NEET Physics Class 11 Chapter 8 Heat Transfer Multiple Choice Question And Answers

NEET Physics Class 11 Chapter 8 Heat Transfer Multiple Choice Question And Answers

Question 1. A wall has two layers A and B, each made of different material. Both the layers have the same thickness. The thermal conductivity for A is twice that of B. Under steady state, the temperature difference across the whole wall is 36°C. Then the temperature difference across layer A is

1. 6°C
2. 12°C
3. 18°C
4. 24°C

Answer: 2. 12°C

Question 2. A heat flux of 4000 J/s is to be passed through a copper rod of length 10 cm and an area of cross-section 100 sq. cm. The thermal conductivity of copper is 400 W/mC. The two ends of this rod must be kept at a temperature difference of–

1. 1ºC
2. 10ºC
3. 100ºC
4. 1000ºC

Answer: 3. 100ºC

Question 3. If two conducting slabs of thickness d₁ and d₂, and thermal conductivity K₁ and K₂ are placed together face to face as shown in the figure the steady state temperatures of outer surfaces are θ₁ and θ₂. The temperature of the common surface is–

1. \(\frac{K_1 \theta_1 d_1+K_2 \theta_2 d_2}{K_1 d_1+K_2 d_2}\)
2. \(\frac{K_1 \theta_1+K_2 \theta_2}{K_1+K_2}\)
3. \(\frac{K_1 \theta_1+K_2 \theta_2}{\theta_1+\theta_2}\)
4. \(\frac{K_1 \theta_1 d_2+K_2 \theta_2 d_1}{K_1 d_2+K_2 d_1}\)

Answer: 4. \(\frac{K_1 \theta_1 d_2+K_2 \theta_2 d_1}{K_1 d_2+K_2 d_1}\)

Question 4. Which of the following qualities suit a cooking utensil?

1. High specific heat and low thermal conductivity
2. High specific heat and high thermal conductivity
3. Low specific heat and low thermal conductivity
4. Low specific heat and high thermal conductivity

Answer: 4. Low specific heat and high thermal conductivity

Question 5. The lengths and radii of two rods made of the same material are in the ratios 1: 2 and 2 : 3 respectively; If the temperature difference between the ends of the two rods is the same, then in the steady state, the amount of heat flowing per second through them will be in the ratio:

1. 1 : 3
2. 4 : 3
3. 8: 9
4. 3: 2

Answer: 3. 8: 9

Question 6. Two metal cubes with 3 cm-edges of copper and aluminum are arranged as shown in the figure (K_CU =385 W/m-K, K_AL = 209 W/m-K).

1. The total thermal current from one reservoir to the other is :

1. 1.42 × 10³ W
2. 2.53 × 10³ W
3. 1.53 × 10⁴ W
4. 2.53 × 10⁴ W

Answer: 1. 1.42 × 10³ W

2. The ratio of the thermal current carried by the copper cube to that carried by the aluminum cube is: –

1. 1.79
2. 1.69
3. 1.54
4. 1.84

Answer: 4. 1.84

Question 7. Two rods having thermal conductivities in the ratio of 5 : 3 and having equal length and equal cross section are joined face-to-face (series combination). If the temperature of the free end of the first rod is 100ºC and the free end of the second rod is 20ºC, the temperature of the junction is–

1. 50ºC
2. 70ºC
3. 85ºC
4. 90ºC

Answer: 2. 70ºC

Question 8. One end of a metal rod of length 1.0m and area of cross-section 100 cm² is maintained at 100ºC. If the other end of the rod is maintained at 0ºC, the quantity of heat transmitted through the rod per minute will be (coefficient of thermal conductivity of the material of rod = 100W/Kg/K)

1. 3 × 103 J
2. 6 × 103 J
3. 9 × 103 J
4. 12 × 103 J

Answer: 2. 6 × 103 J

Question 9. The coefficients of thermal conductivity of a metal depends on

1. Temperature difference between the two sides
2. Thickness of the metal plate
3. Area of the plate
4. None of the above

Answer: 4. None of the above

Question 10. Two identical square rods of metal are welded end to end as shown in the figure

1. Assume that 10 cal of heat flows through the rods in 2 min. Now the rods are welded as shown in the figure.
2. The time it would take for 10 cal to flow through the rods now, is

1. 0.75 min
2. 0.5 min
3. 1.5 min
4. 1 min

Answer: 2. 0.5 min

Question 11. The area of cross-section of two rods of equal lengths are A₁ and A₂ and thermal conductivities are K₁ and K₂. Specific heats are S₁ and S₂. Condition for equal heat flow is–

1. \(\mathrm{K}_1=\mathrm{K}_2\)
2. \(\mathrm{K}_1 \mathrm{~S}_1=\mathrm{K}_2 \mathrm{~S}_2\)
3. \(\frac{K_1}{A_1 S_1}=\frac{K_2}{A_2 S_2}\)
4. \(\mathrm{K}_1 \mathrm{~A}_1=\mathrm{K}_2 \mathrm{~A}_2\)

Answer: 4. \(\mathrm{K}_1 \mathrm{~A}_1=\mathrm{K}_2 \mathrm{~A}_2\)

Question 12. If two metallic plates of equal thickness, equal cross-section area, and thermal conductivities K₁ and K₂ are put together face to face (series combination) and a common plate is constructed, then the equivalent thermal conductivity of this plate will be

1. \(\frac{K_1 \quad K_2}{K_1+K_2}\)
2. \(\frac{2 K_1 K_2}{K_1+K_2}\)
3. \(\frac{\left(K_1^2+K_2^2\right)^{3 / 2}}{K_1 K_2}\)
4. \(\frac{\left(K_1^2+K_2^2\right)^{3 / 2}}{2 K_1 K_2}\)

Answer: 2. \(\frac{2 K_1 K_2}{K_1+K_2}\)

Question 13. Consider a compound slab consisting of two different materials having equal thicknesses, equal cross-section area, and thermal conductivities k and 2k respectively. If they are connected in parallel combination, the equivalent thermal conductivity of the slab is–

1. \(\sqrt{2}\)
2. 3k
3. \(\frac{4}{3} \mathrm{k}\)
4. \(\frac{2}{3} \mathrm{k}\)

Answer: 3. \(\frac{4}{3} \mathrm{k}\)

Question 14. The two ends of a rod of length L and a uniform cross-sectional area A kept at two temperatures T₁ and T₂(T₁>T₂ ). The rate of heat transfer,\(\frac{d Q}{d t}\) through the rod in a steady state is given by

1. \(\frac{d Q}{d t}=\frac{K L\left(T_1-T_2\right)}{A}\)
2. \(\frac{d Q}{d t}=\frac{K\left(T_1-T_2\right)}{L A}\)
3. \(\frac{d Q}{d t}=K L A\left(T_1-T_2\right)\)
4. \(\frac{d Q}{d t}=\frac{K A\left(T_1-T_2\right)}{L}\)

Answer: 4. \(\frac{d Q}{d t}=\frac{K A\left(T_1-T_2\right)}{L}\)

Question 15. A square is made of four rods of the same material one of the diagonals of a square is at a temperature difference of 100°C, then the temperature difference of the second diagonal :

