JEE Main & Advanced Physics Transmission of Heat Question Bank

done Topic Test - Transmission Of Heat Total Questions - 35

• question_answer1)
  If a rod is in variable state (not in steady state), then
  A)
  temperature gradient remains constant done clear
  B)
  temperature of rod is changing with distance from one end and with time also done clear
  C)
  temperature of rod is not depending on time done clear
  D)
  temperature of rod is not depending on distance from one end done clear
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• question_answer2)
  A body cools down from \[{{70}^{o}}C\] to \[{{60}^{o}}\] in 5 min. It will cool down from \[{{100}^{o}}C\] to \[{{90}^{o}}C\] in (Assume cooling by radiation alone)
  A)
  More than 5 min done clear
  B)
  less than 5 min done clear
  C)
  5 min done clear
  D)
  Can't be computed from information provided done clear
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• question_answer3)
  A glass full of hot milk is poured on the table. It begins to cool gradually. Which of the following is incorrect?
  A)
  The rate of cooling is constant still milk attains the temperature of the surrounding. done clear
  B)
  The temperature of milk falls off exponentially with time done clear
  C)
  While cooling, there is a flow of heat from milk to the surrounding as well as from surrounding to the milk but the net flow of heat is from milk to the surrounding and that is why it cools. done clear
  D)
    All three phenomenon, conduction, convection and radiation are responsible for the loss of heat from milk to the surroundings. done clear
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• question_answer4)
  Three discs A, B and C having radii 2 m, 4 m and 6 m respectively on coated with carbon black on their outer surfaces. The wavelength corresponding to maximum intensities are 300 nm, 400 nm and 500 nm respectively. The power radiated by them are \[{{Q}_{A}},\,{{Q}_{B}}\] and \[{{Q}_{C}}\] respectively
  A)
  \[{{Q}_{A}}\] is maximum done clear
  B)
  \[{{Q}_{B}}\] is maximum done clear
  C)
  \[{{Q}_{C}}\] is maximum done clear
  D)
  \[{{Q}_{A}}={{Q}_{B}}={{Q}_{C}}\] done clear
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• question_answer5)
  Water is being boiled in a flat bottom kettle placed on a stove. The area of the bottom is \[3000\text{ }c{{m}^{2}}\] and the thickness is 2 mm. If the amount of steam produced is 1 g/min. Calculate the difference of temperature between the inner and outer surface of the bottom. Thermal conductivity for the material of kettle is \[0.5\,cal/{{\,}^{o}}C/s/cm\] and the latent heat of steam is 540 cal/gm.
  A)
  \[1.2\times {{10}^{-3}}{{\,}^{o}}C\]   done clear
  B)
  \[2.4\times {{10}^{-3}}{{\,}^{o}}C\] done clear
  C)
  \[3.6\times {{10}^{-3}}{{\,}^{o}}C\]               done clear
  D)
  \[4.8\times {{10}^{-3}}{{\,}^{o}}C\] done clear
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• question_answer6)

  A ring consisting of two parts ADB and ACB of same conductivity k carries an amount of heat H. The ADB part is now replaced with another metal keeping the temperatures \[{{T}_{1}}\] and \[{{T}_{2}}\] constant. The heat carried increases to 2H. What should be the conductivity of the new ADB part? Given \[\frac{ACB}{ADB}=3\].

