Saturday, 6 September 2014

Radiant heat energy problems


                    Radiant heat energy problems

Stefan-Boltzmann constant = 5.7x10-8 Wm2K-4 

1. Discuss Newton's and Stefan's laws of cooling, point¬ing out the processes to which they refer and the conditions under which each is valid. How would these laws apply to the cooling of a hot jacket potato, and how could its rate of cooling be increased? 

2. Explain or discuss the following.
(a) The temperature of the inside of a greenhouse is higher than that outside on a sunny day, although glass is opaque to infrared radiation.
(b) Cavity walls are filled with foam although foam is a better conductor of heat than air.
(c) The wavelength at which most energy is radiated by a body may be used to determine its temperature.
(d) The colour of an incandescent body changes as its temperature rises.
(e) What factors affect the rate at which steady state is achieved when one end of a cold metal rod is heated?
(f) The emission of radiation from a body forms the basis of the quantum theory.
(g) A block of wood and a block of metal are kept at the same temperature. When the blocks feel cold the metal feels colder than the wood and when the blocks feel hot the metal feels hotter than the wood. Explain this. At what temperature will the blocks feel equally hot? 

3. Find the net rate of energy lost by radiation from the following black bodies:
(a) a sphere of radius 10 cm at a temperature of 500 oC in an enclosure whose temperature is 20 oC;
(b) a person of surface area 1.2 m2 at a temperature of 37 oC in an enclosure whose temperature is 0 oC. Comment on your answer. 

4. The average distance of Pluto from the Sun is about 40 times that of the Earth's. If the Sun behaves as a black body at 6000 K, and if it has a radius of 7.0x108 m and is 1.5 x 1011 m from the Earth, calculate the surface temperature of Pluto. 

5. A certain integrated circuit operates at 70 oC and generates heat at a rate of 2.5 W. It is fixed to an aluminium rod 20 mm long and of cross-sectional area 50 mm2. The other end of the rod is fixed to a finned heat sink that can transfer heat to its surroundings at 90 Wm2of its surface per Kelvin of excess temperature above its surroundings.
(a) If the surroundings are at 20 oC, what area of heat sink is needed and what is its equilibrium temperature?
(b) Discuss whether the equilibrium temperature will be different if the integrated circuit does not make good contact with the rod. [O] 
(Thermal conductivity of aluminium = 200 Wm-1 K-1

6. The surface area of a domestic hot water radiator made of iron 2 mm thick is 4 m2. If the water in the pipes is maintained at 60 oC and the temperature of the room is 20 oC, calculate the quantity of heat supplied to the room per hour. (Assume the emissivity of the radiator surface is 0.4) 

7. A black body radiates heat at 2 Wm2 when at 0 oC. Find the rate of fall in temperature of a copper sphere of radius 3 cm when at 1000 oC in air at 0 oC. 
(Assume that the density of copper is 8930 kgm-3 and its specific heat capacity is 385 J kg-1 K-1.) 

8. Given that the energy received from the Sun at the surface of the Earth is 1400 Jm-2 s-1 determine the effective solar temperature, assuming that the Sun behaves as a perfect black body. 

9. The normal operating conditions of a variable-intensity car headlamp are 2.5 A and 12 V. The temperature of the filament is 1750 oC. The intensity is now altered so that the lamp runs at 2.2 A and 12.5 V. 
Calculate the new operating temperature assuming that the filament behaves as a black body. 

10. A certain 100 W tungsten filament lamp operates at a temperature of 1500 oC. Assuming that it behaves as a perfect black body, estimate the surface area of the filament. 

11. A black body at 1000 K emits radiation, with maximum energy emitted at a wavelength of 2500 nm. Calculate the wavelengths at which maximum energy is emitted by the following, assuming that they all behave as black bodies:
(a) a piece of iron heated in a Bunsen flame to 800 oC
(b) a star with a surface temperature of 7000 oC
(c) the plasma in a fusion reaction at 106 oC. 

12. Using the information given at the start of question 11, calculate the temperatures of black bodies which emit maximum energy at the following wavelengths: (a) 5 nm, (b) 50 nm, (c) 500 nm, (d) 5000 nm, (e) 50 000 nm. 

13. A metal sphere of 1 cm diameter, whose surface acts as a black body, is placed at the focus of a concave mirror with an aperture of 60 cm directed towards the Sun. 
If the solar constant is 1400 Wm2 and the mean temperature of the surroundings is 27 oC, calculate the maximum theoretical temperature that the sphere could attain, stating any assumptions that you make. 

14. Sketch graphs to show the distribution of radiant energy with temperature for two black bodies, one with a temperature of 2000 oC and the other with a temperature of 500 oC. Label your diagram clearly. 