1. 0°C
2. \(\frac{100}{\ell}\)
3. \(\frac{100}{2 \ell}\)
4. 100°C

Answer: 1. 0°C

Question 16. Three rods made of the same material and having the same cross-section are joined as shown in Fig. Each rod is of the same length. The left and right ends are kept at 0°C and 90°C respectively. The temperature of the junction of the three rods will be:

1. 45°C
2. 60°C
3. 30°C
4. 20°C

Answer: 2. 60°C

Question 17. Two containers, one containing ice at 0°C and the other containing boiling water at 100°C are connected by two identical rods. When rods are in parallel the rate of heat transfer is Q₁ and when rods are in series, the rate of heat transfer is Q₂. Then Q₂ /Q₁ will be:

1. 2: 1
2. 1: 2
3. 4: 1
4. 1: 4

Answer: 4. 1: 4

Question 18. 2 litre water at 27°C is heated by a 1 kW heater in an open container. On average heat is lost to surroundings at the rate of 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

Answer: 1. 8 min 20 sec

Question 19. If the temperature difference on the two sides of a wall increases from 100°C to 200°C, its thermal conductivity

1. Remains unchanged
2. Is doubled
3. Is halved
4. Becomes four times

Answer: 1. Remains unchanged

Question 20. A cylindrical rod having temperature T₁ and T₂ at its ends. The rate of flow of heat is Q₁cal/sec. If all the linear dimensions are doubled keeping the temperature constant then the rate of flow of heat Q₂ will be–

1. 4Q₁
2. 2Q₁
3. \(\frac{Q_1}{4}\)
4. \(\frac{Q_1}{2}\)

Answer: 2. 2Q₁

Question 21. One end of a thermally insulated rod is kept at a temperature of T₁ and the other at T₂. The rod is composed of two sections of lengths L₁ and L₂ and thermal conductivities k₁ and k₂ respectively. The temperature at the interface of the sections is

1. \(\frac{\left(\begin{array}{ll}
   K_2 & L_2 T_1+K_1 L_1 T_2
   \end{array}\right)}{\left(K_1 L_1+K_2 L_2\right)}\)
2. \(\frac{\left(\begin{array}{ll}
   K_2 L_1 T_1+K_1 L_2 T_2
   \end{array}\right)}{\left(K_2 L_1+K_1 L_2\right)}\)
3. \(\frac{\left(\begin{array}{ll}
   K_1 & L_2 T_1+K_2 L_1 T_2
   \end{array}\right)}{\left(K_1 L_2+K_2 L_1\right)}\)
4. \(\frac{\left(\begin{array}{ll}
   K_1 L_1 T_1+K_2 L_2 T_2
   \end{array}\right)}{\left(K_1 L_1+K_2 L_2\right)}\)

Answer: 3. \(\frac{\left(\begin{array}{ll}
K_1 & L_2 T_1+K_2 L_1 T_2
\end{array}\right)}{\left(K_1 L_2+K_2 L_1\right)}\)

Question 22. Three rods A, B, and C of the same length and same cross-section area are joined as shown in the figure. Their thermal conductivities are in the ratio 1: 2: 1.5. If the open ends of A and C are at 200°C and 18°C respectively, the temperature at the junction of A and B in equilibrium is-

1. 156°C
2. 116°C
3. 74°C
4. 148°C

Answer: 2. 116°C

Question 23. In the above question, the temperature at the junction of B and C will be

1. 124°C
2. 124°K
3. 74°C
4. 74°K

Answer: 3. 74°C

Question 24. The ends of the two rods of different materials with their thermal conductivities, radii of cross-section, and lengths in the ratio 1: 2 are maintained at the same temperature difference. If the rate of flow of heat in the larger rod is 4 cal/sec., that in the shorter rod will be (in cal/sec)

1. 1
2. 2
3. 8
4. 16

Answer: 2. 2

Question 25. The coefficients of thermal conductivity of copper, mercury, and glass are respectively K_c, K_m, and Kg such that K_c> K_m> K_g. If the same quantity of heat is to flow per second per unit area of each and corresponding temperature gradients are X_c, X_m, and X_g.

1. X_c= X_m= K_g
2. X_c> X_m> X_g
3. X_c< X_m< X_g
4. X_m< X_c< X_g

Answer: 3. X_c< X_m< X_g

Question 26. A compound slab is composed of two parallel layers of different materials, with thicknesses of 3 cm and 2 cm. The temperatures of the outer faces of the compound slab are maintained at 100°C and 0°C. If conductivities are 0.036 cal/cm-sec-°C and 0.016 cal/cm-sec-°C then the temperature of the junction is-

1. 40°C
2. 60°C
3. 100°C
4. 50°C

Answer: 2. 60°C

Question 27. The intensity of heat radiation by a point source measured by a thermopile placed at a distance d is Ι, If the distance of the thermopile is doubled then the intensity of radiation will be

1. Ι
2. 2Ι
3. \(\frac{\mathrm{I}}{4}\)
4. \(\frac{\mathrm{I}}{2}\)

Answer: 3. \(\frac{\mathrm{I}}{4}\)

Question 28. Two rods of copper and brass of the same length and area of cross-section are joined as shown. One end is kept at 100°C and the other at 0°C. The temperature at the mid-point will be

1. More if A is at 100°C and B at 0°C
2. More if A is at 0°C and B at 100°C
3. Will be the same in both the above cases, but not 50°C
4. 50°C in both the above cases

Answer: 1. More if A is at 100°C and B at 0°C

Question 29. Two identical square rods of metal are welded end to end as shown in Fig.

1. 20 cal. of heat flows through it in 4 min. If the rods are welded as shown in Fig.
2. The same amount of heat will flow through the rods in

1. 1 min.
2. 2 min.
3. 3 min.
4. 16 min.

Answer: 1. 1 min.

Question 30. A wall consists of alternating blocks with length ‘d’ and coefficient of thermal conductivity k₁ and k₂. The cross sectional area of the blocks is the same. The equivalent coefficient of thermal conductivity of the wall between left and right is:-

1. \(\mathrm{K}_1+\mathrm{K}_2\)
2. \(\frac{\left(K_1+K_2\right)}{2}\)
3. \(\frac{K_1 K_2}{K_1+K_2}\)
4. \(\frac{2 K_1 K_2}{K_1+K_2}\)

Answer: 2. \(\frac{\left(K_1+K_2\right)}{2}\)

Question 31. Five rods of the same dimensions are arranged as shown in the fig. They have thermal conductivities, k₁, k₂, k₅, k_4, and k₃ when points A and B are maintained at different temperatures. No heat flows through the central rod if-

1. \(k_1 k_4=k_2 k_3\)
2. \(\mathrm{k}_1=\mathrm{k}_4 \text { and } \mathrm{k}_2=\mathrm{k}_3\)
3. \(\frac{k_1}{k_4}=\frac{k_2}{k_3}\)
4. \(k_1 k_2=k_3 k_4\)

Answer: 4. \(k_1 k_2=k_3 k_4\)

Question 32. Three metal rods made of copper, aluminum, and brass, each 20 cm long and 4 cm in diameter, are placed end to end with aluminum between the other two. The free ends of copper and brass are maintained at 100 and 0°C respectively. Assume that the thermal conductivity of copper is twice that of aluminum and four times that of brass. The equilibrium temperatures of the copper-aluminium and aluminium-brass junctions are respectively.

