College Physics For Ap® Courses
16th Edition
ISBN: 9781938168932
Author: Gregg Wolfe, Irina Lyublinskaya, Douglas Ingram
Publisher: OpenStax
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Textbook Question
Chapter 15, Problem 7PE
(a) What is the average
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Question B3
Consider the following FLRW spacetime:
t2
ds² = -dt² +
(dx²
+ dy²+ dz²),
t2
where t is a constant.
a)
State whether this universe is spatially open, closed or flat.
[2 marks]
b) Determine the Hubble factor H(t), and represent it in a (roughly drawn) plot as a function
of time t, starting at t = 0.
[3 marks]
c) Taking galaxy A to be located at (x, y, z) = (0,0,0), determine the proper distance to galaxy
B located at (x, y, z) = (L, 0, 0). Determine the recessional velocity of galaxy B with respect
to galaxy A.
d) The Friedmann equations are
2
k
8πG
а
4πG
+
a²
(p+3p).
3
a
3
[5 marks]
Use these equations to determine the energy density p(t) and the pressure p(t) for the
FLRW spacetime specified at the top of the page.
[5 marks]
e) Given the result of question B3.d, state whether the FLRW universe in question is (i)
radiation-dominated, (ii) matter-dominated, (iii) cosmological-constant-dominated, or (iv)
none of the previous. Justify your answer.
f)
[5 marks]
A conformally…
SECTION B
Answer ONLY TWO questions in Section B
[Expect to use one single-sided A4 page for each Section-B sub question.]
Question B1
Consider the line element
where w is a constant.
ds²=-dt²+e2wt dx²,
a) Determine the components of the metric and of the inverse metric.
[2 marks]
b) Determine the Christoffel symbols. [See the Appendix of this document.]
[10 marks]
c)
Write down the geodesic equations.
[5 marks]
d) Show that e2wt it is a constant of geodesic motion.
[4 marks]
e)
Solve the geodesic equations for null geodesics.
[4 marks]
Page 2
SECTION A
Answer ALL questions in Section A
[Expect to use one single-sided A4 page for each Section-A sub question.]
Question A1
SPA6308 (2024)
Consider Minkowski spacetime in Cartesian coordinates th
=
(t, x, y, z), such that
ds² = dt² + dx² + dy² + dz².
(a) Consider the vector with components V" = (1,-1,0,0). Determine V and V. V.
(b) Consider now the coordinate system x' (u, v, y, z) such that
u =t-x,
v=t+x.
[2 marks]
Write down the line element, the metric, the Christoffel symbols and the Riemann curvature
tensor in the new coordinates. [See the Appendix of this document.]
[5 marks]
(c) Determine V", that is, write the object in question A1.a in the coordinate system x'. Verify
explicitly that V. V is invariant under the coordinate transformation.
Question A2
[5 marks]
Suppose that A, is a covector field, and consider the object
Fv=AAμ.
(a) Show explicitly that F is a tensor, that is, show that it transforms appropriately under a
coordinate transformation.
[5 marks]
(b)…
Chapter 15 Solutions
College Physics For Ap® Courses
Ch. 15 - Describe the photo of the tea kettle at the...Ch. 15 - The first law of thermodynamics and the...Ch. 15 - Heat transfer Q and work done W are always energy...Ch. 15 - How do heat transfer and internal energy differ?...Ch. 15 - If you run down some stairs and stop, what happens...Ch. 15 - Give an explanation of how food energy (calories)...Ch. 15 - Identify the type of energy transferred to your...Ch. 15 - A great deal of effort time, and money has been...Ch. 15 - One method of converting heat transfer to doing...Ch. 15 - Would the previous question make any sense for an...
