Principles of Physics: A Calculus-Based Text
5th Edition
ISBN: 9781133104261
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Textbook Question
Chapter 17.6, Problem 17.5QQ
Characterize the paths in Figure 17.10 as isobaric, isovolumetric, isothermal, or adiabatic. For path B, Q = 0. The blue curves are isotherms.
Figure 17.10 (Quick Quiz 17.5)
Identify the nature of paths A, B, C, and D.
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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.
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Chapter 17 Solutions
Principles of Physics: A Calculus-Based Text
Ch. 17.2 - Prob. 17.1QQCh. 17.3 - Prob. 17.2QQCh. 17.3 - Prob. 17.3QQCh. 17.5 - Prob. 17.4QQCh. 17.6 - Characterize the paths in Figure 17.10 as...Ch. 17.7 - (i) How does the internal energy of an ideal gas...Ch. 17.10 - Prob. 17.7QQCh. 17 - Prob. 1OQCh. 17 - A 100-g piece of copper, initially at 95.0C, is...Ch. 17 - Prob. 3OQ
Ch. 17 - Prob. 4OQCh. 17 - Prob. 5OQCh. 17 - Prob. 6OQCh. 17 - Prob. 7OQCh. 17 - Prob. 8OQCh. 17 - Prob. 9OQCh. 17 - Prob. 10OQCh. 17 - Star A has twice the radius and twice the absolute...Ch. 17 - If a gas is compressed isothermally, which of the...Ch. 17 - When a gas undergoes an adiabatic expansion, which...Ch. 17 - Ethyl alcohol has about one-half the specific heat...Ch. 17 - Prob. 15OQCh. 17 - Prob. 1CQCh. 17 - Prob. 2CQCh. 17 - Pioneers stored fruits and vegetables in...Ch. 17 - Why is a person able to remove a piece of dry...Ch. 17 - Prob. 5CQCh. 17 - Prob. 6CQCh. 17 - It is the morning of a day that will become hot....Ch. 17 - You need to pick up a very hot cooking pot in your...Ch. 17 - Rub the palm of your hand on a metal surface for...Ch. 17 - Prob. 10CQCh. 17 - Prob. 11CQCh. 17 - Prob. 12CQCh. 17 - On his honeymoon, James Joule traveled from...Ch. 17 - Consider Joules apparatus described in Figure...Ch. 17 - Prob. 3PCh. 17 - Prob. 4PCh. 17 - Prob. 5PCh. 17 - Prob. 6PCh. 17 - Prob. 7PCh. 17 - Prob. 8PCh. 17 - Prob. 9PCh. 17 - Prob. 10PCh. 17 - Prob. 11PCh. 17 - Prob. 12PCh. 17 - Prob. 13PCh. 17 - Prob. 14PCh. 17 - In an insulated vessel, 250 g of ice at 0C is...Ch. 17 - Prob. 16PCh. 17 - Prob. 17PCh. 17 - Prob. 18PCh. 17 - A 1.00-kg block of copper at 20.0C is dropped into...Ch. 17 - A resting adult of average size converts chemical...Ch. 17 - Prob. 21PCh. 17 - Prob. 22PCh. 17 - An ideal gas is enclosed in a cylinder with a...Ch. 17 - Prob. 24PCh. 17 - Prob. 25PCh. 17 - A sample of an ideal gas goes through the process...Ch. 17 - A thermodynamic system undergoes a process in...Ch. 17 - A gas is taken through the cyclic process...Ch. 17 - Consider the cyclic process depicted in Figure...Ch. 17 - Why is the following situation impossible? An...Ch. 17 - An ideal gas initially at 300 K undergoes an...Ch. 17 - In Figure P17.32, the change in internal energy of...Ch. 17 - Prob. 33PCh. 17 - Prob. 34PCh. 17 - Prob. 35PCh. 17 - Prob. 36PCh. 17 - Prob. 37PCh. 17 - One mole of an ideal gas does 3 000 J of work on...Ch. 17 - A 1.00-mol sample of hydrogen gas is heated at...Ch. 17 - A sample of a diatomic ideal gas has pressure P...Ch. 17 - Prob. 41PCh. 17 - Prob. 42PCh. 17 - Prob. 43PCh. 17 - Review. This problem is a continuation of Problem...Ch. 17 - Prob. 45PCh. 17 - A 2.00-mol sample of a diatomic ideal gas expands...Ch. 17 - Prob. 47PCh. 17 - An ideal gas with specific heat ratio confined to...Ch. 17 - Prob. 49PCh. 17 - Prob. 50PCh. 17 - Prob. 51PCh. 17 - Prob. 52PCh. 17 - Air (a diatomic ideal gas) at 27.0C and...Ch. 17 - Prob. 54PCh. 17 - Prob. 55PCh. 17 - Prob. 56PCh. 17 - Prob. 57PCh. 17 - Prob. 58PCh. 17 - Prob. 59PCh. 17 - Prob. 60PCh. 17 - Prob. 61PCh. 17 - Prob. 62PCh. 17 - The surface of the Sun has a temperature of about...Ch. 17 - Prob. 64PCh. 17 - At high noon, the Sun delivers 1 000 W to each...Ch. 17 - A theoretical atmospheric lapse rate. Section 16.7...Ch. 17 - Prob. 67PCh. 17 - A sample of a monatomic ideal gas occupies 5.00 L...Ch. 17 - An aluminum rod 0.500 m in length and with a...Ch. 17 - Prob. 70PCh. 17 - Prob. 71PCh. 17 - Prob. 72PCh. 17 - Prob. 73PCh. 17 - Prob. 74PCh. 17 - Prob. 75PCh. 17 - Prob. 76PCh. 17 - Prob. 77PCh. 17 - Prob. 78PCh. 17 - Prob. 79PCh. 17 - Prob. 81PCh. 17 - Prob. 82PCh. 17 - Prob. 84PCh. 17 - Prob. 85PCh. 17 - Prob. 86PCh. 17 - Prob. 87PCh. 17 - Prob. 88PCh. 17 - Water in an electric teakettle is boiling. The...
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