  A)
  \[\frac{7}{3}k\] done clear
  B)
  \[2k\] done clear
  C)
  \[\frac{5}{2}k\] done clear
  D)
  \[3k\] done clear
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• question_answer7)
  The emissivity and the surface area of filament of electric bulb are 0.7 and \[5\times {{10}^{-5}}{{m}^{2}}\]. The operating temperature of the filament is 3000 K. The power of the bulb is approximately \[[\sigma =5.67\times {{10}^{-8}}watt/{{m}^{2}}-{{K}^{4}}]\]
  A)
  230 W done clear
  B)
  160 W done clear
  C)
  9000 W done clear
  D)
  4150 W done clear
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• question_answer8)
  A rod of length I (laterally thermally insulated) of uniform cross-sectional area A consists of a material whose thermal conductivity varies with temperature as \[K=\frac{{{k}_{0}}}{a+bT},\] where,  \[{{k}_{0}},\] a and b are constants. \[{{T}_{1}}\] and \[{{T}_{2}}(<{{T}_{1}})\] are the temperature of two ends of rod. Then, rate of flow of heat across the rod is
  A)
  \[\frac{A{{k}_{0}}}{bl}\left[ \frac{a+b{{T}_{1}}}{a+b{{T}_{2}}} \right]\] done clear
  B)
  \[\frac{A{{k}_{0}}}{bl}\left[ \frac{a+b{{T}_{2}}}{a+b{{T}_{1}}} \right]\] done clear
  C)
  \[\frac{A{{k}_{0}}}{bl}\ln \left[ \frac{a+b{{T}_{1}}}{a+b{{T}_{2}}} \right]\] done clear
  D)
  \[\frac{A{{k}_{0}}}{al}\ln \left[ \frac{a+b{{T}_{2}}}{a+b{{T}_{1}}} \right]\] done clear
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• question_answer9)
  At a specific temperature, the energy densities for a black body for three different wavelengths are 10, 19 and 7 units. For these wavelengths if the absorption coefficient of a body is respectively 0.8, 0.3 and 0.9 then the emissive powers of this body for these wavelengths are in the ratio
  A)
  10 : 19 : 7 done clear
  B)
   8 : 3 : 9 done clear
  C)
  8 : 5.7 : 6.3 done clear
  D)
   8 : 9.5 : 4.3 done clear
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• question_answer10)
  The two ends of a conducting rod of varying cross. section are maintained at \[\text{20}{{\text{0}}^{\text{o}}}\text{C}\] and \[{{\text{0}}^{\text{o}}}\text{C}\] respectively in steady state
  A)
  temperature difference across AB is less than that of across CD   done clear
  B)
  temperature difference across AB is greater than of across CD done clear
  C)
  temperature difference across AB is less than that of across CD done clear
  D)
  temperature difference may be equal or different depending on the thermal conductivity done clear
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• question_answer11)
  Two rods having thermal conductivities in the ratio of 5 : 3 having equal lengths and equal cross-sectional area are joined in series. If the temperature of the free end of the first rod is \[{{100}^{o}}C\] and free end of the second rod is \[{{20}^{o}}C\]. Then temperature of the junction is
  A)
  \[~{{70}^{o}}C\] done clear
  B)
  \[~{{60}^{o}}C\] done clear
  C)
  \[{{50}^{o}}C\] done clear
  D)
  \[{{90}^{o}}C\] done clear
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• question_answer12)
  All the rods have same conductance ‘K’ and same area of cross section ‘A’. If ends A and Care maintained at temperature 2Ty and T respectively then which of the following is/are correct:                           
  A)
  Rate of heat flow through ABC, AOC and ADC is same          done clear
  B)
  Rate of heat flow through BO and OD is not same                 done clear
  C)
  Total Rate of heat flow from A to C is \[\frac{{{P}_{o}}}{{{P}_{He}}}=\frac{1}{8}\] done clear
  D)
  Temperature at junctions B, O and D are same done clear
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• question_answer13)

  Direction: In the following questions, more than one of one answers given are correct. Select the correct answers and mark it according to the following codes:

  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 some. The two bodies emit total radian power at the same rate. The wavelength \[{{\lambda }_{B}}\] corresponding to maximum spectral radiancy in the radiation from B is shifted from the wa9.-velength corresponding to maximum spectral radiancy in the radiation from A, by \[1.00\,\mu m\]. If the temperature of A is 5802 K

  (1) The temperature of B is 1934 K

  (2) \[{{\lambda }_{B}}=1.5\,\mu m\]