15. A black body at 2000 K emits radiation with λm = 1250 mm. Use this information to calculate the surface temperature of the star Betelgeuse if λm for Betelgeuse is 780 nm. (Assume Betelgeuse behaves as a black body.
                               Stefan-Boltzmann constant = 5.7x10-8 Wm2K-4 

1. Discuss Newton's and Stefan's laws of cooling, point¬ing out the processes to which they refer and the conditions under which each is valid. How would these laws apply to the cooling of a hot jacket potato, and how could its rate of cooling be increased? 

2. Explain or discuss the following.
(a) The temperature of the inside of a greenhouse is higher than that outside on a sunny day, although glass is opaque to infrared radiation.
(b) Cavity walls are filled with foam although foam is a better conductor of heat than air.
(c) The wavelength at which most energy is radiated by a body may be used to determine its temperature.
(d) The colour of an incandescent body changes as its temperature rises.
(e) What factors affect the rate at which steady state is achieved when one end of a cold metal rod is heated?
(f) The emission of radiation from a body forms the basis of the quantum theory.
(g) A block of wood and a block of metal are kept at the same temperature. When the blocks feel cold the metal feels colder than the wood and when the blocks feel hot the metal feels hotter than the wood. Explain this. At what temperature will the blocks feel equally hot? 

3. Find the net rate of energy lost by radiation from the following black bodies:
(a) a sphere of radius 10 cm at a temperature of 500 oC in an enclosure whose temperature is 20 oC;
(b) a person of surface area 1.2 m2 at a temperature of 37 oC in an enclosure whose temperature is 0 oC. Comment on your answer. 

4. The average distance of Pluto from the Sun is about 40 times that of the Earth's. If the Sun behaves as a black body at 6000 K, and if it has a radius of 7.0x108 m and is 1.5 x 1011 m from the Earth, calculate the surface temperature of Pluto. 

5. A certain integrated circuit operates at 70 oC and generates heat at a rate of 2.5 W. It is fixed to an aluminium rod 20 mm long and of cross-sectional area 50 mm2. The other end of the rod is fixed to a finned heat sink that can transfer heat to its surroundings at 90 Wm2of its surface per Kelvin of excess temperature above its surroundings.
(a) If the surroundings are at 20 oC, what area of heat sink is needed and what is its equilibrium temperature?
(b) Discuss whether the equilibrium temperature will be different if the integrated circuit does not make good contact with the rod. [O] 
(Thermal conductivity of aluminium = 200 Wm-1 K-1

6. The surface area of a domestic hot water radiator made of iron 2 mm thick is 4 m2. If the water in the pipes is maintained at 60 oC and the temperature of the room is 20 oC, calculate the quantity of heat supplied to the room per hour. (Assume the emissivity of the radiator surface is 0.4) 

7. A black body radiates heat at 2 Wm2 when at 0 oC. Find the rate of fall in temperature of a copper sphere of radius 3 cm when at 1000 oC in air at 0 oC. 
(Assume that the density of copper is 8930 kgm-3 and its specific heat capacity is 385 J kg-1 K-1.) 

8. Given that the energy received from the Sun at the surface of the Earth is 1400 Jm-2 s-1 determine the effective solar temperature, assuming that the Sun behaves as a perfect black body. 

9. The normal operating conditions of a variable-intensity car headlamp are 2.5 A and 12 V. The temperature of the filament is 1750 oC. The intensity is now altered so that the lamp runs at 2.2 A and 12.5 V. 
Calculate the new operating temperature assuming that the filament behaves as a black body. 

10. A certain 100 W tungsten filament lamp operates at a temperature of 1500 oC. Assuming that it behaves as a perfect black body, estimate the surface area of the filament. 

11. A black body at 1000 K emits radiation, with maximum energy emitted at a wavelength of 2500 nm. Calculate the wavelengths at which maximum energy is emitted by the following, assuming that they all behave as black bodies:
(a) a piece of iron heated in a Bunsen flame to 800 oC
(b) a star with a surface temperature of 7000 oC
(c) the plasma in a fusion reaction at 106 oC. 

12. Using the information given at the start of question 11, calculate the temperatures of black bodies which emit maximum energy at the following wavelengths: (a) 5 nm, (b) 50 nm, (c) 500 nm, (d) 5000 nm, (e) 50 000 nm. 

13. A metal sphere of 1 cm diameter, whose surface acts as a black body, is placed at the focus of a concave mirror with an aperture of 60 cm directed towards the Sun. 
If the solar constant is 1400 Wm2 and the mean temperature of the surroundings is 27 oC, calculate the maximum theoretical temperature that the sphere could attain, stating any assumptions that you make. 

14. Sketch graphs to show the distribution of radiant energy with temperature for two black bodies, one with a temperature of 2000 oC and the other with a temperature of 500 oC. Label your diagram clearly. 

15. A black body at 2000 K emits radiation with λm = 1250 mm. Use this information to calculate the surface temperature of the star Betelgeuse if λm for Betelgeuse is 780 nm. (Assume Betelgeuse behaves as a black body.