Chapter 34: Q23CQ (page 1237)
State a necessary condition for a system to be chaotic.
It is considered to be chaotic if states that differ by a little amount in the starting circumstances diverge as the system evolves.
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Not only is liquid nitrogen a cheaper coolant than liquid helium, its boiling point is higher (\({\rm{77 K}}\)vs\({\rm{4}}{\rm{.2 K}}\)). How does higher temperature help lower the cost of cooling a material? Explain in terms of the rate of heat transfer being related to the temperature difference between the sample and its surroundings.
Using data from the previous problem, find the increase in rotational kinetic energy, given the core’s mass is\({\rm{1}}{\rm{.3}}\)times that of our Sun. Where does this increase in kinetic energy come from?
(a) Calculate the approximate age of the universe from the average value of the Hubble constant,\({{\rm{H}}_{\rm{0}}}{\rm{ = 20km/s}} \cdot {\rm{Mly}}\). To do this, calculate the time it would take to travel\({\rm{1 Mly}}\)at a constant expansion rate of\({\rm{20 km/s}}\). (b) If deceleration is taken into account, would the actual age of the universe be greater or less than that found here? Explain.
Distances to the nearest stars (up to\({\rm{500 ly}}\)away) can be measured by a technique called parallax, as shown in Figure\({\rm{34}}{\rm{.26}}\). What are the angles\({{\rm{\theta }}_{\rm{1}}}\)and\({{\rm{\theta }}_{\rm{2}}}\)relative to the plane of the Earth’s orbit for a star\({\rm{4}}{\rm{.0 ly}}\)directly above the Sun?
(a) What is the approximate force of gravity on a\({\rm{70 - kg}}\)person due to the Andromeda galaxy, assuming its total mass is\({\rm{1}}{{\rm{0}}^{{\rm{13}}}}\)that of our Sun and acts like a single mass\({\rm{2 Mly}}\)away? (b) What is the ratio of this force to the person’s weight? Note that Andromeda is the closest large galaxy.
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