Question
(a) Determine the power associated with the Io-to-Jupiter current described in Example Variation Problem 41 . (b) Compare your answer in (a) with humankind's electrical energy consumption rate, approximately $22,000 \mathrm{TWh}$ per year.
Step 1
In Example Variation Problem 41, we found that the current between Io and Jupiter is approximately 5 million amperes (5 x 10^6 A). The electric potential difference between Io and Jupiter is about 400,000 volts (4 x 10^5 V). Show more…
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(a) Estimate the amount of energy radiated by Jupiter over the last 4.55 billion years (see the equation below. $$E \sim-\frac{3}{10} \frac{G M^{2}}{R}$$ (b) Estimate the rate of energy output from Jupiter due to gravitational collapse alone, assuming that the rate has been constant over its lifetime. (c) Compare your answer for part (b) with the value for the flux that was given in the text. What does this say about the rate of energy output in the past? Discuss the implications for the evolution of the Galilean moons.
The total power consumption by all humans on earth is approximately $10^{13}$ W. Let's compare this to the power of incoming solar radiation. The intensity of radiation from the sun at the top of the atmosphere is $1380 \mathrm{W} / \mathrm{m}^{2} .$ The earth's radius is $6.37 \times 10^{6} \mathrm{m} .$ a. What is the total solar power received by the earth? b. By what factor does this exceed the total human power consumption?
The total power consumption by all humans on earth is approximately 1013 W. Let’s compare this to the power of incoming solar radiation. The intensity of radiation from the sun at the top of the atmosphere is 1380 W/m2. The earth’s radius is 6.37 * 106 m. a. What is the total solar power received by the earth? b. By what factor does this exceed the total human power consumption?
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