  (3) The temperature of B is 11604 K

  (4) The temperature of B is 2901 K

  Codes:
  A)
  1, 2 and 3 are correct      done clear
  B)
  1 and 2 are correct done clear
  C)
  2 and 4 are correct done clear
  D)
  1 and 3 are correct done clear
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• question_answer14)

  Direction: In the following questions, more than one of one answers given are correct. Select the correct answers and mark it according to the following codes:

  A cane is taken out from a refrigerator at \[0{}^\circ C\]. The atmospheric temperature is \[25{}^\circ C\]. If \[{{t}_{1}}\] is the time taken to heat from \[0{}^\circ C\] to \[5{}^\circ C\] and \[{{t}_{2}}\] is the time taken from \[10{}^\circ C\] to  \[15{}^\circ C,\] then the wrong statements are to \[{{15}^{o}}C,~\] then the wrong statements are

  (1) \[{{t}_{1}}>{{t}_{2}}\]

  (2) \[{{t}_{1}}={{t}_{2}}\]

  (3) There is no relation

  (4) \[{{t}_{1}}<{{t}_{2}}\]

  Codes:
  A)
  1, 2 and 3 are correct      done clear
  B)
  1 and 2 are correct done clear
  C)
  2 and 4 are correct done clear
  D)
  1 and 3 are correct done clear
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• question_answer15)

  Direction: In the following questions, more than one of one answers given are correct. Select the correct answers and mark it according to the following codes:

  The rate of loss of heat from a body cooling under conditions of forced convection is proportional to its

