Climate scientists use the Stefan-Boltzmann Law R=oT4 to estimate the change in the earth's average temperature T (in kelvins) that results from a change in the radiation R (in joules per square meter per second) that the earth receives from the sun. Here, o = 5.67 x 10-8 Js-'m-²K-4. Calculate d R/dt, assuming that T = 283 and 4 = 0.05 K/year. What are the units of dR/dt? %3D dt
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- As the very first rudiment of climatology, estimate the temperature of Earth. Assume it is a perfect sphere and its temperature is uniform. Ignore the greenhouse effect. Thermal radiation from the Sun has an intensity (the "solar constant" S) of about 1370 W/m2 at the radius of Earth's orbit. (a) Assuming the Sun's rays are parallel, what area must S be multiplied by to get the total radiation intercepted by Earth? It will be easiest to answer in tens of Earth's radius, R. (b) Assume that Earth reflects about 30% of the solar energy it intercepts. In other words, Earth has an albedo with a value of A=0.3 . In terms of S, and R, what is the rate at which Earth absorbs energy from the Sun? (c) Find the temperature at which Earth radiates energy at the same rate. Assume that at the infrared wavelengths where it radiates, the emissivity e is 1. Does your result show that the greenhouse effect is important? (d) How does your answer depend on the area of Earth?Earth’s surface absorbs an average of about 960. W/m2 from the Sun’s irradiance. The power absorbed is Pabs = (960. W/m2) (Adisc), where Adisc = π(RE)2 is Earth’s projected area. An equal amount of power is radiated so that Earth remains in thermal equilibrium with its environment at nearly 0 K. Estimate Earth’s surface temperature by setting the radiated power from Stefan’s law equal to the absorbed power and solving for the temperature in Kelvin. In Stefan’s law, assume e = 1 and take the area to be A = 4π(RE)2, the surface area of a spherical Earth. (Note : Earth’s atmosphere acts like a blanket and warms the planet to a global average about 30 K above the value calculated here.)A child has a temperature of 101◦F .If her total skin area is 2 m2, find the energyloss per second due to radiation, assuming theemissivity is 1. Assume the room temperatureis 70◦F. The Stephan-Boltzmann constant is5.6696 × 10^−8 W/m2· K4.Answer in units of W.
- Even when shut down after a period of normal use, a large commercial nuclear reactor transfers thermal energy at the rate of 150 MW by the radioactive decay of fission products. This heat transfer causes a rapid increase in temperature if the cooling system fails.(1 watt = 1 joule/second or 1 W = 1 J/s and 1 MW = 1 megawatt)(a) Calculate the rate of temperature increase in degreesCelsius per second (ºC/s) if the mass of the reactor core is 1.60×105 kg and it has an average specific heat of 0.3349 kJ/kgº ⋅ C . (b) How long would it take to obtain a temperature increase of 2000ºC , which could cause some metals holding the radioactive materials to melt? (The initial rate of temperature increase would be greater than thatcalculated here because the heat transfer is concentrated in a smaller mass. Later, however, the temperature increase would slow down because the 5×105-kg steel containment vessel would also begin to heat up.)As radioactive plutonium isotopes decay, they generate heat as a byproduct. Pu-239 generates 1.9W/kg of heat. How much heat will 1.25molof Pu-239 release after decaying for three hours? Express this quantity in units of calories. Assume Pu-239 has a molecular weight of 244g/mol.I was hoping that you could check to make sure I’m using the correct units. For some reason I am having a hard time understanding when to use 4186 for specific heat of water or 4.186. For the latent heat of fusion, I have it in kg•cal degrees C. In my book it has it in J/kg. Since the book says it is 3.33 X 10^5, how do I get my answer to show in those terms? Thank you!
- The volume of air taken in by a warm-blooded vertebrate is 236 L/day at standard temperature and pressure (i.e., 0.0°C and 1.00 atm). If the air in the lungs is at 37.2°C, under a pressure of 450 mm Hg, and assuming that the vertebrate takes in an average volume of 112 cm3 per breath at the temperature and pressure of its lungs, how many breaths does this vertebrate take per day?A body whose surface area is 0.2 m2, emissivity is 0.8, and temperature is 100°C is placed in a large, evacuated chamber whose walls are at 25°C. What is the rate at which radiation is emitted by the surface, in W? What is the net rate at which radiation is exchanged between the surface and the chamber walls, in W?Even when shut down after a period of normal use, a large commercial nuclear reactor transfers thermal energy at the rate of 150 MW by the radioactive decay of fission products. This heat transfer causes a rapid increase in temperature if the cooling system fails (1 watt = 1 joule/second or 1 W = 1 J/s and 1 MW = 1 megawatt). (a) Calculate the rate of temperature increase in degrees Celsius per second (ºC/s) if the mass of the reactor core is 1.60×10^5kg and it has an average specific heat of 0.3349 kJ/kgº⋅C.
- Even when shut down after a period of normal use, a large commercial nuclear reactor transfers thermal energy at the rate of 150 MW by the radioactive decay of fission products. This heat transfer causes a rapid increase in temperature if the cooling system fails (1 watt = 1 joule/second or 1 W = 1 J/s and 1 MW = 1 megawatt) (a) Calculate the rate of temperature increase in degrees Celsius per second (ºC/s) if the mass of the reactor core is 1.60×105 kg and it has an average specific heat of 0.3349 kJ/kgº ⋅ C . (b) How long would it take to obtain a temperature increase of 2000ºC , which could cause some metals holding the radioactive materials to melt? (The initial rate of temperature increase would be greater than that calculated here because the heat transfer is concentrated in a smaller mass. Later, however, the temperature increase would slow down because the 5×105-kg steel containment vessel would also begin to heat up.)A sphere of radius 4.3 mm is at 3499 K. Calculate the rate of radiation of energy (in W) by the sphere, if its emissivity is 1.A water heater is operated by solar power. If solar collector has an area of 6.00m2 , and the Intensity delivered by sunlight is 550W/m2 , how long does it take to increase the temperature of 1m3 of water from 20°Cto 60°C?