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 20.77AP
Water in an electric teakettle is boiling. The power absorbed by the water is 1.00 kW. Assuming the pressure of vapor in the kettle equals atmospheric pressure, determine the speed of effusion of vapor from the kettle’s spout if the spout has a cross-sectional area of 2.00 cm2. Model the steam as an ideal gas.
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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)
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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
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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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