  (1) surface area

  (2) excess of temperature over that of surrounding

  (3) heat capacity

  (4) absolute temperature

  Codes:
  A)
  1, 2 and 3 are correct      done clear
  B)
  1 and 2 are correct done clear
  C)
  2 and 4 are correct done clear
  D)
  1 and 3 are correct done clear
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• question_answer16)
  The maximum spectral emissive power for a black body at temperature 5000K is obtained at\[{{\lambda }_{m}}=6000\overset{o}{\mathop{A}}\,.\] If the temperature is increased by 10% then decrease in \[{{\lambda }_{m}}\] will be (approximately)
  A)
  3.5% done clear
  B)
  7.5%    done clear
  C)
  10% done clear
  D)
  5% done clear
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• question_answer17)
  Find the equivalent thermal resistance of combination of rods as shown in figure. Every rod has same length I and cross-sectional area A. Thermal conductivities are mentioned in figure.
  A)
  \[\frac{1}{4KA}\] done clear
  B)
  \[\frac{7l}{4KA}\] done clear
  C)
  \[\frac{7l}{12KA}\] done clear
  D)
  \[\frac{l}{12KA}\] done clear
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• question_answer18)
  A long metallic bar is carrying heat from one of its ends to the other end under steady state. The variation of temperature 0 along the length x of the bar from its hot end is best described by which of the following graph options?
  A)
  done clear
  B)
  done clear
  C)
    done clear
  D)
  done clear
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• question_answer19)
  Three conducting rods of same material and cross-section are shown in figure. Temperatures of A, D and C are maintained at \[20{}^\circ C,\text{ }90{}^\circ C\] and \[0{}^\circ C\]. The ratio of lengths of BD and BC if there is no heat flow in AB is:
  A)
  2/7 done clear
  B)
  7/2 done clear
  C)
  9/2 done clear
  D)
  2/9 done clear
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• question_answer20)
  The energy spectrum of a black body exhibits a maximum around a wavelength \[{{\lambda }_{0}}\]. The temperature of the black body is now changed such that the energy is maximum around a wavelength \[3{{\lambda }_{0}}/4\]. The power radiated by the black body will now increase by a factor of
  A)
  256/81 done clear
  B)
  64/27 done clear
  C)
  16/9 done clear
  D)
  4/3 done clear
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• question_answer21)
  When a body cools by radiation, the rate of decrease of its temperature depends upon
  A)
  Specific heat of the body done clear
  B)
  Mass of the body done clear
  C)
  Nature of the surface of the body done clear
  D)
  All of these done clear
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• question_answer22)
  Two different metal rods of equal lengths & equal cross section area have their ends kept at the same temperatures \[{{\theta }_{1}}\And {{\theta }_{2}}.\] If \[{{K}_{1}}\And {{K}_{2}}\] be the thermal conductivities of rod, \[{{\rho }_{1}}\And {{\rho }_{2}}\] are their densities and \[{{s}_{1}},{{s}_{2}}\] are their specific heats, then the rate of flow of heat in the two rods will be same if
  A)
  \[\frac{{{K}_{1}}}{{{K}_{2}}}=\frac{{{\rho }_{1}}{{s}_{1}}}{{{\rho }_{2}}{{s}_{2}}}\] done clear
  B)
  \[\frac{{{K}_{1}}}{{{K}_{2}}}=\frac{{{\rho }_{1}}{{s}_{2}}}{{{\rho }_{2}}{{s}_{1}}}\] done clear
  C)
  \[\frac{{{K}_{1}}}{{{K}_{2}}}=\frac{{{\theta }_{1}}}{{{\theta }_{2}}}\] done clear
  D)
  \[{{K}_{1}}={{K}_{2}}\] done clear
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• question_answer23)
  A and B are two points on a uniform metal ring whose centre is C. The angle \[ACB=\theta \]. A and B are maintained at two different constant temperatures. When \[\theta ={{180}^{o}},\] the rate of total heat flow from A to B is 1.2W. When \[\theta ={{90}^{o}},\] this rate will be
  A)
  0.6 W done clear
  B)
  0.9 W done clear
  C)
  1.6 W done clear
  D)
  1.8 W done clear
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• question_answer24)
  One day in a room a heater connected to supply maintained temperature \[20{}^\circ C\] when outside temperature was \[-20{}^\circ C\]. Another day with the same heater, in the same room, temperature was \[10{}^\circ C\] when outside temperature was \[-40{}^\circ C\]. If temperature of heater is same both the days. Find this value. (use \[\frac{dT}{dt}=k(T-{{T}_{0}})\] and k is same for both days).
  A)
  \[120{}^\circ C\] done clear
  B)
  \[30{}^\circ C\] done clear
  C)
  \[40{}^\circ C\] done clear