1. 68 °C and 75 °C
2. 75 °C and 68 °C
3. 57 °C and 86 °C
4. 86 °C and 57 °C

Answer: 3. 57 °C and 86 °C

Question 33. 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?

1. 75ºC
2. 67ºC
3. 33ºC
4. 25ºC

Answer: 1. 75ºC

Question 34. The heat conduction coefficient of copper is 9 times the heat conduction coefficient of steel. The junction temperature of the combined cylindrical rod shown in the figure will be.

1. 75°C
2. 67°C
3. 33°C
4. 25°C

Answer: 1. 75°C

Question 35. Water is usually heated by

1. Conduction
2. Convection
3. Radiation
4. All the above processes

Answer: 2. Convection

Question 36. In natural convection a heated portion of a liquid moves because-

1. Its molecular motion becomes aligned
2. Of molecular collisions within it
3. Its density is less than that of the surrounding fluid
4. Of currents of the surrounding fluid

Answer: 3. Its density is less than that of the surrounding fluid

Question 37. It is hotter at the same distance over the top of the fire than it is on the side of it mainly because

1. Heat is radiated upwards
2. Air conducts heat upwards
3. Convection takes more heat upwards
4. Conduction, convection, and radiation all contribute significantly to transferring heat upwards

Answer: 3. Convection takes more heat upwards

Question 38. Ventilators are provided at the top of the room

1. To bring oxygen for breathing
2. So that sunlight may enter the room
3. To maintain convection currents to keep the air fresh in the room
4. To provide an outlet for carbon dioxide

Answer: 3. To maintain convection currents to keep the air fresh in the room

Question 39. The mode of transmission of heat in which heat is carried by moving particles is:

1. Wave motion
2. Convection
3. Conduction
4. Radiation

Answer: 2. Convection

Question 40. The temperature of a piece of metal is increased from 27°C to 327°C. The rate of emission of heat by radiation by a metal will become-

1. Double
2. Four times
3. Eight times
4. Sixteen times

Answer: 4. Sixteen times

Question 41. Radiation emitted by a surface is directly proportional to-

1. The third power of its temperature
2. The fourth power of its temperature
3. Twice the power of its temperature
4. None of above

Answer: 2. Fourth power of its temperature

Question 42. If the temperature of the surface of the sun becomes half then the energy emitted by it to the earth per second will reduce to –

1. 1/2
2. 1/4
3. 1/16
4. 1/64

Answer: 3. 1/16

Question 43. If the distance between point sources and the screen is doubled then the intensity of light becomes-

1. Four times
2. Doubled
3. Half
4. One fourth

Answer: 4. One fourth

Question 44. At T = 200K a black body emits maximum energy at a wavelength of 14 μm. Then at T = 1000K, the body will emit maximum energy at a wavelength of-

1. 70 mm
2. 70 μm
3. 2.8 μm
4. 2.8 mm

Answer: 3. 2.8 μm

Question 45. If the temperature of a black body is raised by 50%, then the energy emitted per second will be increased by an order of-

1. 50%
2. 100%
3. 200%
4. 400%

Answer: 4. 400%

Question 46. What represents the color of the star-

1. Density
2. Distance
3. Energy
4. Temperature

Answer: 4. Temperature

Question 47. The black body spectrum is-

1. Continuous spectrum with black lines
2. Continuous spectrum with black bands
3. Continuous spectrum
4. None of the above

Answer: 3. Continuous spectrum

Question 48. There is a black spot on the body. If the body is heated and carried in a dark room then it glows more. This can be explained based on-

1. Newton’s law of cooling
2. Vien’s law
3. Kirchoff’s law
4. Stefan’s

Answer: 3. Kirchoff’s law

Question 49. A heated body emits radiation which has maximum intensity at frequency νm. If the temperature of the body is doubled:

1. The maximum intensity radiation will be at frequency 2 νm
2. The maximum intensity radiation will be at frequency νm.
3. The total emitted energy will increase by a factor of 2.
4. None of these

Answer: 1. The maximum intensity radiation will be at frequency 2 νm

Question 50. If λ_m denotes the wavelength at which the radiative emission from a black body at a temperature T K is maximum, then-

1. \(\lambda_{\mathrm{m}} \propto \mathrm{T}^4\)
2. \(\lambda_{\mathrm{m}}\) is independent of T
3. \(\lambda_{\mathrm{m}} \propto \mathrm{T}\)
4. \(\lambda_m \propto \mathrm{T}^{-1}\)

Answer: 4. \(\lambda_m \propto \mathrm{T}^{-1}\)

Question 51. A black body at 1227°C emits radiations with maximum intensity at a wavelength of 5000 Å. If the temperature of the body is increased by 1000°C, the maximum intensity will be at

1. 4000 Å
2. 5000Å
3. 6000 Å
4. 3000Å

Answer: 4. 3000Å

Question 52. A black body is at 727°C. It emits energy at a rate which is proportional to

1. (277)²
2. (1000)⁴
3. (1000)²
4. (727)⁴

Answer: 2. (1000)⁴

Question 53. If the temperature of the body increases by 10%, then the increase in radiated energy of the body is :

1. 10%
2. 40%
3. 46%
4. 1000%

Answer: 3. 46%

Question 54. Infrared radiations are detected by

1. Spectrometer
2. Pyrometer
3. Nanometer
4. Photometer

Answer: 2. Pyrometer

Question 55. The plots of intensity vs. wavelength for three black bodies at temperatures T₁, T_2, and T₃ respectively are as shown. Their temperatures are such that-

1. T₁> T₂> T₃
2. T₁> T₃> T₂
3. T2> T₃> T₁
4. T₃> T₂> T₁

Answer: 2. T₁> T₃> T₂

Question 56. In which of the following phenomenon heat convection does not take place

1. Land and sea breeze
2. Boiling of water
3. Heating of glass surface due to filament of the bulb
4. The air around the furnace

Answer: 3. Heating of glass surface due to a filament of the bulb

Question 57. The energy radiated by a black body is directly proportional to :

1. T²
2. T^-2
3. T⁴
4. T

Answer: 3. T⁴

Question 58. When a substance is gradually heated, its initial color is

1. Red
2. Green
3. Yellow
4. White

Answer: 1. Red

Question 59. If the temperature becomes double, the emitted radiation will be :

1. 16 times
2. 8 times
3. times
4. 32 times

Answer: 1. 16 times

Question 60. If at temperature T₁= 1000 K, the wavelength is 1.4 × 10^-6 m, then at what temperature the wavelength will be 2.8 × 10^-6m?

