INTRO.TO PHYSICAL SCIENCE NSU PKG >IC<
14th Edition
ISBN: 9781305765443
Author: Shipman
Publisher: CENGAGE C
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Chapter 5, Problem WM
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Question 04
in 20
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 5 Solutions
INTRO.TO PHYSICAL SCIENCE NSU PKG >IC<
Ch. 5.1 - We talk about temperature, but what does it...Ch. 5.1 - Are there any limits on the lowest and highest...Ch. 5.1 - Show that a temperature of 40 is the same on both...Ch. 5.2 - Prob. 1PQCh. 5.2 - Most substances contract with decreasing...Ch. 5.3 - What is specific about specific heat?Ch. 5.3 - Prob. 2PQCh. 5.3 - Prob. 5.2CECh. 5.3 - How much heat must be removed from 0.20 kg of...Ch. 5.4 - What are the three methods of heat transfer?
Ch. 5.4 - Prob. 2PQCh. 5.5 - Prob. 1PQCh. 5.5 - Prob. 2PQCh. 5.6 - In the ideal gas law, pressure is directly...Ch. 5.6 - Prob. 2PQCh. 5.6 - Prob. 5.4CECh. 5.7 - Prob. 1PQCh. 5.7 - Prob. 2PQCh. 5 - Prob. AMCh. 5 - Prob. BMCh. 5 - Prob. CMCh. 5 - Prob. DMCh. 5 - Prob. EMCh. 5 - Prob. FMCh. 5 - Prob. GMCh. 5 - Prob. HMCh. 5 - Prob. IMCh. 5 - Prob. JMCh. 5 - Prob. KMCh. 5 - Prob. LMCh. 5 - Prob. MMCh. 5 - Prob. NMCh. 5 - Prob. OMCh. 5 - Prob. PMCh. 5 - Prob. QMCh. 5 - Prob. RMCh. 5 - Prob. SMCh. 5 - Prob. TMCh. 5 - Prob. UMCh. 5 - Prob. VMCh. 5 - Prob. WMCh. 5 - Prob. XMCh. 5 - Prob. YMCh. 5 - Prob. 1MCCh. 5 - Which unit of the following is smaller? (5.2) (a)...Ch. 5 - Prob. 3MCCh. 5 - Prob. 4MCCh. 5 - Prob. 5MCCh. 5 - Prob. 6MCCh. 5 - Prob. 7MCCh. 5 - Which of the following has a definite volume but...Ch. 5 - If the average kinetic energy of the molecules in...Ch. 5 - When we use the ideal gas law, the temperature...Ch. 5 - Prob. 11MCCh. 5 - Prob. 12MCCh. 5 - When a bimetallic strip is heated, it bends away...Ch. 5 - Prob. 2FIBCh. 5 - Prob. 3FIBCh. 5 - Prob. 4FIBCh. 5 - Prob. 5FIBCh. 5 - Prob. 6FIBCh. 5 - Prob. 7FIBCh. 5 - The ___ phase of matter has no definite shape, and...Ch. 5 - Prob. 9FIBCh. 5 - In the ideal gas law, pressure is ___ proportional...Ch. 5 - Prob. 11FIBCh. 5 - Prob. 12FIBCh. 5 - When the temperature changes during the day, which...Ch. 5 - Prob. 2SACh. 5 - The two common liquids used in liquid-in-glass...Ch. 5 - An older type of thermostat used in furnace and...Ch. 5 - Heat may be thought of as the middleman of energy....Ch. 5 - When one drinking glass is stuck inside another,...Ch. 5 - Prob. 7SACh. 5 - What does the specific heat of a substance tell...Ch. 5 - When eating a piece of hot apple pie, you may find...Ch. 5 - Prob. 10SACh. 5 - When you exhale outdoors on a cold day, you can...Ch. 5 - Compare the SI units of specific heat and latent...Ch. 5 - Give two examples each of good thermal conductors...Ch. 5 - Prob. 14SACh. 5 - Prob. 15SACh. 5 - Thermal underwear is made to fit loosely. ( Fig....Ch. 5 - What determines the phase of a substance?Ch. 5 - Give descriptions of a solid, a liquid, and a gas...Ch. 5 - Prob. 19SACh. 5 - How does the kinetic theory describe a gas?Ch. 5 - Prob. 21SACh. 5 - Prob. 22SACh. 5 - Prob. 23SACh. 5 - In terms of kinetic theory, explain why a...Ch. 5 - Prob. 25SACh. 5 - Prob. 26SACh. 5 - Prob. 27SACh. 5 - Prob. 28SACh. 5 - What can be said about the total entropy of the...Ch. 5 - Prob. 30SACh. 5 - Prob. 31SACh. 5 - Prob. 1VCCh. 5 - Prob. 1AYKCh. 5 - Prob. 2AYKCh. 5 - Prob. 3AYKCh. 5 - Prob. 4AYKCh. 5 - Prob. 5AYKCh. 5 - Prob. 6AYKCh. 5 - When you freeze ice cubes in a tray, there is a...Ch. 5 - Prob. 8AYKCh. 5 - Prob. 1ECh. 5 - Prob. 2ECh. 5 - Prob. 3ECh. 5 - Prob. 4ECh. 5 - Researchers in the Antarctic measure the...Ch. 5 - Prob. 6ECh. 5 - A college student produces about 100 kcal of heat...Ch. 5 - Prob. 8ECh. 5 - A pound of body fat stores an amount of chemical...Ch. 5 - Prob. 10ECh. 5 - On a brisk walk, a person burns about 325 Cal/h....Ch. 5 - Prob. 12ECh. 5 - How much heat in kcal must be added to 0.50 kg of...Ch. 5 - Prob. 14ECh. 5 - (a) How much energy is necessary to heat 1.0 kg of...Ch. 5 - Equal amounts of heat are added to equal masses of...Ch. 5 - How much heat is necessary to change 500 g of ice...Ch. 5 - A quantity of steam (300 g) at 110C is condensed,...Ch. 5 - Prob. 19ECh. 5 - A fire breaks out and increases the Kelvin...Ch. 5 - A cylinder of gas is at room temperature (20C)....Ch. 5 - A cylinder of gas at room temperature has a...Ch. 5 - A quantity of gas in a piston cylinder has a...Ch. 5 - If the gas in Exercise 23 is initially at room...
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