The Physics
Hypertextbook
Opus in profectus

## Problems

### practice

1. Determine the temperature of the following light sources from their spectra. (A graph and data file are provided for each source.)
1. bb-candle.txt
A candle flame
2. bb-tungsten.txt
A tungsten filament, incandescent light bulb. For extra credit, determine the surface area of the light bulb's filament given a power output of 15 W.
3. bb-daylight.txt
The Sun. Daylight is almost the same spectrum as sunlight, but it's less likely to burn out your spectrometer. For extra credit, determine the luminosity of the Sun (its radiant power).
2. Dyson sphere
1. Given a Dyson sphere as big as the Earth's orbit surrounding the Sun, determine…
1. its surface temperature and
2. the peak wavelength of the radiation emitted.
2. Given a Dyson sphere with an interior temperature suitable for human habitation surrounding the Sun, determine…
2. the peak wavelength of the radiation emitted.
3. Given a Dyson sphere with an interior temperature suitable for human habitation and a surface gravity equal to 1 g surrounding a white dwarf star with the mass of the Sun and the radius of the Earth, determine…
1. the Dyson sphere's radius and
2. the surface temperature of the white dwarf.

Magnify

3. This problem is about the greenhouse effect on the Earth. Determine…
1. the irradiance of the Sun at the Earth
2. the effective solar irradiance absorbed by the Earth
3. the surface temperature of the Earth if there was no atmosphere
4. the effective emissivity of the atmosphere
Data for the Sun and Earth
Sun Earth
mean radius 6.957 × 108 m 6.378 × 106 m
mean surface temperature 5,772 K 288 K (15 °C)
luminosity 3.828 × 1026 W n/a
orbital radius n/a 1.496 × 1011 m
albedo n/a 0.297
surface emissivity 1 1
4. vostok.txt
Snow rarely gets a chance to melt in Antarctica, even in the summer when the sun never sets. In the interior of the continent, the temperature of the air hasn't been above the freezing point of water in any significant way for the last 900,000 years. The snow that falls there accumulates and accumulates and accumulates until it compresses into rock solid ice — up to 4.5 km thick in some regions. Since the snow that falls is originally fluffy with air, the ice that eventually forms still holds remnants of this air — very, very old air. By examining the isotopic composition of the gases in carefully extracted ice cores we can learn things about the climate of the past. By extension we might also be able to predict some things about the climate of the future.
Columns:
1. Age of air (years before present)
2. Temperature anomaly with respect to the mean recent time value (°C)
3. Carbon dioxide concentration (ppm)
4. Dust concentration (ppm)
Source: Adapted from Petit, et al. 1999.

Questions…

1. CO2
1. Construct a set of overlapping time series graphs for CO2concentration and temperature anomaly.
2. Construct a scatter plot of temperature anomaly vs. CO2concentration.
3. How are atmospheric carbon dioxide concentration and temperature anomaly related?
4. What temperature anomaly might one expect given current atmospheric CO2levels?
2. Dust
1. Construct a set of overlapping time series graphs for dust and temperature anomaly.
2. Construct a scatter plot of temperature anomaly vs. dust concentration.
3. How are atmospheric dust concentration and temperature anomaly related?
4. What global average temperature anomaly might one expect from exceptionally high levels of atmospheric dust?

### conceptual

1. These three conceptual questions are a part of a larger worksheet (heat-transfer.pdf).
1. Describe a food preparation activity that involves heat transfer by radiation and explain how the rate of this heat transfer is controlled by the behavior of or the decisions made by the cook.
2. Describe how a typical house in your neighborhood loses heat to or gains heat from the environment by radiation and explain how the rate of this heat transfer is controlled by the behavior of its occupants or by the way in which the building was constructed.
3. Describe how animals lose heat to or gain heat from their environment by radiation and explain how the rate of this heat transfer is controlled through physiological or behavioral adaptations.
2. Signs declaring "Bridge ices before road" are common on US highways. What factor affecting heat loss is most responsible for this phenomenon?
3. Two related food questions. For each question, state the reasoning behind your answer.
1. Which cooks faster when plunged into boiling water: a kilogram of spaghetti noodles or a kilogram of lasagna noodles? Assume both forms of pasta are cooked in the same amount of boiling water to the same degree of chewiness.
2. Which cools faster: a kilogram of french fries or a kilogram of baked potatoes. Assume both forms of potato are served at the same temperature to diners seated at the same table.
1. Is an orange in a fruit bowl a blackbody?
2. Is an orange-hot, glowing coal in a barbecue pit a blackbody?

### numerical

1. Determine the peak wavelength and frequency for the thermal radiation coming from the surface of the Sun (T = 5,772 K). Using your favorite reference source determine the type of radiation and its color if it is visible.

### investigative

1. Compute the rate at which your body radiates heat to a 20 °C room when unclothed. Assume a skin temperature of 34 °C. Use one of the following empirical formulas to compute your body surface area in square meters [m2]. Pay attention to the height and mass units used. They vary between equations. (A = surface area, h = height, m = mass.)
Empirical formulas for estimating body surface area * Use for children 3–30 kg.
source formula units
DuBois & DuBois (1916) A = 0.007184 h0.725m0.425 m, kg
Boyd (1935) A = 0.0003207 h0.3m(0.7285 - 0.0188 log(m)) cm, g
Gehan & George (1970) A = 0.0235 h0.42246m0.51456 cm, kg
Haycock, et al. (1978) A = 0.024265 h0.3964m0.5378 cm, kg
Mosteller (1987) A = √(hm/3600) cm, kg
Current (1997)* A = 0.1321 + 0.03433 m
A ≈ (m + 4)/30
kg
kg