Homework Assignment # 1 (assigned 1/14/99, due beginning of class 1/21/99)
Please use a separate sheet of paper and show your work where appropriate.
1. a) In a distant galaxy, a star slightly smaller than the sun emits radiant energy with maximum emission at a wavelength of 1.2 micrometers (1.2x10-6 m). Using c=ln , what frequency does this wavelength correspond to? Express this in exponential notation.
b) Using Wien's Law, calculate the temperature of the star in part (a) above. (Assume that the star behaves like a blackbody.) Convert your answer into degrees Fahrenheit.
2. a) Assume Mars has a surface temperature of 193 K. What is the wavelength of maximum emission by the surface of Mars? (Assume that Mars behaves like a blackbody.) Express your answer in both micrometers (microns) and meters.
b) Based on your answer to part (a), which gas do you think would be an important contributor to a "greenhouse effect" on Mars? Explain. (Assume that all of these gases are present in the Martian atmosphere in concentrations similar to those found on Earth.):
Water vapor: absorbs mainly at 2.7m m (and
shorter wavelengths) and at 6.3 m m
Carbon dioxide: absorbs mainly at 15 m m
and longer wavelengths
Ozone: absorbs mainly at 9.6 m m
Methane: absorbs mainly at 2.3 m m and 6.1
m
m
Nitrous oxide: absorbs mainly at 4.7 m m
and 7.5 m m
3) A large metal tank is full of completely frozen water (ice). Using a thermometer, you measure the temperature of the tank as precisely 0° C. The mass of the ice is exactly 1000 kg (kilograms). You turn on a heater underneath the tank, and the tank conducts heat from the heater to the ice inside of the tank, melting some of the ice.
a) What is the temperature of the liquid water in the tank?
b) What is the temperature of the remaining ice?
c) How much energy is required to melt all of the ice in the tank? (Hint: the latent heat of melting/freezing is 3.34x105 Joules per kilogram.)
4) Now all of the ice in the tank in Problem 3 has been turned into liquid water. The temperature of the water is 0° C. Once again, you turn on the heater underneath the tank.
a) How much energy is required to raise the temperature of the water to 30° C? (Hint: the specific heat of liquid water is approximately 1 calorie per gram per degree Celsius, or 4.2x103 Joules per kilogram per degree Kelvin.)
b) Which has more heat: the water in the tank (at 30° C), or 50 kg of water at 99° C? Why?
5. a) Using the data in Figure 3.10 in the textbook, determine the average temperature in Richmond and in San Francisco during January, April, and July. Convert all your answers into degrees Celsius and degrees Kelvin.
b) Using the following table, calculate the total precipitation received
in each city (in inches) during a typical year. Convert your answer into
meters (Hint: one inch equals approximately 2.54 centimeters, or 2.54x10-2
meters).
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c) If a San Francisco native asked you to describe the climate of Richmond relative to that of San Francisco, how would you respond? When is the "rainy season" at each location? Where is the seasonal temperature range greatest? Why do you think this is? How do you think the daily range of temperature in San Francisco compares with the daily range of temperature in Richmond? Explain.
6. a) For each example below, state which energy transfer mechanism(s) is operating and briefly explain your choice (there may be more than one correct answer for each):
- you place a pot of water on an electric stove
- you get a sunburn
- the handle of your fireplace poker heats up when you stir the fire
- you listen to the radio
- snow melts off the hood of your car after you start the engine
- vultures circle carrion on a hot summer day without moving their
wings
b) For each example below, state the form(s) of energy present and briefly explain your choice (again, there may be more than one correct answer for each):
- you eat breakfast in the morning
- you see a lump of silly putty on the ground
- you pick up the silly putty and lift it up to eye level
- you drop the silly putty (which weighs 0.5 kg), and right before
it hits the ground it is travelling at 2 meters per second. Calculate the
external kinetic energy of the silly putty.
- when the silly putty hits the ground, it stops and deforms. Where
do you think the energy went? (Hint: if you throw the putty against a wall
repeatedly, it gets warm).