14.7 Radiation

Conversely, dark space is very cold, about $\text{3K} (− \text{454}º \text{F})$, so that the Earth radiates energy into the dark sky. Owing to the fact that clouds have lower emissivity than either oceans or land masses, they reflect some of the radiation back to the surface, greatly reducing heat transfer into dark space, just as they greatly reduce heat transfer into the atmosphere during the day. The rate of heat transfer from s…

Two ideal, black-body radiators have temperatures of 275 K and 1100 K. The rate of heat transfer from the latter radiator is how many times greater than the rate of the former radiator?

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

At what net rate does heat radiate from a $\text{275} -\text{m}^{2}$ black roof on a night when the roof’s temperature is $\text{30}. 0º \text{C}$ and the surrounding temperature is $\text{15}. 0º \text{C}$? The emissivity of the roof is 0.900.

Radiation makes it impossible to stand close to a hot lava flow. Calculate the rate of heat transfer by radiation from $1 . \text{00} \textrm{ }\text{m}^{2}$ of $\text{1200}º \text{C}$ fresh lava into $\text{30} . 0º \text{C}$ surroundings, assuming lava’s emissivity is 1.00.

Find the net rate of heat transfer by radiation from a skier standing in the shade, given the following. She is completely clothed in white (head to foot, including a ski mask), the clothes have an emissivity of 0.200 and a surface temperature of $\text{10} . 0º \text{C}$, the surroundings are at $- \text{15} . \text{0}º\text{C}$, and her surface area is $1 . \text{60} \text{m}^{2}$.

A large body of lava from a volcano has stopped flowing and is slowly cooling. The interior of the lava is at $\text{1200}º\text{C}$, its surface is at $\text{450}º\text{C}$, and the surroundings are at $\text{27} . \text{0}º\text{C}$. (a) Calculate the rate at which energy is transferred by radiation from $1 . \text{00 } \textrm{ }\text{m}^{2}$ of surface lava into the surroundings, assuming the emissivity is 1.00. (b) Suppose heat conduction to the surface occurs at the same rate. What is the thickness…

(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 $\text{34} . \text{0}º\text{C}$ and has an emissivity of 0.970. The exposed area of skin is $0 . \text{400} \textrm{ }\text{m}^{2}$. He receives radiation at the rate of 20.0 W—half what you would calculate if the entire region behind him wa…

Large meteors sometimes strike the Earth, converting most of their kinetic energy into thermal energy. (a) What is the kinetic energy of a $\text{10}^{9} \textrm{ }\text{kg}$ meteor moving at 25.0 km/s? (b) If this meteor lands in a deep ocean and $\text{80}\%$ of its kinetic energy goes into heating water, how many kilograms of water could it raise by $5 . \text{0}º\text{C}?\text{ }$ (c) Discuss how the energy of the meteor is more likely to be deposited in the ocean and…

(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 $5 . \text{00}º\text{C}$. What is the necessary flow rate of air in $\text{m}^{3} /\text{s}$? (b) Is your result consistent with the large cooling towers used by many large electrical power plants?

A 76.0-kg person suffering from hypothermia comes indoors and shivers vigorously. How long does it take the heat transfer to increase the person’s body temperature by $2 . \text{00}º\text{C}$ if all other forms of heat transfer are balanced?

Heat transfers from your lungs and breathing passages by evaporating water. (a) Calculate the maximum number of grams of water that can be evaporated when you inhale 1.50 L of $37º \text{C}$ air with an original relative humidity of 40.0%. (Assume that body temperature is also $37º \text{C}$.) (b) How many joules of energy are required to evaporate this amount? (c) What is the rate of heat transfer in watts from this meth…

Hot air rises because it has expanded. It then displaces a greater volume of cold air, which increases the buoyant force on it. (a) Calculate the ratio of the buoyant force to the weight of $50.0º \text{C}$ air surrounded by $20.0º \text{C}$ air. (b) What energy is needed to cause $1.00 \text{ m}^{3}$ of air to go from $20.0º \text{C}$ to $50.0º \text{C}$? (c) What gravitational potential energy is gained by this volume of air if it rises 1.00 m? Will this cause a significa…

(a) What is the temperature increase of an 80.0 kg person who consumes 2500 kcal of food in one day with 95.0% of the energy transferred as heat to the body? (b) What is unreasonable about this result? (c) Which premise or assumption is responsible?

(a) Calculate the rate of heat transfer by conduction through a window with an area of $1 .\text{00} \textrm{ }\text{m}^{2}$ that is 0.750 cm thick, if its inner surface is at $\text{22}.\text{0}º\text{C}$ and its outer surface is at $\text{35}.\text{0}º\text{C}$. (b) What is unreasonable about this result? (c) Which premise or assumption is responsible?