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- Homework Statement
- Consider a black body of surface area 20.0 cm.^2 and temperature 5 000 K. Find the spectral power per wavelength at 1.00 nm (an x or gamma ray.
- Relevant Equations
- See below
The format is not helpful. Relevant equations and attempt at solution are supposed to separate sections, formatted in a way that individual parts can be replied to. What you have done is as if a form asked for surname, given name, and address, and you squeezed all information into surname, on a sticker label (rather than typing it into each section).jjson775 said:It’s shown in the post, every step.
Do you know what the answer is supposed to be? I find it surprising to see a question in which the answer seems to be so infinitesimal, but I don't see any major error.jjson775 said:Duh. I fixed P = IA but still don’t have the right answer. Am I missing something about the phenomena or just another math error?
View attachment 278131
According to my textbook, Serway Beichner Physics for Scientists and engineers, the correct answer is 9.42 x 10 ^1226. The numerator must be right, just multiplying constants, and I got the right power of 10 in the denominator. Beats me. Thanks very much for feedback.haruspex said:Do you know what the answer is supposed to be? I find it surprising to see a question in which the answer seems to be so infinitesimal, but I don't see any major error.
You rounded the exponent of e to 2880, then rounded 2880 log_{10}e to an integer also. To get the same leading digit as in the book you will need to keep a bit more precision. But in practical terms, when the power of ten is -1226, the leading digit of the mantissa is somewhat irrelevant. "Immeasurably small" should suffice.jjson775 said:According to my textbook, Serway Beichner Physics for Scientists and engineers, the correct answer is 9.42 x 10 ^-1226 W/M. The numerator must be right, just multiplying constants, and I got the right power of 10 in the denominator
That’s right but doesn’t change my last reply.hutchphd said:##20 cm^2=20(10^{-4} m^2)=2(10^{-3})m^2 ##
Only because you rounded to a whole number in the exponent.jjson775 said:the denominator is just a power of 10
Black body radiation is the thermal electromagnetic radiation emitted by an object due to its temperature. It is a fundamental concept in thermodynamics and plays a key role in understanding the behavior of objects at high temperatures.
1.00 nm is a unit of measurement used to describe the wavelength of electromagnetic radiation. In the context of black body radiation, it is commonly used to represent the peak wavelength at which the object emits the most radiation.
The power of black body radiation is directly proportional to the fourth power of the object's temperature. This relationship is known as the Stefan-Boltzmann law and is a fundamental principle in understanding the behavior of black bodies.
Yes, the power of black body radiation can be calculated for any wavelength using the Planck's law, which describes the spectral distribution of black body radiation. The power at a specific wavelength is determined by the temperature of the object and its emissivity.
The power of black body radiation at 1.00 nm is closely related to the color of the object. Objects that emit a higher power at this wavelength tend to appear more red, while objects with a lower power appear more blue. This is due to the relationship between wavelength and color in the visible spectrum.