MCQs

1. If the absolute temperature of a radiating body is suddenly halved, the radiating power will reduce approximately by
   a.   25%                
   b. 12.5%                     
   c. 6.25%                     
   d. 3.12%
2. Which relation for emissive power and temperature is correct?
   a. [latex]E\propto T[/latex]            
   b. [latex]E\propto T^2[/latex]               
   c. [latex]E\propto T^4[/latex]                 
   d. [latex]E\propto T^{-4}[/latex]
3. The most appropriate material for making a cooking pot is the one having
   a. Low specific heat and high conductivity                  
   b. Low specific heat and low conductivity
   c. High specific heat and low conductivity
   d. High specific heat and high conductivity
4. Two stars radiate maximum energy at 320 nanometer and 400 nanometer respectively. The ratio of their Kelvin temperature is
   a. 5:4                  
   b. 4:5                          
   c. 2:5                          
   d. 4:25
5. Instrument used to measure temperature by radiation method is
   a. Pyrometer                               
   b. Radio micrometer
   c. Thermometer                          
   d. Barometer
6. The ratio of maximum wavelength of sun and moon is in the ratio 1:4000. What is the ratio of their temperature?
   a. 200:1                          
   b. 400:1                      
   c. 1:200                      
   d. 1:400
7. Unit of the coefficient of thermal conductivity is
   a. [latex]watt\ Km^{-1}[/latex]                                    
   b. [latex]Joule\ sK^{-1}[/latex]    
   c. [latex]watt\ K^{-1}m^{-1}[/latex]                                
   d. [latex]Joule\ s^{-1}K[/latex]
8. If temperature of black body is increased by 50% percentage increase in emitted radiation
   a. 50                               
   b. 100                         
   c. 500                         
   d. 400
9. From 0^oC the coefficient of thermal expansion of water is
   a. Positive but not zero                                      
   b. negative
   c. zero                                                                
   d. Infinite
10. A black body is heated from 27^oC to 127^oC the ratio of their energies of radiation is
    a. 9:16                            
    b. 27:64                      
    c. 81:256                    
    d. 3:4
11. A perfectly black body emits radiation at temperature [latex]T_1K[/latex]. If it is to radiate 16 times this power, its temperature [latex]T_2K[/latex] will be
    a. [latex]T_2 = 16T_1[/latex]            
    b. [latex]T_2 = 8T_1[/latex]               
    c. [latex]T_2 = 4T_1[/latex]                 
    d. [latex]T_2 = 2T_1[/latex]
12. Two rods of same length and diameter having thermal conductivities 2 and 3 units respectively are joined in series. The equivalent thermal conductivity is            
    a. 1.0                              
    b. 2.0                          
    c. 3.0                          
    d. none

Answers

1.c	2.c	3.a	4.a	5.a	6.b	7.c	8.d	9.b	10.c
11.d	12.d

CONCEPTUAL PROBLEMS

1. Cooking utensils are blackened at the bottom and polished on the upper surface. Explain, why?
2. What is the physical meaning of emissivity? Write its unit.
3. Why are the polar regions much cooler than the equatorial regions despite the fact that the polar regions are periodically tilted towards sun?
4. Air is a bad conductor of heat. Why do you feel cool without cloth in your body?
5. Although aluminium is good conductor of heat, how can aluminium foil with shining surface can be used to keep food hot for a long time?
6. Birds often swell their feathers in winter. Why?
7. Animals curl into a ball, when they feel very cold. Why?
8. Why are two thin blankets warmer than a single blanket of double the thickness?
9. Why are good absorbers always good emitters?
10. What is a blackbody? How is it realized in practice?
11. How are water pipes used in the room painted black?
12. Metal knob of door is colder than wooden parts at the same temperature. Why?

THEORY BASED PROBLEMS

13. Discuss the methods of heat transmission. Define reflection, transmission and absorption coefficient of heat radiation and relate them.
14. What is radiation and how does this mode of heat transfer differ from conduction and convection?
15. Define thermal conductivity. Derive an expression for thermal conductivity of a good conductor in steady state by Searle’s method.
16. What do you mean by perfectly black body. State and explain Stefan’s law of black body radiation.