  D)
  \[60{}^\circ C\] done clear
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• question_answer25)
  A rod of length i and cross section area A has a variable thermal conductivity given by  \[k=\alpha T,\] where a is a positive constant and T is temperature in kelvin. Two ends of the rod are maintained at temperatures \[{{T}_{1}}\] and \[{{T}_{2}}({{T}_{1}}>{{T}_{2}})\]. Heat current flowing through the rod will be
  A)
  \[\frac{A\alpha (T_{1}^{2}-T_{2}^{2})}{\ell }\] done clear
  B)
  \[\frac{A\alpha (T_{1}^{2}+T_{2}^{2})}{\ell }\] done clear
  C)
  \[\frac{A\alpha (T_{1}^{2}+T_{2}^{2})}{3\ell }\]        done clear
  D)
  \[\frac{A\alpha (T_{1}^{2}-T_{2}^{2})}{2\ell }\] done clear
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• question_answer26)
  One end of a conducting rod is maintained at temperature \[50{}^\circ C\] and at the other end, ice is melting at \[0{}^\circ C\]. The rate of melting of ice is doubled if:
  A)
  the temperature is made \[200{}^\circ C\] and the area of cross-section of the rod is doubled done clear
  B)
  the temperature is made \[100{}^\circ C\] and length of rod is made four times done clear
  C)
  area of cross-section of rod is halved and length is doubled done clear
  D)
  the temperature is made \[100{}^\circ C\] and the area of cross-section of rod and length both are doubled done clear
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• question_answer27)
  Twelve conducting rods form the riders of a uniform cube of side ‘l’. If in steady state, B and H ends of the rod are at \[100{}^\circ C\] and \[0{}^\circ C\]. Find the temperature of the junction ‘A’:
  A)
  \[{{80}^{o}}C\] done clear
  B)
  \[{{60}^{o}}C\] done clear
  C)
  \[{{40}^{o}}C\] done clear
  D)
  \[{{70}^{o}}C\] done clear
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• question_answer28)
  A metallic sphere having radius 0.08 m and mass m = 10 kg is heated to a temperature of \[227{}^\circ C\] and suspended inside a box whose walls are at a temperature of \[27{}^\circ C\]. The maximum rate at which its temperature will fall, is (Take \[e=1,\] Stefan's constant \[\sigma =5.8\times {{10}^{-8}}W{{m}^{-2}}{{K}^{-4}}\] and specific heat of the metal \[s=90\,cal/kg/\deg ,\,J=4.2\]  joules/calorie)
  A)
  \[{{0.055}^{o}}C/s\] done clear
  B)
  \[{{0.066}^{o}}C/s\] done clear
  C)
  \[{{0.044}^{o}}C/s\]    done clear
  D)
  \[{{0.033}^{o}}C/s\] done clear
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• question_answer29)
  A sphere, a cube and a thin circular plate all made of the same material and having the same mass, are initially heated to a temperature of \[200{}^\circ C\]. Which of these objects will cool slowest when left in air at room temperature?
  A)
   the sphere done clear
  B)
  the cube done clear
  C)
  the circular plate done clear
  D)
  all will cool at same rate done clear
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• question_answer30)
  An electric heater, assumed to be a black body has a temperature of \[727{}^\circ C\]. If its temperature is raised to \[1727{}^\circ C,\] the amount of energy radiated per unit time now as compared with that in the first case will be
  A)
  twice done clear
  B)
  4 times done clear
  C)
  16 times done clear
  D)
   100 times done clear
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• question_answer31)
  A bucket full of hot water is kept in a room and it cools from \[75{}^\circ C\] to \[70{}^\circ C~\] in \[{{T}_{1}}\] minutes, from \[70{}^\circ C\] to \[65{}^\circ C\] in \[{{T}_{2}}\] minutes and from \[65{}^\circ C\] to \[60{}^\circ C~\] in \[{{T}_{3}}\] minutes. Then
  A)
  \[{{T}_{1}}={{T}_{2}}={{T}_{3}}\] done clear
  B)
  \[{{T}_{1}}<{{T}_{2}}<{{T}_{3}}\] done clear
  C)
  \[{{T}_{1}}>{{T}_{2}}>{{T}_{3}}\] done clear
  D)
  \[{{T}_{1}}<{{T}_{3}}<{{T}_{2}}\] done clear
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• question_answer32)
  Assuming the sun to be a spherical body of radius R at a temperature of TK, evaluate the total radiant power, incident on earth, at a distance from the sun. Where r0 is the radius of the earth and a is Stefan’s constant.
  A)
  \[4\pi r_{0}^{2}\,{{R}^{2}}\,\sigma {{T}^{4}}/\,{{r}^{2}}\] done clear
  B)
  \[\pi r_{0}^{2}\,{{R}^{2}}\,\sigma {{T}^{4}}/\,{{r}^{2}}\] done clear
  C)
  \[r_{0}^{2}\,{{R}^{2}}\,\sigma {{T}^{4}}/4\pi \,{{r}^{2}}\] done clear
  D)
  \[{{R}^{2}}\,\sigma {{T}^{4}}/\,{{r}^{2}}\] done clear
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• question_answer33)

