Webassign Printed Access Card For Serway/jewett's Physics For Scientists And Engineers, 10th, Single-term
10th Edition
ISBN: 9781337699266
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 19, Problem 31AP
You have a particular interest in automobile engines, so you have secured a co-op position at an automobile company while you attend school. Your supervisor is helping you to learn about the operation of an internal combustion engine. She gives you the following assignment, related to a simulation of a new engine she is designing. A gas, beginning at PA = 1.00 atm, VA = 0.500 L, and TA = 27.0°C, is compressed from point A on the PV diagram in Figure P19.31 (page 530) to point B. This represents the compression stroke in a fourcycle gasoline engine. At that point, 132 J of energy is delivered to the gas at constant volume, taking the gas to point C. This represents the transformation of potential energy in the gasoline to internal energy when the spark plug fires. Your supervisor tells you that the internal energy of a gas is proportional to temperature (as we shall find in Chapter 20), the internal energy of the gas at point A is 200 J, and she wants to know what the temperature of the gas is at point C.
Figure P19.31
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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
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[5 marks]
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Chapter 19 Solutions
Webassign Printed Access Card For Serway/jewett's Physics For Scientists And Engineers, 10th, Single-term
Ch. 19.2 - Prob. 19.1QQCh. 19.3 - Suppose the same process of adding energy to the...Ch. 19.5 - Prob. 19.3QQCh. 19.5 - Characterize the paths in Figure 19.12 as...Ch. 19.6 - Prob. 19.5QQCh. 19 - Prob. 1PCh. 19 - The highest waterfall in the world is the Salto...Ch. 19 - Prob. 3PCh. 19 - The temperature of a silver bar rises by 10.0C...Ch. 19 - You are working in your kitchen preparing lunch...
Ch. 19 - If water with a mass mk at temperature Tk is...Ch. 19 - An aluminum calorimeter with a mass of 100 g...Ch. 19 - An electric drill with a steel drill bit of mass m...Ch. 19 - A 3.00-g copper coin at 25.0C drops 50.0 m to the...Ch. 19 - How much energy is required to change a 40.0-g ice...Ch. 19 - Prob. 11PCh. 19 - A 3.00-g lead bullet at 30.0C is fired at a speed...Ch. 19 - In an insulated vessel, 250 g of ice at 0C is...Ch. 19 - Prob. 14PCh. 19 - One mole of an ideal gas is warmed slowly so that...Ch. 19 - (a) Determine the work done on a gas that expands...Ch. 19 - A thermodynamic system undergoes a process in...Ch. 19 - Why is the following situation impossible? An...Ch. 19 - A 2.00-mol sample of helium gas initially at 300...Ch. 19 - (a) How much work is done on the steam when 1.00...Ch. 19 - A 1.00-kg block of aluminum is warmed at...Ch. 19 - In Figure P19.22, the change in internal energy of...Ch. 19 - A student is trying to decide what to wear. His...Ch. 19 - A concrete slab is 12.0 cm thick and has an area...Ch. 19 - Two lightbulbs have cylindrical filaments much...Ch. 19 - Prob. 26PCh. 19 - (a) Calculate the R-value of a thermal window made...Ch. 19 - Prob. 28PCh. 19 - Gas in a container is at a pressure of 1.50 atm...Ch. 19 - Prob. 30APCh. 19 - You have a particular interest in automobile...Ch. 19 - You are working in a condensed-matter laboratory...Ch. 19 - Prob. 33APCh. 19 - Prob. 34APCh. 19 - Prob. 35APCh. 19 - Prob. 36APCh. 19 - An ice-cube tray is filled with 75.0 g of water....Ch. 19 - Prob. 38APCh. 19 - An iron plate is held against an iron wheel so...Ch. 19 - One mole of an ideal gas is contained in a...Ch. 19 - Prob. 41APCh. 19 - Prob. 42APCh. 19 - Prob. 43APCh. 19 - A student measures the following data in a...Ch. 19 - (a) The inside of a hollow cylinder is maintained...Ch. 19 - A spherical shell has inner radius 3.00 cm and...Ch. 19 - Prob. 47CP
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