NUMERICAL PROBLEMS

1. A bar 0.2 m in length and 2.5 cm² in cross section is ideally lagged. One end is maintained at 100^oC and the other end is maintained at 0^oC by immersing in melting ice. Calculate the mass of ice melt in one hour. Thermal conductivity of the material of the bar is 4 x 10² Wm^-1K^-1. Ans: 0.5292 kg
2. A pot with a steel bottom 8.5 mm thick rest on a hot stove. The area of the bottom of the pot is 0.15 m². The water inside the pot is at 100^oC and 390 gm of water is evaporated every 3 minutes. Find the temperature of lower surface of the pot which is in contact with the stove. (Thermal conductivity of pot = 50.2 Wm^-1K^-1, latent heat of vaporization = 2256 x 10³ J/Kg). Ans: 105.52^oC
3. A rod 1.3 m long consists of a 0.8 m length of aluminium joined end to end to a 0.5 m length of brass. The free end of the aluminium section is maintained at 150^oC and the free end of the brass piece is maintained at 20^oC. No heat is lost through the sides of the rod. At a steady state, what is the temperature at the point where the two metals are joined? (Thermal Conductivity of aluminium = 205.0 Wm^-1K^-1, thermal conductivity of brass = 109.0 Wm^-1K^-1). Ans: 90.2^oC
4. A bar 0.2 m in length and of cross – sectional area 2.5 x 10^-4 m² is ideally lagged. One end is maintained at 373 K while the other is maintained at 273 K by immersing in melting ice. Calculate the rate at which the ice melts owing to the flow of heat along the bar. (Thermal conductivity of the material of the bar = 4 x 10² Wm^-1K^-1). Ans: 1.5 x 10^-4 kg/sec
5. A slab of stone of area 0.36 m² and thickness 10 cm is exposed on the lower surface to steam at 100^oC. A block of ice at 0^oC rests on the upper surface of the slab. In one hour, 4.8 kg of ice is melted. Calculate the thermal conductivity of stone. Ans: 1.24 Wm^-1K^-1
6. A metal rod of length 20 cm and cross-sectional area 3.14 cm² is covered with non – conducting substance. One of its ends is maintained at 100^oC while the other end is put in ice at 0^oC. It is found that 25 gram of ice melts in 5 minutes. Calculate the thermal conductivity of the metal. Ans: 178.3 Wm^-1K^-1
7. An ice box is made of wood 1.75 cm, thick lined inside with cork 2 cm thick. If the temperature of inner surface of the cork is steady at 0^oC and that of the outer surface of the wood is steady at 12^oC, what is the temperature of the interface? The thermal conductivity of wood is five times that of cork. Ans: 10.2^oC
8. Estimate the rate of heat loss through a glass window of area 2 m² and thickness 4 mm when the temperature of the room is 300 K and that of air outside is 5^oC. (Thermal Conductivity of glass = 1.2 Wm^-1K^-1). Ans: 13200 W
9. Assuming that the thermal insulation provided by a wooden glove is equivalent to the layer of quiescent air 3 mm thick, determine the heat loss per minute from a man’s hand, surface area 200 cm² on a winter day when the atmospheric air temperature is – 3^oC. The skin temperature is to be taken as 35^oC and thermal conductivity of air as 24 x 10^-3 Wm^-1K^-1. Ans: 364.8 J
10. Estimate the rate of heat loss through a glass window of area 2 m² and thickness 3 mm when the temperature of the room is 20^oC and that of air outside is 5^oC. (Thermal Conductivity of glass = 1.2 Wm^-1K^-1). Ans: 12 x 10³ W
11. Estimate the rate at which ice would melt in a wooden box 2.5 cm thick of inside measurement 100 cm x 60 cm x 40 cm assuming that the external temperature is 35^oC and thermal conductivity of wood is 0.168 Wm^-1K^-1. Ans: 1.736 x 10^-3 Kgs^-1
12. The Sun is a black body of a surface temperature about 6000 K. If Sun’s radius is 7 x 10⁸ m, calculate the energy per second radiated from its surface. The earth is about 1.5 x 10¹¹ m from the Sun. Assuming all the radiation from the Sun falls on the surface of sphere of this radius, estimate the energy per second per meter square received by the earth. (Stefan’s Constant = 5.7 x 10^-8 Wm^-2K^-4). Ans: 4.546 x 10²⁶ Watt, 1609 W/m²
13. A sphere of radius 2.00 cm with a black surface is cooled and then suspended in a large evacuated enclosure with black walls maintained at 27^oC. If the rate of change of thermal energy of sphere is 1.85 Js^-1 when its temperature is – 73^oC, calculate the value of Stefan’s constant. Ans: 5.6 x 10^-8 Wm^-2K^-4
14. Estimate the power loss through unit area from a perfectly black body at 327^oC to the surrounding environment at 27^oC. (Stefan’s Constant = 5.67 x 10^-8 Wm^-2K^-4). Ans: 6889.05 watt
15. A spherical blackbody of radius 5 cm has its temperature 127^oC and its emissivity is 0.6. Calculate its radiant power. (Stefan’s Constant = 5.67 x 10^-8 Wm^-2K^-4). Ans: 27.37 watt
16. Estimate the radiant power loss from a human body at a temperature 38^oC to the environment at 0^oC if the surface area of the body is 1.5 m² and its emissivity is 0.6. (Stefan’s Constant = 5.67 10^-8 Wm^-2K^-4). Ans: 193.93 watt
17. The element of an electric fire with an output of 1.5 kW is a cylinder of 0.3 m long and 0.04 m in radius. Calculate its temperature if it behaves as a black body. (Stefan’s Constant = 5.67 10^-8 Wm^-2K^-4). Ans: 769.6 K
18. A man, the surface area of whose skin is 2 m², is sitting in a room where the air temperature is 20^oC. If his skin temperature is 37^oC, find the rate at which his body loses heat. The emissivity of his skin is 0.97. (Stefan’s Constant = 5.67 10^-8 Wm^-2K^-4). Ans: 205.2 W
19. What is the ratio of the energy per second radiated by the filament of a lamp at 2500 K to that radiated at 2000 K assuming the filament is a black body radiator? Ans: 2.44