Problem 2 A black body emits radiation in proportion to the fourth power of its

Question

Problem 2 A black body emits radiation in proportion to the fourth power of its temperature where F is the flux of radiation (w m), Tis the temperature of the black body (K) and ? is the Stefan-Boltzmann constant a) The units of flux are watts per metre squared (W m2) and the units of temperature are kelvin (K). Use this information and Eq. (1) to determine the units ora in these units, ?-5.67 x 104, We may model the radiation emitted upwards by thick clouds as being equal to the emission by an ideal black body with a temperature equal to that of the cloud top. b) Given the mean temperature structure of the troposphere, explain how one could use the outgoing longwave radiation (OLR) measured by a satellite to infer the height of cloud tops? c) Suppose the OLR is measured to be F-225 w m-2, what is the rough height of the cloud top? Assume the atmospheric temperature profile is the one given in Fig. 2. d) What are some of the sources of error in your answer to part b? 20 200 +10 400 600 temperature 2.5 800 1000+ 200 300 temp/potential temp. (K) 350 Fig. 2

Explanation / Answer

2. given

Flux, F = sigma*T^4

c. F = 225 W/m^2

then

225 = 5.67*10^-8*T^4

T = 250.986212 K

from the graph

height is about 8 km

d. sources of errors can be

1. instrumen reading

2. human error while matching data onto the graph

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