1. 2000 K
2. 500 K
3. 250 K
4. None of these

Answer: 2. 500 K

Question 61. A black body is heated from 27°C to 927°C the ratio of radiations emitted will be :

1. 1: 256
2. 1: 64
3. 1: 16
4. 1: 4

Answer: 1. 1: 256

Question 62. Water is used to cool the radiators of engines in cars because :

1. Of its low boiling point
2. Of its high specific heat
3. Of its low-density
4. Of its easy availability

Answer: 2. Of its high specific heat

Question 63. The color of the star indicates its :

1. Temperature
2. Distance
3. Velocity
4. Size

Answer: 1. Temperature

Question 64. The means of energy transfer in a vacuum are:

1. Irradiation
2. Convection
3. Radiation
4. Conduction

Answer: 3. Radiation

Question 65. The temperature of the black body increases from T to 2T. The factor by which the rate of emission will increase is

1. 4
2. 2
3. 16
4. 8

Answer: 3. 16

Question 66. Let there be four articles having colors blue, red, black, and white. When they are heated together and allowed to cool, which article will cool at the earliest?

1. Blue
2. Red
3. Black
4. White

Answer: 2. Red

Question 67. A piece of red glass when heated in dark to red hot states will appear to be :

1. White
2. Red
3. Green
4. Invisible

Answer: 3. Green

Question 68. What is the mode of heat transfer by which a hot cup of coffee loses most of its heat?

1. Condition
2. Convection
3. Evaporation
4. Radiation

Answer: 1. Condiction

Question 69. Which one of the following processes depends on gravity :

1. Conduction
2. Convection
3. Radiation
4. None of the above

Answer: 2. Convection

Question 70. For a black body at a temperature of 727°C, its radiating power is 60 watts and the temperature of surrounding is 227°C. If the temperature of the black body is changed to 1227°C then its radiating power will be

1. 304 W
2. 320 W
3. 240 W
4. 120 W

Answer: 2. 320 W

Question 71. Wien’s displacement law expresses a relation between-

1. Wavelength corresponds to maximum energy and temperature.
2. Radiation energy and wavelength
3. Temperature and wavelength
4. Color of light and temperature

Answer: 1. Wavelength corresponds to maximum energy and temperature.

Question 72. The unit of Stefan’s constant is-

1. Watt-m²-K⁴
2. Watt-m²/K⁴
3. Watt/m²-K
4. Watt/m²K⁴

Answer: 4. Watt/m²K⁴

Question 73. Which of the following radiations has the least wavelength?

1. γ-rays
2. β-rays
3. α-rays
4. X-rays

Answer: 1. γ-rays

Question 74. If the temperature of the sun were to increase from T to 2T and its radius from R to 2R, then the ratio of the radiant energy received on Earth to what it was previously would be

1. 4
2. 16
3. 32
4. 64

Answer: 4. 64

Question 75. Assuming the sun to be a spherical body of radius R at a temperature of T K, evaluate the total radiant power, incident on Earth, at a distance r from the Sun. (earth radius = r₀)

1. \(\frac{R^2 \sigma T^4}{r^2}\)
2. \(\frac{4 \pi r_0^2 \quad R^2 \sigma T^4}{r^2}\)
3. \(\frac{\pi r_0^2 \quad R^2 \sigma T^4}{r^2}\)
4. \(\frac{r_0^2 \quad R^2 \sigma T^4}{4 \pi r^2}\)

Answer: 3. \(\frac{\pi r_0^2 \quad R^2 \sigma T^4}{r^2}\)

Question 76. The energy emitted per second by a black body at 1227ºC is E. If the temperature of the black body is increased to 2727ºC, the energy emitted per second in terms of E is –

1. 16 E
2. E
3. 4E
4. 2E

Answer: 1. 16 E

Question 77. Temp. of a black body is 3000 k. When the black body cools, then change in wavelength Δ λ = 9 microns corresponding to maximum energy density. Now temp. of a black body is-

1. 300 K
2. 2700 K
3. 270 K
4. 1800 K

Answer: 1. 300 K

Question 78. If the radius of the sun is RS, the radius of the orbit of the earth about the sun is Reand σ is Stefan’s constant, then the amount of radiation falling per second on a unit area of the earth’s surface is-

1. \(\left(\frac{R_s}{R_e}\right)^2 \sigma \mathrm{T}^4\)
2. \(\left(\frac{R_e}{R_s}\right)^2 \sigma \mathrm{T}^4\)
3. \(\frac{\sigma}{T^4}\left(\frac{R_s}{R_e}\right)^2\)
4. \(\left(\frac{R_e}{R_s}\right)^2 \frac{T^4}{\sigma}\)

Answer: 1. \(\left(\frac{R_s}{R_e}\right)^2 \sigma \mathrm{T}^4\)

Question 79. Which of the following surfaces will absorb maximum radiant energy-

1. Black
2. Rough
3. Smooth white
4. Rough black

Answer: 4. Rough black

Question 80. After heating two pieces of iron, they are taken to a dark room. One of them appears red and another appears blue, then-

1. The temperature of the red piece will be higher.
2. The temperature of the blue piece will be higher.
3. The temperature of both pieces will be the same.
4. Nothing can be said about their temp.

Answer: 2. The temperature of the blue piece will be higher.

Question 81. If the temperature of a lamp is about 600K, then the wavelength at which maximum emission takes place will be (Wien’s constant b = 3 × 10^-3 m-K)

1. 500 A°
2. 5000 A°
3. 50000 A°
4. 500000 A°

Answer: 3. 50000 A°

Question 82. The rate of cooling of a sphere of thermal capacity 1000 cal/K is 400 J/s, and its rate of fall of temperature is-

1. 0.095 K/min
2. 0.62 K/min
3. 2.8 K/min
4. 5.7 K/min

Answer: 4. 5.7 K/min

Question 83. If maximum spectral emissivity at temperature T₁ K is at wavelength λ₁, then the wavelength of maximum emissivity at temperature T₂ K will be

1. \(\frac{\lambda_1 T_2}{2}\)
2. \(\lambda_1\left(\frac{T_1}{T_2}\right)^4\)
3. \(\lambda_1\left(\frac{T_1}{T_2}\right)^5\)
4. \(\frac{\lambda_1 \mathrm{~T}_1}{\mathrm{~T}_2}\)

Answer: 4. \(\frac{\lambda_1 \mathrm{~T}_1}{\mathrm{~T}_2}\)

Question 84. The spectral emissive power of a black body at a temperature of 6000K is maximum at λ_m= 5000 A°. If the temperature is increased by 10%, then the decrease in λ_m will be

1. 2.5%
2. 5.0%
3. 7.5%
4. 10%

Answer: 4. 10%

Question 85. The rate of emission of energy by a unit area of a body is 10 watts and that of the sun is 106 watts. The emissive power of the body is 0.1. If the temperature of the sun is 6000K, then the temperature of the body will be

1. 6000K
2. 600K
3. 60010K
4. (600 10)K

Answer: 2. 600K

Question 86. The ratio of masses of two copper spheres of identical surfaces is 8: 1. If their temperatures are 2000K and 1000K respectively then the ratio of energies radiated per second by the two is-

1. 128: 1
2. 64: 1
3. 16: 1
4. 4: 1

Answer: 2. 64: 1

Question 87. A solid body is heated upto very high temperatures. As we go on heating, its brightness increases and it appears white at the end. The sequence of the color observed as the temperature of the body increases will be

1. Yellow, green, red, white.
2. Green, yellow, red, white.
3. Red, green, yellow, white.
4. Red, yellow, green, white.

Answer: 4. Red, yellow, green, white.

