shifted from the wavelength corresponding to maximum spectral radiancy in the radiation from A, by 1.00 m . If the temperature of A is 5802 K : (IIT - 1994) (A) the temperature of B is 1934 K (B) 1.5   B  m (C) the temperature of B is 11604 K (D) the temperature of B is 2901 K MATRIX MATCHING TYPE QUESTIONS 17. Match the following Column I and II Column I (A) Wien’s displacement explains (B)Planck’s law explains (C) Kirchhoff’s law explains (D) Newton’s law of cooling explains Column II (p) Why days are hot and nights cold in deserts (q) Why a blackened platinum wire, when gradually heated, appears first dull red and then blue (r) The distribution of energy in black body spectrum at shorter as well as longer wavelengths (s) Why some stars are hot ter than other 18. COLUMN - I A) Aperfect reflecting body B) Aperfect black body C) An ordinary smooth body D) An ordinary rough body COLUMN - II P) absorbs radiation Q) reflects radiation R) emits radiations S) transfer heat COMPREHENSIVE TYPE QUESTIONS Passage : 1 A body is kept inside a container the temeprature of the body is T1 and the temeprature of the con- tainer is T2 . the rate at which body absorbs the energy is  . The emissivity of the body is e. The radiation striking the body is either absorbed or reflected. 19. After a long time, the temperature of the body will be A) T1 B) T2 C)  1 2  1 2 T T T   D) none of these 20. At what rate, the body will emit the radiant energy A) If t is the time, rate is T T t 1 2   B) e C) both of the above D) none of the above 21. At what rate the body will basorb the radi- ant energy A)  , but e  B) T T t 1 2  / , where t is the time C) e, but e =  D) None of the above 22. A good absorber is A) good reflector B) poor reflector C) average reflector D) assessment not possible
NISHITH Multimedia India (Pvt.) Ltd., 121 JEE MAINS - CW - VOL - I JEE ADVANCED - VOL - IV TRANMISSION OF HEAT NISHITH Multimedia India (Pvt.) Ltd., ASSERTION & REASON TYPE QUESTIONS Note : Each question contains STATEMENT-1 (Assertion) and STATEMENT-2 (Reason). Each question has 5 choices (A), (B), (C), (D) and (E) out of which ONLY ONE is correct. (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1. (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1. (C) Statement -1 is True, Statement-2 is False. (D) Statement -1 is False, Statement-2 is True. (E) Statement -1 is False, Statement-2 is False 23. Statement -1 : If an ideal gas expands in vacuum in an insulated chamber, Q, U and W all are zero. Statement -2 : Temperature of the gas remains constant. 24. Statement -1 : At a given temperature the specific heat of a gas at constant volume is always greater than its specific heat at constant pressure. Statement -2 : When a gas is heated at constant volume some extra heat is needed compared to that at constant pressure for doing work in expansion. 25. Statement -1 : Internal energy change is zero if the temp is constant, irrespective of the process being cyclic or non-cyclic. Statement -2 : dU = n Cv dT for all process and is independent of path. 26. Statement -1 : As the temperature of the blackbody increases, the wavelength at which the spectral intensity (E ) is maximum decreases. Statement -2 :The wavelength at which the spectral intensity will be maximum for a black body is proportional to the fourth power of its absolute temperature. 27. Statement -1 : The specific heat of a gas in an adiabatic process is zero but it is infinite in an isothermal process. Statement -2 : Specific heat of a gas directly proportional to heat exchanged with the system and inversely proportional to change in temperature. INTEGER TYPE QUESTIONS 28. A rod of length l with thermally insulated lateral surface is made of a material whose thermal conductivity varies as K = C/T. where C is a constant. The ends are kept at temperatures T1 and T2 . The temperature at a distance x from the first end where the temperature is T1 , nx / 2 2 1 1 T T T T l        . Find the value of n? 29. A solid copper sphere of density ,specific heat c and radius r is at temperature T1 . It is suspended inside a chamber whose walls are at temperature 0 K. The time required for the temperature of sphere to drop to T2 is 3 3 2 1 r c 1 1 xe T T         . Find the value of x? Take the emmissivity of teh sphere to be equal to e. 30. Two identical conducting rods are first, connected independently to two vessels, one containing water at 100°C and the other containing ice at 0°C. In the second case, rods are joined end to end and are connected to the same vessels. If q1 and q2 (in g/s) are the rates of melting of ice in two cases, then find the ratio of q1 /q2 . 31. Two spherical bodies A (radius 6 cm) and B (radius 18 cm) are at temperatures T1 and T2 respectively. The maximum intensity in the emission spectrum of A is at 500 nm and in that of B is at 1500 nm. Considering them to be black bodies, what will be the ratio of total energy radiated by A to that of B?(IIT- 2010)