**AME 517, Fall 2009**

**Problem set #5**

**Assigned: 11/13/2009**

**Due: 11/24/2009, 4:30 pm**

** **

Note: the special symbols seem to work only
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version of the assignment.

**Chapter 9: **

9.4.
Hints:

- The heat generation QÕÕÕ is
**„**á**q**= dq/dz, where z is the direction parallel to the sunÕs rays, with z = 0 at the surface of the medium - Note that the incident radiation I(z=0) = 0
for all incident angles other than the direction parallel to the sunÕs
rays
- You need the index of refraction n to
calculate the reflectivity of the surface, which is given by Eq. 3.80.
- Answer: QÕÕÕ = -(1-r)q
_{sun}k*e*^{-}^{k}^{z}

9.8.
Answers:

where µ = cos(q)

QÕÕÕ(r = 0) = 1.33 x 10^{7}
W/m^{3}

QÕÕÕ(r = R) = 8.16 x 10^{7}
W/m^{3}

9.10. Answer: 40%

9.14. Answers:

a)

b)

**Chapter 10:**

** **

10.2. Answer:
4338K

10.6. Answer:
1.2 cm^{-1}.

10.7 Answers: Elsasser 0.491, Goody 0.368, Malkmus
0.329. Note that the Òintegrated
absorption coefficientÓ is actually the Òline strengthÓ S which has units of cm^{-2}
per (g/cm^{3}) which is the same units (but not the same look and feel)
as cm^{-1} per g/m^{-2}.
Use S to compute the dimensionless optical thickness parameter x = SX/2¹b_{L} (Eq. 10.37) which in turn is one of
the two parameters you need for the narrow band models. Note that the Elsasser model needs x
and beta = ¹ b_{L}/d (Eq.
10.54) which is the dimensionless line width, whereas the statistical models
use b and t = 2bx.

10.9 Answers: (a) 0.785, (b) 0.615; hints: (a) show that these conditions fall
into the strong absorption line limit and use the result from the Goody or
Malkmus model in this limit, (b) use Eq. 10.24 to determine the line width for
this part knowing the line width at conditions for part (a) and the
temperatures and pressures for both parts. Also for some reason Modest uses frequency (n), not wavenumber (h), for this problem; recall c = n/h.