PHYSICS FOR SCI. & ENGR(LL W/WEBASSIGN)
10th Edition
ISBN: 9781337888721
Author: SERWAY
Publisher: CENGAGE L
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Textbook Question
Chapter 21, Problem 20P
(a) Prepare a table like Table 21.1 for the following occurrence. You toss four coins into the air simultaneously and then record the results of your tosses in terms of the numbers of heads (H) and tails (T) that result. For example, HHTH and HTHH are two possible ways in which three heads and one tail can be achieved. (b) On the basis of your table, what is the most probable result recorded for a toss?
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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]
Chapter 21 Solutions
PHYSICS FOR SCI. & ENGR(LL W/WEBASSIGN)
Ch. 21.1 - The energy input to an engine is 4.00 times...Ch. 21.2 - The energy entering an electric heater by...Ch. 21.4 - Three engines operate between reservoirs separated...Ch. 21.6 - (a) Suppose you select four cards at random from a...Ch. 21.7 - An ideal gas is taken from an initial temperature...Ch. 21.7 - True or False: The entropy change in an adiabatic...Ch. 21 - A particular heat engine has a mechanical power...Ch. 21 - The work done by an engine equals one-fourth the...Ch. 21 - Suppose a heat engine is connected to two energy...Ch. 21 - During each cycle, a refrigerator ejects 625 kJ of...
Ch. 21 - A freezer has a coefficient of performance of...Ch. 21 - A heat pump has a coefficient of performance equal...Ch. 21 - One of the most efficient heat engines ever built...Ch. 21 - Why is the following situation impossible? An...Ch. 21 - If a 35.0% -efficient Carnot heat engine (Fig....Ch. 21 - An ideal refrigerator or ideal heat pump is...Ch. 21 - A heat engine is being designed to have a Carnot...Ch. 21 - A power plant operates at a 32.0% efficiency...Ch. 21 - You are working on a summer job at a company that...Ch. 21 - A Carnot heat engine operates between temperatures...Ch. 21 - An electric generating station is designed to have...Ch. 21 - Suppose you build a two-engine device with the...Ch. 21 - A heat pump used for heating shown in Figure...Ch. 21 - A gasoline engine has a compression ratio of 6.00....Ch. 21 - An idealized diesel engine operates in a cycle...Ch. 21 - (a) Prepare a table like Table 21.1 for the...Ch. 21 - Prob. 21PCh. 21 - A Styrofoam cup holding 125 g of hot water at 100C...Ch. 21 - A 1 500-kg car is moving at 20.0 m/s. The driver...Ch. 21 - A 2.00-L container has a center partition that...Ch. 21 - Calculate the change in entropy of 250 g of water...Ch. 21 - What change in entropy occurs when a 27.9-g ice...Ch. 21 - When an aluminum bar is connected between a hot...Ch. 21 - When a metal bar is connected between a hot...Ch. 21 - How fast are you personally making the entropy of...Ch. 21 - Prob. 30APCh. 21 - The energy absorbed by an engine is three times...Ch. 21 - In 1993, the U.S. government instituted a...Ch. 21 - In 1816, Robert Stirling, a Scottish clergyman,...Ch. 21 - Suppose an ideal (Carnot) heat pump could be...Ch. 21 - Review. This problem complements Problem 44 in...Ch. 21 - A firebox is at 750 K, and the ambient temperature...Ch. 21 - A 1.00-mol sample of an ideal monatomic gas is...Ch. 21 - A system consisting of n moles of an ideal gas...Ch. 21 - A heat engine operates between two reservoirs at...Ch. 21 - You are working as an assistant to a physics...Ch. 21 - Prob. 41APCh. 21 - You are working as an expert witness for an...Ch. 21 - An athlete whose mass is 70.0 kg drinks 16.0...Ch. 21 - Prob. 44APCh. 21 - Prob. 45APCh. 21 - A sample consisting of n moles of an ideal gas...Ch. 21 - The compression ratio of an Otto cycle as shown in...
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