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(a) A shirtless rider under a circus tent feels the heat radiating from the sunlit portion of the tent. Calculate the temperature of the tent canvas based on the following information: The shirtless rider’s skin temperature is 34 . 0ºC size 12{"34" "." "0°C"} {} and has an emissivity of 0.970. The exposed area of skin is 0 . 400  m 2 size 12{0 "." "400"`m rSup { size 8{2} } } {} . He receives radiation at the rate of 20.0 W—half what you would calculate if the entire region behind him was hot. The rest of the surroundings are at 34 . 0ºC size 12{"34" "." "0°C"} {} . (b) Discuss how this situation would change if the sunlit side of the tent was nearly pure white and if the rider was covered by a white tunic.

(a) 48 . C size 12{"48" "." 5°C} {}

(b) A pure white object reflects more of the radiant energy that hits it, so a white tent would prevent more of the sunlight from heating up the inside of the tent, and the white tunic would prevent that heat which entered the tent from heating the rider. Therefore, with a white tent, the temperature would be lower than 48 . C size 12{"48" "." 5°C} {} , and the rate of radiant heat transferred to the rider would be less than 20.0 W.

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Integrated Concepts

One 30 . 0ºC size 12{"30" "." "0°C"} {} day the relative humidity is 75 . 0% size 12{"75" "." "0%"} {} , and that evening the temperature drops to 20 . 0ºC size 12{"20" "." "0°C"} {} , well below the dew point. (a) How many grams of water condense from each cubic meter of air? (b) How much heat transfer occurs by this condensation? (c) What temperature increase could this cause in dry air?

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Integrated Concepts

Large meteors sometimes strike the Earth, converting most of their kinetic energy into thermal energy. (a) What is the kinetic energy of a 10 9  kg size 12{"10" rSup { size 8{9} } `"kg"} {} meteor moving at 25.0 km/s? (b) If this meteor lands in a deep ocean and 80% size 12{"80%"} {} of its kinetic energy goes into heating water, how many kilograms of water could it raise by 5 . 0ºC? size 12{5 "." "0°C? "} {} (c) Discuss how the energy of the meteor is more likely to be deposited in the ocean and the likely effects of that energy.

(a) 3 × 10 17  J size 12{3 times "10" rSup { size 8{"17"} } `J} {}

(b) 1 × 10 13  kg size 12{1 times "10" rSup { size 8{"13"} } `"kg"} {}

(c) When a large meteor hits the ocean, it causes great tidal waves, dissipating large amount of its energy in the form of kinetic energy of the water.

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Integrated Concepts

Frozen waste from airplane toilets has sometimes been accidentally ejected at high altitude. Ordinarily it breaks up and disperses over a large area, but sometimes it holds together and strikes the ground. Calculate the mass of 0ºC size 12{"0°C"} {} ice that can be melted by the conversion of kinetic and gravitational potential energy when a 20 .0  kg size 12{"20" "." 0`"kg"} {} piece of frozen waste is released at 12.0 km altitude while moving at 250 m/s and strikes the ground at 100 m/s (since less than 20.0 kg melts, a significant mess results).

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Integrated Concepts

(a) A large electrical power facility produces 1600 MW of “waste heat,” which is dissipated to the environment in cooling towers by warming air flowing through the towers by 5 . 00ºC size 12{5 "." "00°C"} {} . What is the necessary flow rate of air in m 3 /s size 12{m rSup { size 8{3} } "/s"} {} ? (b) Is your result consistent with the large cooling towers used by many large electrical power plants?

(a) 3 . 44 × 10 5  m 3 /s size 12{3 "." "44" times "10" rSup { size 8{5} } `m rSup { size 8{3} } "/s"} {}

(b) This is equivalent to 12 million cubic feet of air per second. That is tremendous. This is too large to be dissipated by heating the air by only C size 12{5°C} {} . Many of these cooling towers use the circulation of cooler air over warmer water to increase the rate of evaporation. This would allow much smaller amounts of air necessary to remove such a large amount of heat because evaporation removes larger quantities of heat than was considered in part (a).

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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