ATM OCN (Meteorology) 100

Answers for Homework 2: Energy, Heat & Radiation

Fall 2000 Lecture 2

Date Due: Tuesday, 4 October 2000

The total maximum points were 50. Point distribution for each question noted below.
[Note:  Extra points for the optional Weather on the Web Question added separately.] 

1. SEASONALITY

Assume that the sun is to the left of this page and produces a circle of illumination (the vertical lines) upon the globe for each of the four dates. Upon each globe:

a. Mark and label the North and South Poles.

b. Draw and label the Equator.

c. Draw and label the i.) Tropics of Cancer and Capricorn and ii.) the Arctic and Antarctic Circles.

d. Mark with the letter "V" that latitude where the sun appears to be directly overhead at local solar noon.

e. Mark with the letter "T" that latitude at the edge of the polar night where the sun appears to be just on the local horizon at local solar noon.  (Hint: Where is the edge of polar night?)

(20 pts) 

21 MARCH         21 JUNE           23 SEPTEMBER       23 DECEMBER
See also satellite images (courtesy of DataStreme and Project Atmosphere, the education initiative of the American Meteorological Society) 
21 MARCH         21 JUNE           23 SEPTEMBER       23 DECEMBER

3. THE SOLAR RADIATION BUDGET -- Please use the appropriate units!

a. The solar constant for the earth is approximately:

(2 pts)
 

1.97 cal per sq. cm. per min or 1372 Watts per sq. meter. 
These values were provided and discussed in lecture.

b. A mythical planet has an orbit with an average planet-sun distance exactly half  that of the earth's. What would be the solar constant for this mythical planet? [Hint: make use of your answer from above.]

(4 pts)
 

The inverse square law means that the planet at one half the distance would have 4 times (2 squared) the amount of energy per unit area per unit time. 

7.88 cal per sq. cm. per min or 5488 Watts per sq. meter.

c. What is the planetary albedo of the planet earth?

(2 pts)
 

From lecture: 

Planetary albedo = 30 - 31 percent .

4. RADIATION LAWS

Object A and Object B are ideal radiators. If A were hotter than B, then:

a. Which object would radiate more energy?

b. Which object would radiate more of its energy at a shorter wavelength?

(1 pt. each or 2 pts)
 

a. A (A consequence of Stefan-Boltzmann law) 

b. A (A consequence of Wien's Displacement law)

5. WIND CHILL EQUIVALENT TEMPERATURE

Using the Wind Chill Equivalent Temperature tables in your textbook:

a. What is the wind chill equivalent temperature if the ambient air temperature were -5°F and the wind speed were 15 mph?

b. What is the wind chill equivalent temperature if the ambient air temperature remained at -5°F, but the wind speed increased to 30 mph?

c. What has caused the difference between your answers a and b above? Why?

d. To what temperature does your automobile reach in part a? in part b?

(11 pts)
 

Note that Table 3.3B (for English units) should be used: 

a. -38° F is the wind chill equivalent temperature 

b. -56° F is the wind chill equivalent temperature 

c.  The increased wind speed causes the difference in the wind chill equivalent temperatures. The convective heat loss      from the human body increases with increased winds. A statement about the air being colder is not correct since the ambient air temperature remains the same. 

d.  The temperature of your automobile can only reach the ambient air temperature of  -5° F in both cases, and go no lower.  The wind-chill equivalent temperature is not relevant here.   However, in the second case, the stronger winds would hasten the cooling process, causing the engine block to cool to the ambient at a faster rate.

6. HEAT AND TEMPERATURE

-- [Please use the appropriate units!]

a. How much energy is required to entirely melt 1 gram of ice at the ice point?

b. How much energy is required to evaporate 1 gram of liquid water at room temperature?

c. How would the temperature of 1 kilogram of liquid water originally at 20°C change if 5000 calories were used in the heating process (assume no phase transformations)? If a temperature change would take place, indicate the amount of change (and the direction of the temperature change).

[Please show your work and include units!]

(11 pts)
 

a. 80 cal (This is the latent heat of melting.) 

b. 590 cal (Note: The latent heat of evaporation is a function of temperature, being 590 cal at 20° C and decreasing to 540 cal at 100° C.  The reason for this change in latent heat is that at room temperature water molecules are more tightly attracted to one another and would require more energy to break these "hydrogen bonds" of attraction than at higher temperatures when the water molecules are more active.) 

c. 3 Celisus degree heating

Since 1 calorie is the heat needed to raise 1 gram of water 1 Celsius degree, then 3000 calories would raise 1000 grams by 3 Celsius degrees (making the liquid warm from 20° C to 23° C)

Current Weather on the Web (5 extra credit pts.)
See http://www.aos.wisc.edu/~hopkins/aos100/homework/f00hmk2k.html
This portion of the homework was designed to have you access to a location on the Internet where you can find the times of sunrise and sunset for many locations throughout the country.
Any "reasonable answer" that fell within the range of values for the week's sunset times in Madison was accepted .
NOTE:  Just by being outside in the early evening, you should have recognized that sunset should be within 15 minutes of 7:00 PM CDT during the week following the autumnal equinox.  Therefore adding an additional hour to the daily listing would not have made sense.

Last revision: 28 September 2000 (1815 UTC)
Produced by Edward J. Hopkins, Ph.D.
Department of Atmospheric and Oceanic Sciences
University of Wisconsin-Madison, Madison, WI 53706
hopkins@meteor.wisc.edu

 

 

URL Address: aos100/homework/f00hmk01a.html


 
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