Question 88. The effective area of a black body is 0.1 m² and its temperature is 100 K. The amount of radiation emitted by it per minute is –

1. 1.34 cal
2. 8.1 cal
3. 5.63 cal
4. 1.34 J

Answer: 2. 8.1 cal

Question 89. What is the energy of emitted radiation from the Sun when the temperature is doubled-

1. 2
2. 4
3. 8
4. 16
5. Answer: 4. 16

Question 90. Newton’s law of cooling is a special case of

1. Wien’s displacement law
2. Kirchoff’s law
3. Stefan’s law
4. Planck’s law

Answer: 3. Stefan’s law

Question 91. A hot liquid is kept in a big room. Its temperature is plotted as a function of time. Which of the following curves may represent the plot?

1. a
2. c
3. d
4. b

Answer: 1. a

Question 92. A body takes 4 minutes to cool from 100°C to 70°C. To cool from 70°C to 40°C it will take-(room temperature is 15°C)

1. 7 minutes
2. 6 minutes
3. 5 minutes
4. 4 minutes

Answer: 1. 7 minutes

Question 93. A cup of tea cools from 80°C to 60°C in one minute. The ambient temperature is 30°C. In cooling from 60°C to 50°C it will take-

1. 30 seconds
2. 60 seconds
3. 96 seconds
4. 48 seconds

Answer: 4. 48 seconds

Question 94. A hot liquid cools from 70°C to 60°C in 5 minutes. The time needed by the same liquid to cool from 60°C to 50°C will be

1. Less than 5 minutes
2. More than 5 minutes
3. Equal to 5 minutes
4. Less or more than 5 minutes depends on the density of the liquid

Answer: 2. More than 5 minutes

Question 95. Which of the following is a true statement?

1. A good absorber is a bad conductor
2. Each body emits and absorbs radiation at each temperature
3. In a black body energy of emitted radiation is equal for all wavelength
4. Planck’s law gives the relation between the maximum wavelength of black body radiation and its temperature.

Answer: 2. Each body emits and absorbs radiation at each temperature

Question 96. A body takes 10 minutes to cool down from 62°C to 50°C. If the temperature of the surroundings is 26°C then in the next 10 minutes temperature of the body will be :

1. 38°C
2. 40°C
3. 42°C
4. 44°C

Answer: 3. 42°C

Question 97. A body cools from 60°C to 50°C in 10 minutes. If the room temperature is 25°C and assuming Newton’s law of cooling to hold good, the temperature of the body at the end of the next 10 minutes will be :

1. 45°C
2. 41.67°C
3. 40°C
4. 38.5°C

Answer: 2. 41.67°C

Question 98. Two spheres of radii in the ratio 1: 2 and densities in the ratio 2: 1 and of the same specific heat, are heated to the same temperature and left in the same surrounding. Their rate of cooling will be in the ratio :

1. 2: 1
2. 1: 1
3. 1: 2
4. 1: 4

Answer: 2. 1: 1

Question 99. The formation of ice is started in a lake with water at 0°C. When the atmospheric temperature is –10°C. If the time taken for 1 cm of ice to be formed is 7 hours, the time taken for the thickness of ice to increase from 1cm to 2 cm is :

1. Less than 7 hours
2. 7 hours
3. More than 14 hours
4. More than 7 hours but less than 14 hours

Answer: 3. More than 14 hours

Question 100. Two circular discs A and B with equal radii are blackened. They are heated to the same temperature and are cooled under identical conditions. What inference do you draw from their cooling curves?

1. A and B have the same specific heats
2. The specific heat of A is less
3. The specific heat of B is less
4. Nothing can be said

Answer: 2. Specific heat of A is less

Question 101. According to Newton’s law of cooling, the rate of cooling of a body is proportional to (Δθ)n, where Δθ is the difference between the temperature of the body and the surroundings, and n is equal to

1. 2
2. 3
3. 4
4. 1

Answer: 4. 1

Question 102. A liquid cools down from 70° C to 60°C in 5 min. The time taken to cool it from 60°C to 50°C will be

1. 5 min
2. Lesser than 5 min
3. Greater than 5 min
4. Lesser or greater than 5 minutes depending upon the density of the liquid

Answer: 3. Greater than 5 min

Question 103. The heat capacities of three liquids A, B, and C of the same volumes are in the ratio 3: 2: 1. They are allowed to cool in the same surroundings and same conditions for the same temperature difference. Which of these will cool first?

1. A
2. B
3. C
4. All will cool at the same time

Answer: 3. C

Question 104. The temperature of a room is 30°C. A body kept in it takes 4 minutes to cool from 61°C to 59°C. The time taken by the body to cool from 51°C to 49°C will be

1. 4 min.
2. 5 min.
3. 6 min.
4. 8 min.

Answer: 3. 6 min.

Question 105. Two cylindrical conductors A and B of the same metallic material have their diameters in the ratio 1: 2 and lengths in the ratio 2: 1. If the temperature difference between their ends is the same, the ratio of heat conducted respectively by A and B per second is,

1. 1: 2
2. 1: 4
3. 1: 16
4. 1: 8

Answer: 4. 1: 8

Question 106. According to Kirchoff’s law-

1. a_λe_λ= E_λ
2. E_λa_λ= e_λ
3. a_λ= e_λE_λ
4. E_λ, a_λ, e_λ= const.

Answer: 2. E_λa_λ= e_λ

Question 107. A spherical solid black body of radius ‘r’ radiates power ‘H’ and its rate of cooling is ‘C’. If the density is constant then which of the following is/are true?

1. H ∝ r and c ∝ r²
2. H ∝ r² and c ∝
3. H ∝ r and c ∝ 2
4. H ∝ r² and c ∝ r²

Answer: 2. H ∝ r² and c ∝

Question 108. Which of the following is nearest to Blackbody-

1. An enclosure with a small hole
2. Carbon black
3. Ebonite
4. None of these

Answer: 1. An enclosure with a small hole

Question 109. Which of the following processes is reversible?

1. Transfer of heat by radiation
2. Electrical heating of nichrome wire
3. Transfer of heat by conduction
4. Isothermal compression

Answer: 4. Isothermal compression

Question 110. Assuming the sun to have a spherical outer surface of radius r, radiating like a black body at temperature t°C, the power received by a unit surface, (normal to the incident rays) at a distance R from the center of the sun is (considering solar constant to be uniform)

1. \(\frac{4 \pi r^2 t^4}{R^2}\)
2. \(\frac{r^2 \sigma(t+273)^4}{4 \pi R^2}\)
3. \(\frac{16 \pi^2 r^2 \sigma t^4}{R^2}\)
4. \(\frac{r^2 \sigma(t+273)^2}{R^2}\)

Answer: 4. \(\frac{r^2 \sigma(t+273)^2}{R^2}\)

Question 111. Which of the following is more close to a black body?