Ch. 15 - We ordinarily say that U=0 for an isothermal...Ch. 15 - The temperature of a rapidly expanding gas...Ch. 15 - Which cyclical process represented by the two...Ch. 15 - A real process may be nearly adiabatic if it...Ch. 15 - It is unlikely that a process can be isothermal...Ch. 15 - Imagine you are driving a car up Pike’s Peak in...Ch. 15 - Is a temperature difference necessary to operate a...Ch. 15 - Definitions of efficiency vary depending on how...Ch. 15 - Whyother than the fact that the second law of...Ch. 15 - Think about the drinking bird at the beginning of...Ch. 15 - Can improved engineering and materials be employed...Ch. 15 - Does the second law of thermodynamics alter the...Ch. 15 - Explain why heat pumps do not work as well in very...Ch. 15 - In some Northern European nations, homes are being...Ch. 15 - Why do refrigerators, air conditioners, and heat...Ch. 15 - Grocery store managers contend that there is less...Ch. 15 - Can you cool a kitchen by leaving the refrigerator...Ch. 15 - A woman shuts her summer cottage up in September...Ch. 15 - Consider a system with a certain energy content,...Ch. 15 - Does a gas become more orderly when it liquefies?...Ch. 15 - Explain how water’s entropy can decrease when it...Ch. 15 - Is a uniform-temperature gas more or less orderly...Ch. 15 - Give an example of a spontaneous process in which...Ch. 15 - What is the change in entropy in an adiabatic...Ch. 15 - Does the entropy at a star increase or decrease as...Ch. 15 - Explain why a building made of bricks has smaller...Ch. 15 - Explain why a building made of bricks has smaller...Ch. 15 - What is the change in internal energy of a car if...Ch. 15 - How much heat transfer occurs from a system, if...Ch. 15 - A system does 1.80108J of work while 7.50108J of...Ch. 15 - What is the change in internal energy of a system...Ch. 15 - Suppose a woman does 500 J of work and 9500 J of...Ch. 15 - (a) How much food energy will a man metabolize in...Ch. 15 - (a) What is the average metabolic rate in watts of...Ch. 15 - (a) How long will the energy in a 1470kJ (350kcal)...Ch. 15 - (a) A woman climbing the Washington Monument...Ch. 15 - A car tire contains 0.0380m3 S of air at a...Ch. 15 - A heliumfilled toy balloon has a gauge pressure of...Ch. 15 - Steam to drive an old—fashioned steam locomotive...Ch. 15 - A hand—driven tire pump has a piston with a 2.50cm...Ch. 15 - Calculate the net work output of a heat engine...Ch. 15 - What is the net work output of a heat engine that...Ch. 15 - Unreasonable Results What is wrong with the claim...Ch. 15 - (a) A cyclical heat engine, operating between...Ch. 15 - Construct Your Own Problem Consider a car's...Ch. 15 - Construct Your Own Problem Consider a car trip...Ch. 15 - A certain heat engine does 10.0 kJ of work and...Ch. 15 - With 2.56106J of heat transfer into this engine, a...Ch. 15 - (a) What is the work output of a cyclical heat...Ch. 15 - (a) What is the eficiency of a cyclical heat...Ch. 15 - The engine of a large Ship does 2.00108J of work...Ch. 15 - (a) How much heat transfer occurs to the...Ch. 15 - Assume that the turbines at a coal—powered power...Ch. 15 - This problem compares the energy output and heat...Ch. 15 - A certain gasoline engine has an efficiency of...Ch. 15 - A gascooled nuclear reactor operates between hot...Ch. 15 - (a) What is the hot reservoir temperature of a...Ch. 15 - Steam locomotives have an efficiency of 17.0% and...Ch. 15 - Practical steam engines utilize 450C steam, which...Ch. 15 - A coalfired electrical power station has an...Ch. 15 - Would you be willing to financially back an...Ch. 15 - Unreasonable Results (a) Suppose you want to...Ch. 15 - Unreasonable Results Calculate the cold reservoir...Ch. 15 - What is the coefficient of performance of an ideal...Ch. 15 - Suppose you have an ideal refrigerator that cools...Ch. 15 - What is the best coefficient of performance...Ch. 15 - In a very mild winter climate, a heat pump has...Ch. 15 - (a) What is the best coefficient of performance...Ch. 15 - (a) What is the best coefficient of performance...Ch. 15 - Suppose you want to operate an ideal refrigerator...Ch. 15 - An ideal heat pump is being considered for use in...Ch. 15 - A 4ton air conditioner removes 5.60107J (48,000...Ch. 15 - Show that the coefficients of performance of...Ch. 15 - (a) On a winter day, a certain house loses...Ch. 15 - On a hot summer day, 4.00106J of heat transfer...Ch. 15 - A hot rock ejected from a volcano's lava fountain...Ch. 15 - When 1.60105J of heat transfer occurs into a meat...Ch. 15 - The Sun radiates energy at the rate of 3.801026W...Ch. 15 - (a) In reaching equilibrium, how much heat...Ch. 15 - What is the decrease in entropy of 25.0 g of water...Ch. 15 - Find the increase in entropy of 1.00 kg of liquid...Ch. 15 - A large electrical power station generates 1000 MW...Ch. 15 - (a) How much heat transfer occurs from 20.0 kg of...Ch. 15 - Using Table 15.4, verify the contention that if...Ch. 15 - What percent of the time will you get something in...Ch. 15 - (a) If tossing 100 coins, how many ways...Ch. 15 - (a) What is the change in entropy if you start...Ch. 15 - (a) What is the change in entropy if you start...Ch. 15 - (a) If you toss 10 coins, what percent of the time...Ch. 15 - (a) Construct a table showing the macro states and...Ch. 15 - In an air conditioner, 12.65 MJ of heat transfer...
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