Physics for Scientists and Engineers, Technology Update (No access codes included)
9th Edition
ISBN: 9781305116399
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Textbook Question
Chapter 20, Problem 20.48P
At high noon, the Sun delivers 1 000 W to each square meter of a blacktop road. If the hot asphalt transfers energy only by
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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 20 Solutions
Physics for Scientists and Engineers, Technology Update (No access codes included)
Ch. 20 - Prob. 20.1QQCh. 20 - Suppose the same process of adding energy to the...Ch. 20 - Prob. 20.3QQCh. 20 - Characterize the paths in Figure 19.12 as...Ch. 20 - Prob. 20.5QQCh. 20 - An ideal gas is compressed to half its initial...Ch. 20 - A poker is a stiff, nonflammable rod used to push...Ch. 20 - Assume you are measuring the specific heat of a...Ch. 20 - Prob. 20.4OQCh. 20 - Prob. 20.5OQ
Ch. 20 - Ethyl alcohol has about one-half the specific heat...Ch. 20 - The specific heat of substance A is greater than...Ch. 20 - Beryllium has roughly one-half the specific heat...Ch. 20 - Prob. 20.9OQCh. 20 - A 100-g piece of copper, initially at 95.0C, is...Ch. 20 - Prob. 20.11OQCh. 20 - If a gas is compressed isothermally, which of the...Ch. 20 - Prob. 20.13OQCh. 20 - If a gas undergoes an isobaric process, which of...Ch. 20 - Prob. 20.15OQCh. 20 - Prob. 20.1CQCh. 20 - You need to pick up a very hot cooking pot in your...Ch. 20 - Prob. 20.3CQCh. 20 - Prob. 20.4CQCh. 20 - Prob. 20.5CQCh. 20 - In 1801, Humphry Davy rubbed together pieces of...Ch. 20 - Prob. 20.7CQCh. 20 - Prob. 20.8CQCh. 20 - Prob. 20.9CQCh. 20 - When camping in a canyon on a still night, a...Ch. 20 - Pioneers stored fruits and vegetables in...Ch. 20 - Prob. 20.12CQCh. 20 - Prob. 20.1PCh. 20 - Consider Joules apparatus described in Figure...Ch. 20 - Prob. 20.3PCh. 20 - The highest waterfall in the world is the Salto...Ch. 20 - What mass of water at 25.0C must be allowed to...Ch. 20 - The temperature of a silver bar rises by 10.0C...Ch. 20 - In cold climates, including the northern United...Ch. 20 - A 50.0-g sample of copper is at 25.0C. If 1 200 J...Ch. 20 - An aluminum cup of mass 200 g contains 800 g of...Ch. 20 - If water with a mass mk at temperature Tk is...Ch. 20 - A 1.50-kg iron horseshoe initially at 600C is...Ch. 20 - An electric drill with a steel drill bit of mass m...Ch. 20 - An aluminum calorimeter with a mass of 100 g...Ch. 20 - A 3.00-g copper coin at 25.0C drops 50.0 m to the...Ch. 20 - Two thermally insulated vessels are connected by a...Ch. 20 - A 50.0-g copper calorimeter contains 250 g of...Ch. 20 - Prob. 20.17PCh. 20 - How much energy is required to change a 40.0-g ice...Ch. 20 - A 75.0-g ice cube at 0C is placed in 825 g of...Ch. 20 - A 3.00-g lead bullet at 30.0C is fired at a speed...Ch. 20 - Steam at 100C is added to ice at 0C. (a) Find the...Ch. 20 - A 1.00-kg Mock of copper at 20.0C is dropped into...Ch. 20 - In an insulated vessel, 250 g of ice at 0C is...Ch. 20 - Prob. 20.24PCh. 20 - An ideal gas is enclosed in a cylinder with a...Ch. 20 - Prob. 20.26PCh. 20 - One mole of an ideal gas is warmed slowly so that...Ch. 20 - (a) Determine the work done on a gas that expands...Ch. 20 - An ideal gas is taken through a quasi-static...Ch. 20 - A gas is taken through the cyclic process...Ch. 20 - Consider the cyclic process depicted in Figure...Ch. 20 - Why is the following situation impossible? An...Ch. 20 - A thermodynamic system undergoes a process in...Ch. 20 - A sample of an ideal gas goes through the process...Ch. 20 - A 2.00-mol sample of helium gas initially at 300...Ch. 20 - (a) How much work is done on the steam when 1.00...Ch. 20 - Prob. 20.37PCh. 20 - One mole of an ideal gas does 3 000 J of work on...Ch. 20 - A 1.00-kg block of aluminum is warmed at...Ch. 20 - In Figure P19.22, the change in internal energy of...Ch. 20 - An ideal gas initially at Pi, Vi, and Ti is taken...Ch. 20 - An ideal gas initially at Pi, Vi, and Ti is taken...Ch. 20 - A glass windowpane in a home is 0.620 cm thick and...Ch. 20 - A concrete slab is 12.0 cm thick and has an area...Ch. 20 - A student is trying to decide what to wear. His...Ch. 20 - The surface of the Sun has a temperature of about...Ch. 20 - The tungsten filament of a certain 100-W lightbulb...Ch. 20 - At high noon, the Sun delivers 1 000 W to each...Ch. 20 - Two lightbulbs have cylindrical filaments much...Ch. 20 - Prob. 20.50PCh. 20 - A copper rod and an aluminum rod of equal diameter...Ch. 20 - A box with a total surface area of 1.20 m2 and a...Ch. 20 - (a) Calculate the R-value of a thermal window made...Ch. 20 - At our distance from the Sun, the intensity of...Ch. 20 - A bar of gold (Au) is in thermal contact with a...Ch. 20 - Prob. 20.56PCh. 20 - Prob. 20.57PCh. 20 - A gas expands from I to Fin Figure P20.58 (page...Ch. 20 - Gas in a container is at a pressure of 1.50 atm...Ch. 20 - Liquid nitrogen has a boiling point of 77.3 K and...Ch. 20 - An aluminum rod 0.500 m in length and with a cross...Ch. 20 - Prob. 20.62APCh. 20 - Prob. 20.63APCh. 20 - Prob. 20.64APCh. 20 - Prob. 20.65APCh. 20 - An ice-cube tray is filled with 75.0 g of water....Ch. 20 - On a cold winter day. you buy roasted chestnuts...Ch. 20 - Prob. 20.68APCh. 20 - An iron plate is held against an iron wheel so...Ch. 20 - Prob. 20.70APCh. 20 - A 40.0-g ice cube floats in 200 g of water in a...Ch. 20 - One mole of an ideal gas is contained in a...Ch. 20 - Review. A 670-kg meteoroid happens to be composed...Ch. 20 - Prob. 20.74APCh. 20 - Prob. 20.75APCh. 20 - Prob. 20.76APCh. 20 - Water in an electric teakettle is boiling. The...Ch. 20 - Prob. 20.78APCh. 20 - Prob. 20.79APCh. 20 - A student measures the following data in a...Ch. 20 - Consider the piston cylinder apparatus shown in...Ch. 20 - A spherical shell has inner radius 3.00 cm and...Ch. 20 - Prob. 20.83CPCh. 20 - (a) The inside of a hollow cylinder is maintained...
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