1. Blackboard paint
2. Green leaves
3. Black holes
4. Red roses

Answer: 1. Blackboard paint

Question 112. A black body is at a temperature of 2800 K. The energy of radiation emitted by this object with a wavelength between 499 nm and 500 nm is U₁, between 999 nm and 1000 nm is U_2, and between 1499 nm and 1500 nm is U₃. The Wien constant b = 2.88 × 106 nm K. Then

1. U₁= 0
2. U₃= 0
3. U₁> U₂
4. U₂>U₁

Answer: 4. U₂>U₁

Question 113. The temperature of bodies X and Y vary with time as shown in the figure. If the emissivity of bodies X and Y are e_X and e_Y and absorptive powers are A_X and A_Y, (assume other conditions are identical for both) then:

1. e_Y> e_X, A_Y> A_X
2. e_Y< e_X, A_Y< A_X
3. e_Y> e_X, A_Y< A_X
4. e_Y< e_X, A_Y> A_X

Answer: 1. e_Y> e_X, A_Y> A_X

Question 114. Three discs of the same material A, B, and C of radii 2 cm, 4 cm, and 6 cm respectively are coated with carbon black. Their wavelengths corresponding to maximum spectral radiancy are 300, 400, and 500 nm respectively then maximum power will be emitted by

1. A
2. B
3. C
4. Same for all

Answer: 2. B

Question 115. Three graphs marked 1, 2, and 3 represent the variation of maximum emissive power and wavelength of radiation of the sun, a welding arc, and a tungsten filament. Which of the following combinations is correct

1. 1- tungsten filament, 2 → welding arc, 3 → sun
2. 2- tungsten filament, 3 → welding arc, 1 → sun
3. 3- tungsten filament, 1 → welding arc, 2 → sun
4. 2- tungsten filament, 1 → welding arc, 3 → sun

Answer: 1. 1- tungsten filament, 2 → welding arc, 3 → sun

Question 116. Two rectangular blocks, having identical dimensions, can be arranged either in configuration Ι or in configuration ΙΙ as shown in the figure, One of the blocks has a thermal conductivity of k, and the other 2k. The temperature difference between the ends along the x-axis is the same in both configurations. It takes 9s to transport a certain amount of heat from the hot end to the cold end in configuration 1. The time to transport the same amount of heat in the configuration 2 is:

1. 2.0 s
2. 3.0 s
3. 4.5 s
4. 6.0 s

Answer: 1. 2.0 s

Question 117. Parallel rays of light of intensity Ι = 912 Wm^-2 are incident on a spherical black body kept in surroundings of temperature 300 K. Take Stefan-Biltzmann constant σ = 5.7 × 10^-8 Wm^-2 K^-4 and assume that the energy exchange with the surroundings is only through radiation. The final steady state temperature of the black body is close to:

1. 330 K
2. 660 K
3. 990 K
4. 1550 K

Answer: 1. 330 K

Question 118. Two spherical stars A and B emit blackbody radiation. The radius of A is 400 times that of B and A emits 10⁴ times the power emitted from B. The ratio \(\left(\frac{\lambda_A}{\lambda_B}\right)\) to their wavelengths λ_A and λ_B at which the peaks occur in their respective radiation curves is:

1. 1
2. 2
3. 3
4. 4

Answer: 2. 2

Question 119. The earth radiates in the infrared region of the spectrum. The spectrum is correctly given by :

1. Rayleigh-Jeans law
2. Planck’s law of radiation
3. Stefan’s law of radiation
4. Wien’s law

Answer: 1. Rayleigh-Jeans law

Question 120. Two spheres of different materials one having a radius double of other and a wall thickness 1/4 of the other are filled with ice. If the time required to completely melt the ice is 25 min. for a larger radius sphere and 16 min. for a smaller radius sphere, then the ratio of the thermal conduction coefficient for the material of larger radius to that of the thermal conduction coefficient for the material of smaller radius sphere will be.

1. 4: 5
2. 5: 4
3. 8: 25
4. 1: 25

Answer: 3. 8: 25

Question 121. A black body is at room temperature. It is placed in a furnace, and it is observed that

1. In the beginning, it is seen most black, and later on, it is seen as the brightest.
2. It is always seen as black.
3. It can’t be resolved at any times
4. In the beginning, it is seen mostly black, and later on it can’t be resolved.

Answer: 1. In the beginning it is seen as the most black and later on it is seen brightest.

Question 122. If a liquid takes 30 sec. in cooling of 95°C to 90°C and 70 sec. in cooling of 55°C to 50°C then temp. of the room is-

1. 16.5 °C
2. 22.5 °C
3. 28.5 °C
4. 32.5 °C

Answer: 2. 22.5 °C

Question 123. A body takes 2 minutes in cooling from 365K to 361K. If the room temperature is 293K, then the time taken to cool from 344K to 342K will be

1. 1 min.
2. 1.2 min.
3. 1.4 min.
4. 1.8 min.

Answer: 3. 1.4 min.

Question 124. The reflection and absorption coefficients of a given surface at 0°C for a fixed wavelength are 0.5 (each). At the same temperature and wavelength, the transmission (coefficient) of the surface will be

1. 0.5
2. 1.0
3. Zero
4. In between zero and one

Answer: 3. Zero

Question 125. The earth receives radiation from the sun at the rate of 1400 watts/m². The distance from the center of the sun to the surface of the earth is 1.5 × 1011 m and the radius of the sun is 7.0 × 108 m. Treating the sun as a black body the temperature of the sun will be

1. 6000K
2. 5500K
3. 5800K
4. 6200K

Answer: 3. 5800K

Question 126. The rate of cooling of a heated solid sphere is R cal/min. If it is divided into two hemispheres the rate of cooling at the same temperature will become-

1. 1.25R cal/min.
2. 1.5R cal/min.
3. 1.75R cal/min.
4. 2.5R cal/min.

Answer: 2. 1.5R cal/min.

Question 127. Equal volumes of a liquid of relative density 1.02 and water are allowed to cool from 80°C to 60°C in the same surroundings. The times taken are 8 mts and 15 mts respectively. The specific heat of the liquid in cal/gm-°C is-

1. 0.52
2. 0.81
3. 1.02
4. 1.23

Answer: 1. 0.52

Question 128. Two identical calorimeters of negligible heat capacities are filled with two liquids A & B whose densities are in the ratio 4 : 3. The ratio of times taken in cooling from 80°C to 75°C is 5: 6. The ratio of their specific heats is-

1. 1: 2
2. 5: 6
3. 4 : 3
4. 5: 8

Answer: 4. 5: 8

Question 129. Blackened metal foil receives heat from a heated sphere placed at a distance r from it. It is found that foil receives power P. If the temperature and the distance of the sphere are doubled, then the power received by the foil will be

1. P
2. 2P
3. 8P
4. 4P

Answer: 4. 4P

Question 130. The temperature of the two outer surfaces of a composite slab, consisting of two materials K and 2K, and thickness x and 4x, respectively, are T₂ and T₁(T₂> T₁). The rate of heat transfer through the slab,\(\left(\frac{A\left(T_2-T_1\right) K}{x}\right) f\) with f equal to–

1. 1
2. 1/2
3. 2/3
4. 1/3

Answer: 4. 1/3

Question 131. If the radius of a star is R and it acts as a black body, what would be the temperature of the star, in which the rate of energy production is Q?

