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L'hopitals Rule

Given: ^4] Where is measured in meters, T is the temperature in kelvins, k is Boltzmann's constant. The Rayleigh-Jeans Law agrees with experimental measurements for long wavelengths but disagrees drastically for short wavelengths. [The law predicts that as but experiments have shown that.] This fact is known as the ultraviolet catastrophe. In 1900 Max Planck found a better model (known as Planck's Law) for blackbody radiation: where is measures in meters, T is the temperature in kelvins, and h=Planck's constant=6.6262 * 10^-34 J*s c=speed of light = 2.997925 * 10^8 m/s k=Boltzmann's constrant = 1.3807 * 10^-23 J/K 1. Use L'hopitals rule to show that : and... click for more

Subject:

Math

Topic:

Calculus

Posting ID:

2725

OTA ID:

102827

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Taylor polynomials

Use a taylor polynomial to show that , for a large wavelength, Planck's Law gives approximately the same values as the Rayleigh-Jeans Law. see the attached problem #2

Subject:

Math

Topic:

Calculus

Posting ID:

2727

OTA ID:

102499

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Graphing 1

1. Use a Taylor polynomial to show that, for large wavelengths, Planck's Law gives approximately the same values as the Rayleigh-Jeans Law. 2. Graph f as given by both laws in the same screen and comment on the similarities and differences. Use T= 5700K ( the temperature of the Sun). ( you may want to change from meters to the more convenient unit of micrometers: 1um=10^-6 m. 3. Use you graph in problem 3 to estimate the value of for which is a maximum under Planck's Law. 4. Investigate how the graph of changes as T varies. (use Planck's Law.) In particular, graph for the stars Betelgeuse (T=3400 K), Procyon (T= 6400K), and Sirius( T= 9200K) as well as the Sun. How dose the t... click for more

Subject:

Math

Topic:

Calculus

Posting ID:

2728

OTA ID:

102499

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Graph

Investigate how the graph of changes as T varies. (use Planck's Law.) In particular, graph for the stars Betelgeuse (T=3400 K), Procyon (T= 6400K), and Sirius( T= 9200K) as well as the Sun. How dose the total radiation emitted (the are under the curve) vary with T? Use the graph to comment on why Sirius is known as a blue star and Betelgeuse as a red star.

Subject:

Math

Topic:

Calculus

Posting ID:

2729

OTA ID:

102499

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Related Rates word problem

A highway patrol helicopter hovers 3/10 mile above a level, straight interstate highway which has a posted speed limit of 65 miles per hour. The helicopter pilot sees a car on the highway and determines with radar that at that particular instant, the distance between the helicopter and the car is 1/2 mile and is increasing at a rate of 64 miles per hour. Should the driver of the car be ticketed for speeding? Set up and solve a related rates problem to justify answer. Hint: Find the car's speed along the highway.

Subject:

Math

Topic:

Calculus

Posting ID:

2735

OTA ID:

103020

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