  Direction: Consider a spherical body A of radius R which placed concentrically in a hollow enclosure H, of radius 4R as shown in the figure. The temperature of the body A and H are \[{{T}_{A}}\] and \[{{T}_{H}},\] respectively.

  Emissivity, transitivity and reflectivity of two bodies A and H are \[\text{(}{{e}_{A}},\text{ }{{e}_{H}})\text{ (}{{t}_{A}},\text{ }{{t}_{H}}\text{)}\] and \[({{r}_{A}},\text{ }{{r}_{H}})\] respectively.

  For answering following questions assume no absorption of the thermal energy by the space in-between the body and enclosure as well as outside the enclosure and all radiations to be emitted and absorbed normal to the surface.

  [Take \[\sigma \times \,4\pi {{R}^{2}}\,\times \,{{300}^{4}}=\,\beta J{{s}^{-1}}\]]

  The temperature of A (a perfect black body) is \[{{T}_{A}}=300K\] and temperature of H is \[{{T}_{0}}=OK\]. For H take \[{{e}_{H}}=0.5\] and \[t=0.5\]. For this situation mark out the correct statement(s).
  A)
  The rate at which A loses the energy is \[\beta J{{s}^{-1}}\] done clear
  B)
  The rate at which spherical surface containing P receives the energy is \[\frac{\beta }{2}J{{s}^{-1}}\]. done clear
  C)
  The rate at which spherical surface containing Q receives the energy is \[\beta \,J/{{s}^{-1}}\] done clear
  D)
  All of the above done clear
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• question_answer34)

  Direction: Consider a spherical body A of radius R which placed concentrically in a hollow enclosure H, of radius 4R as shown in the figure. The temperature of the body A and H are \[{{T}_{A}}\] and \[{{T}_{H}},\] respectively.

  Emissivity, transitivity and reflectivity of two bodies A and H are \[\text{(}{{e}_{A}},\text{ }{{e}_{H}})\text{ (}{{t}_{A}},\text{ }{{t}_{H}}\text{)}\] and \[({{r}_{A}},\text{ }{{r}_{H}})\] respectively.

  For answering following questions assume no absorption of the thermal energy by the space in-between the body and enclosure as well as outside the enclosure and all radiations to be emitted and absorbed normal to the surface.

  [Take \[\sigma \times \,4\pi {{R}^{2}}\,\times \,{{300}^{4}}=\,\beta J{{s}^{-1}}\]]

  In above question, if body A has \[{{e}_{A}}=0.5,\] \[{{r}_{A}}=0.5\] and for H, \[{{e}_{H}}=0.5,\] \[r=0.5,\] then mark out the correct statement.
  A)
  The rate at which A loses the energy is done clear
  B)
  The rate at which the spherical surface containing P receives the energy is zero done clear
  C)
  The rate at which the spherical surface containing Q receives the energy is\[\beta \]. done clear
  D)
  All of the above done clear
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• question_answer35)

  Direction: Consider a spherical body A of radius R which placed concentrically in a hollow enclosure H, of radius 4R as shown in the figure. The temperature of the body A and H are \[{{T}_{A}}\] and \[{{T}_{H}},\] respectively.

  Emissivity, transitivity and reflectivity of two bodies A and H are \[\text{(}{{e}_{A}},\text{ }{{e}_{H}})\text{ (}{{t}_{A}},\text{ }{{t}_{H}}\text{)}\] and \[({{r}_{A}},\text{ }{{r}_{H}})\] respectively.

  For answering following questions assume no absorption of the thermal energy by the space in-between the body and enclosure as well as outside the enclosure and all radiations to be emitted and absorbed normal to the surface.

  [Take \[\sigma \times \,4\pi {{R}^{2}}\,\times \,{{300}^{4}}=\,\beta J{{s}^{-1}}\]]

  Consider two cases, first one in which A is a perfect black body and the second in which A is a non-black body. In both the cases, temperature of body A is same equal to 300K and H is at temperature 600K. For H, \[t=0\] and \[a\ne 1\]. For this situation, mark out the correct statement.
  A)
  The bodies lose their distinctiveness inside the enclosure and both of them emit the same radiation as that of the black body. done clear
  B)
  The rate of heat loss by A in both cases is the same and is equal to\[\beta \,J{{s}^{-1}}\]. done clear
  C)
  The rates of heat loss by A in both the cases are different. done clear
  D)
  From this information we can calculate exact rate of heat loss by A in different cases. done clear
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