1. Q /4πR²σ
2. (Q /4πR²σ)–1/2
3. (4πR²Q/σ)1/4
4. (Q/ 4πR²σ)1/4

Answer: 4. (Q/ 4πR²σ)1/4

Question 132. A slab of stone of area 0.36 m² and thickness 0.1 m is exposed on the lower surface to steam at 100°C. A block of ice at 0°C rests on the upper surface of the slab. In one hour 4.8 kg of ice is melted. The thermal conductivity of slab is :(Given latent heat of fusion of ice = 3.36 × 105 J kg^-1) :

1. 1.24 J/m/s/°C
2. 1.29 J/m/s/°C
3. 2.05 J/m/s/°C
4. 1.02 J/m/s/°C

Answer: 1. 1.24 J/m/s/°C

Question 133. A piece of iron is heated in a flame. It first becomes dull red then becomes reddish yellow and finally turns to white hot. The correct explanation for the above observation is possible by using :

1. Wien’s Displacement Law
2. Kirchoff’s Law
3. Newton’s Law of Cooling
4. Stefan’s Law

Answer: 1. Wien’s displacement Law

Question 134. A certain quantity of water cools from 700C to 600C in the first 5 minutes and to 540C in the next 5 minutes. The temperature of the surroundings is;

1. 450C
2. 200C
3. 420C
4. 100C

Answer: 1. 450C

Question 135. On observing light from three different stars P, Q and R, it was found that the intensity of the violet colour is maximum in the spectrum of P, the intensity of the green colour is maximum in the spectrum of R and the intensity of the red colour is maximum in the spectrum in the spectrum of Q. If T_P, T_Q, and T_R are the respective absolute temperature of P, Q, and R, then it can be concluded from the above observations that :

1. T_P> T_R> T_Q
2. T_P< T_R< T_Q
3. T_P< T_Q<T_R
4. T_P >T_QT_R

Answer: 1. T_P> T_R> T_Q

Question 136. The two ends of a metal rod are maintained at temperatures 100ºC and 110ºC. The rate of heat flow in the rod is found to be 4.0 J/s. If the ends are maintained at temperatures 200ºC and 210ºC, the rate of heat flow will be :

1. 16.8 J/s
2. 8.0 J/s
3. 4.0 J/s
4. 44.0 J/s

Answer: 3. 4.0 J/s

Question 137. The coefficient of linear expansion of brass and steel rods are α₁ and α₂. Lengths of brass and steel rods are l₁ and l₂ respectively. If (l₂– l₁) is maintained the same at all temperatures, which one of the following relations holds good?

1. α₁l₁= α₂l₂
2. α₁l₂= α₂l₁
3. α₁l_2² = α₂l_1²
4. α_1²l₂= α_2² l₁

Answer: 1. α₁l₁= α₂l₂

Question 138. A refrigerator works between 4°C and 30°C. it is required to remove 600 calories of heat every second to keep the temperature of the refrigerated space constant. The power required is : (Take 1 cal = 4.2 Joules)

1. 2365 W
2. 2.365 W
3. 23.65 W
4. 236.5 W

Answer: 4. 236.5 W

Question 139. 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 × 10⁵ J/Kg and g = 10 N/kg]

1. 68 km
2. 34 km
3. 544 km
4. 136 km

Answer: 4. 136 km

Question 140. A block body is at a temperature of 5760 K. The energy of radiation emitted by the body at wavelength 250 nm is U₁ at wavelength 500 nm is U₂ and that at 1000 nm is U₃. Wien’s constant, b = 2.88 × 10⁶ nmK. Which of the following is correct?

1. U₂> U₁
2. U₁= 0
3. U₃= 0
4. U₁> U₂

Answer: 1. U₂> U₁

Question 141. Two identical bodies are made of a material for which the heat capacity increases with temperature. One of these is at 100ºC, while the other one is at 0ºC. If the two bodies are brought into contact, then assuming no heat loss, the final common temperature is

1. 0º C
2. 50º C
3. More than 50º C
4. Less than 50º C but greater than 0º C

Answer: 3. More than 50º C

Question 142. A body cools from a temperature of 3T to 2T in 10 minutes. The room temperature is T. Assume that Newton’s law of cooling is applicable. The temperature of the body at the end of next 10 minutes will be

1. T
2. \(\frac{7}{4} \mathrm{~T}\)
3. \(\frac{3}{2} \mathrm{~T}\)
4. \(\frac{4}{3} \mathrm{~T}\)

Answer: 3. \(\frac{3}{2} \mathrm{~T}\)

Question 143. Two rods A and B of different materials are welded together as shown in the figure. Their thermal conductivities are K₁ and K₂. The thermal conductivity of the composite rod will be

1. \(\frac{\mathrm{K}_1+\mathrm{K}_2}{2}\)
2. \(\frac{3\left(\mathrm{~K}_1+\mathrm{K}_2\right)}{2}\)
3. \(\mathrm{K}_1+\mathrm{K}_2\)
4. \(2\left(\mathrm{~K}_1+\mathrm{K}_2\right)\)

Answer: 1. \(\frac{\mathrm{K}_1+\mathrm{K}_2}{2}\)

Question 144. A spherical black body with a radius of 12 cm radiates 450-watt power at 500 K. If the radius were halved and the temperature doubled, the power radiated in watts would be :

1. 225
2. 450
3. 1000
4. 1800

Answer: 4. 1800

Question 145. The power was radiated by a black body in P and it radiated maximum energy at wavelength, λ₀. If the temperature of the black body is now changed so that it radiates maximum energy at wavelength \(\frac{3}{4} \lambda_0\) the power radiated by it becomes nP. The value of n is :

1. \(\frac{3}{4}\)
2. \(\frac{81}{256}\)
3. \(\frac{256}{81}\)
4. \(\frac{4}{3}\)

Answer: 3. \(\frac{256}{81}\)

Question 146. A copper rod of 88 cm and an aluminum rod of unknown length have their increase in length independent of an increase in temperature. The length of aluminium rod is (α_Cu = 1.7 × 10^-5 K^-1 and α_Al = 2.2 × 10^-5 K^-1)

1. 68 cm
2. 6.8 cm
3. 113.9 cm
4. 88 cm

Answer: 1. 68 cm

Question 147. The unit of thermal conductivity is :

1. W m^-1 K^-1
2. J m K^-1
3. J m^-1 K^-1
4. W m K^-1

Answer: 1. W m^-1 K^-1

Question 148. An object kept in a large room having an air temperature of 25ºC takes 12 minutes to cool from 80ºC to 70ºC. The time taken to cool the same object from 70º to 60ºC would be nearly

1. 10 min
2. 12 min
3. 20 min
4. 15 min

Answer: 4. 15 min

Question 149. A deep rectangular pond of surface area A, containing water (density = ρ, specific heat capacity = s), is located in a region where the outside air temperature is at a steady value of –26ºC. The thickness of the ice layer in this pond, at a certain instant, is x. Taking the thermal conductivity of ice as K, and its specific latent heat of fusion as L, the rate of increase of the thickness of the ice layer, at this instant, would be given by

1. 26K/ρx(L-4s)
2. 26K/(ρx2L)
3. 26K/(ρxL)
4. 26K/ρx(L+4s)

Answer: 3. 26K/(ρxL)

Question 150. Three stars A, B, and C have surface temperatures T_A, T_B, and T_C respectively. Star A appears bluish, star B appears reddish, and star C is yellowish. Hence

1. T_A> T_B> T_C
2. T_B> T_C> T_A
3. T_C> T_B> T_A
4. T_A> T_C> T_B

Answer: 4. T_A> T_C> T_B

Question 151. An ideal gas equation can be written as \(\mathrm{P}=\frac{\rho R T}{M_0}\) where ρ and M₀ are respectively,

1. Mass density is, the mass of the gas
2. Number density, molar mass
3. Mass density, molar mass
4. Number density, the mass of the gas

Answer: 3. Mass density, molar mass

Question 152. A cylinder contains hydrogen gas at a pressure of 245 K Pa and a temperature of 270C density is (R=8.3 J mol^-1 K^-1)

1. 0.02 kg/m³
2. 0.5 kg/m³
3. 0.2 kg/m³
4. 0.1 / kg m

Answer: 3. 0.2 kg/m³

Question 153. A cup of coffee cools from 90°C to 80°C in two minutes, when the room temperature is 20°C. The time taken by a similar cup of coffee to cool from 80°C to 60°C at room temperature same at 20°C is

1. \(\frac{13}{5} t\)
2. \(\frac{10}{13} t\)
3. \(\frac{5}{13} t\)
4. \(\frac{13}{10} t\)

Answer: 1. \(\frac{13}{5} t\)

Question 154. A flask containing air at 27ºC is corked up at atmospheric pressure. The cork can be forced out by a pressure of 2.5 atmospheres. To what temperature the flask should be heated to do that?

1. 150 K
2. 300 K
3. 600 K
4. 750 K

Answer: 4. 750 K

Question 155. 1 kcal of heat flowing through a rod of iron per second. When the rod is cut down to 4 pieces then what will be the heat flowing through each piece per second having the same differential temperature (temperature gradient)?

1. (1/2) kcal
2. (1/4) kcal
3. 1 kcal
4. (1/15) kcal

Answer: 3. 1 kcal

Question 156. Black holes in orbit around a normal star are detected from the earth due to the frictional heating of infalling gas into the black hole, which can reach temperatures greater than 106K. Assuming that the infalling gas can be modelled as a blackbody radiator then the wavelength of maximum power lies

1. In the visible region
2. In the X-ray region
3. In the microwave region
4. In the gamma-ray region of the electromagnetic spectrum.

Answer: 2. In the X-ray region

Question 157. Two conductors having the same width and length, thickness d₁ and d₂ thermal conductivity K₁ and K₂ are placed one above the other. Find the equivalent thermal conductivity.

1. \(\frac{\left(d_1+d_2\right)\left(K_1 d_2+K_2 d_1\right)}{2\left(K_1+K_2\right)}\)
2. \(\frac{\left(d_1-d_2\right)\left(K_1 d_2+K_2 d_1\right)}{2\left(K_1+K_2\right)}\)
3. \(\frac{K_1 d_1+K_2 d_2}{d_1+d_2}\)
4. \(\frac{K_1+K_2}{d_1+d_2}\)

Answer: 3. \(\frac{K_1 d_1+K_2 d_2}{d_1+d_2}\)

Question 158. A long metallic bar carries heat from one of its ends to the other end under a steady-state. The variation of temperature θ along the length x of the bar from its hot end is best described by which of the following figures

Answer: 1

Question 159. If a piece of metal is heated to temperature θ and then allowed to cool in a room which is at temperature θ₀, the graph between the temperature T of the metal and time t will be closest to:

Answer: 3

Question 160. Three rods of Copper, brass, and steel are welded together to form a Y-shaped structure. Area of cross section of each rod = 4 cm². The end of the copper rod is maintained at 100°C whereas ends of brass and steel are kept at 0°C. Lengths of the copper, brass, and steel rods are 46, 13, and 12 cm respectively. The rods are thermally insulated from surroundings except at the ends. Thermal conductivities of copper, brass, and steel are 0.92, 0.26, and 0.12 CGS units respectively. The rate of heat flow through copper rod is:

1. 1.2 cal/s
2. 2.4 cal/s
3. 4.8 cal/s
4. 6.0 cal/s

Answer: 4. 6.0 cal/s

Question 161. An ideal gas undergoes a quasi-static, reversible process in which its molar heat capacity C remains constant. If during this process the relation of pressure P and volume V is given by PVⁿ = constant, then n is given by (Here C_p and C_v are molar specific heat at constant pressure and constant volume, respectively ) :

1. \(n=\frac{C-C_p}{C-C_V}\)
2. \(n=\frac{C_p-C}{C-C_V}\)
3. \(n=\frac{C-C}{C-C p}\)
4. \(n=\frac{C_p}{C_V}\)

Answer: 1. \(n=\frac{C-C_p}{C-C_V}\)

Question 162. Temperature difference of 120°C is maintained between two ends of a uniform rod AB of length 2L. Another bent rod PQ, of the same cross-section as AB and length \(\frac{3 L}{2}\), is connected across AB (see figure). In a steady state, the temperature difference between P and Q will be close to :

1. 75°C
2. 45°C
3. 60°C
4. 35°C

Answer: 2. 45°C

Question 163. A heat source at T = 10³ K is connected to another heat reservoir at T = 10² K by a copper slab that is 1m thick. Given that the thermal conductivity of copper is 0.1 WK^-1 m^-1, the energy flux through it in the steady state is :

1. 200 Wm^-2
2. 90 Wm^-2
3. 65 Wm^-2
4. 120 Wm^-2

Answer: 2. 90 Wm^-2

Question 164. A thermometer graduated according to a linear scale reads a value of x₀ when in contact with ice. What is the temperature of an object in °C, if this thermometer in contact with the object reads x₀/2?

1. 35
2. 60
3. 25
4. 40

Answer: 3. 25

Question 165. A cylinder of radius R is surrounded by a cylindrical of inner radius R and outer radius 2R. The thermal conductivity of the material of the inner cylinder is K₁ and that of the outer cylinder is K₂. Assuming no loss of heat, the effective thermal conductivity of the system for the heart flowing along the length of the cylinder is:

1. \(\mathrm{K}_1+\mathrm{K}_2\)
2. \(\frac{2 K_1+3 K_2}{2}\)
3. \(\frac{\mathrm{K}_1+\mathrm{K}_2}{2}\)
4. \(\frac{\mathrm{K}_1+3 \mathrm{~K}_2}{4}\)

Answer: 4. \(\frac{\mathrm{K}_1+3 \mathrm{~K}_2}{4}\)

Question 166. Two rods A and B of identical dimensions are at a temperature of 30°C. If A is heated upto 180°C and B upto T°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. 270°C
2. 200°C
3. 230°C
4. 250°C

Answer: 3. 230°C