College Physics
1st Edition
ISBN: 9781938168000
Author: Paul Peter Urone, Roger Hinrichs
Publisher: OpenStax College
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Textbook Question
Chapter 14, Problem 11PE
How much 
if their heat of fusion is the same as that of water?
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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 14 Solutions
College Physics
Ch. 14 - How is heat transfer related to temperature?Ch. 14 - Describe a situation in which heat transfer...Ch. 14 - When heal transfers into a system, is the energy...Ch. 14 - What three factors affect the heat transfer that...Ch. 14 - The brakes in a car increase in temperature by T...Ch. 14 - Heat transfer can cause temperature and phase...Ch. 14 - How does the latent heat of fusion of water help...Ch. 14 - What is me temperature of ice right after it is...Ch. 14 - If you place 0C ice into 0C water in an insulated...Ch. 14 - What effect does condensation on a glass of ice...
Ch. 14 - In my humid climates where there are numerous...Ch. 14 - In winters, if is often warmer in San Francisco...Ch. 14 - Putting a lid on a boiling pot greatly reduces the...Ch. 14 - Freeze-dried toads have been dehydrated in a...Ch. 14 - When still air cools by radiating at night, it is...Ch. 14 - In a physics classroom demonstration, an...Ch. 14 - What are the main methods of heat transfer front...Ch. 14 - Some electric sieves have a flat ceramic surface...Ch. 14 - Loosefitting white clothing covering most at the...Ch. 14 - One way to make a fireplace more energy efficient...Ch. 14 - On cold, clear nights horses will sleep under the...Ch. 14 - When watching a daytime circus in a large,...Ch. 14 - Satellites designed to observe me radiation from...Ch. 14 - Why are cloudy nights generally warmer than clear...Ch. 14 - Why are thermometers that are used in weather...Ch. 14 - On average, would Earth be warmer or cooler...Ch. 14 - On a hot day, the temperature of an 80,000L...Ch. 14 - Show that 1cal/gC=1kcal/kgC.Ch. 14 - To sterilize a 50.0g glass baby bottle, we must...Ch. 14 - The same heat transfer into identical masses of...Ch. 14 - Rubbing your hands together warms them by...Ch. 14 - A 0.250kg block at a pure material is heated from...Ch. 14 - Suppose identical amounts of heat transfer into...Ch. 14 - (a) The number of kilocalories in food is...Ch. 14 - Following Vigorous exercise, the body temperature...Ch. 14 - Even when shut down after a period of normal use,...Ch. 14 - How much heat transfer (in kilocalories) is...Ch. 14 - A bag containing 0C ice is much more effective in...Ch. 14 - (a) How much heat transfer is required to raise...Ch. 14 - The formation of condensation on a glass of ice...Ch. 14 - On a trip, you notice that a 3.50kg bag of ice...Ch. 14 - On a certain dry sunny day, a swimming pool’s...Ch. 14 - (a) How much heat transfer is necessary to raise...Ch. 14 - In 1986, a gargantuan iceberg broke away from the...Ch. 14 - How many grams of coffee must evaporate from 350 g...Ch. 14 - (a) It is difficult to extinguish a fire on a...Ch. 14 - The energy released from condensation in...Ch. 14 - To help prevent from damage, 4.00 kg at 0C water...Ch. 14 - A 0.250kg aluminum bowl holding 0.800 kg of soup...Ch. 14 - A 0.0500kg ice cube at 30.0C is placed in 0.400 kg...Ch. 14 - If you pour 0.0100 kg of 20.0C water onto a 1.20kg...Ch. 14 - Indigenous people sometimes cook in watertight...Ch. 14 - What would be the final temperature of the pan and...Ch. 14 - In some countries, liquid nitrogen is used on...Ch. 14 - Some gun fanciers make their own bullets, which...Ch. 14 - (a) Calculate the rate of heat conduction through...Ch. 14 - The rate of heat conduction out of a window on a...Ch. 14 - Calculate the rate of heat conduction out of the...Ch. 14 - Suppose you stand with one foot on ceramic...Ch. 14 - A man consumes 3000 kcal of food in one day....Ch. 14 - (a) A firewalker runs across a bed of hot coals...Ch. 14 - (a) What is the rate of heat conduction through...Ch. 14 - A walrus transfers energy by conduction through...Ch. 14 - Compare the rate of heat conduction through a...Ch. 14 - Suppose a person is covered head to foot by wool...Ch. 14 - Some stove tops are smooth ceramic for easy...Ch. 14 - One easy way to reduce heating (and cooling) costs...Ch. 14 - (a) Calculate the rate of heat conduction through...Ch. 14 - Many decisions are made on the basis of the...Ch. 14 - For the human body, what is the rate of heat...Ch. 14 - At what wind speed does 10C air cause the same...Ch. 14 - At what temperature does still air cause the same...Ch. 14 - The “steam” above a freshly made cup of instant...Ch. 14 - (a) How many kilograms of water must evaporate...Ch. 14 - On a hot dry day, evaporation from a lake has just...Ch. 14 - One winter day, the climate control system of a...Ch. 14 - The Kilauea volcano in Hawaii is the world’s most...Ch. 14 - During heavy exercise, the body pumps 2.00 L of...Ch. 14 - A person inhales and exhales 2.00 L of 37.0C air,...Ch. 14 - A glass coffee pot has a circular bottom with a...Ch. 14 - At what net rate does heat radiate from a 275m2...Ch. 14 - (a) Cherry-red embers in a fireplace are at 850C...Ch. 14 - Radiation makes it impossible to stand close to a...Ch. 14 - (a) Calculate the rate of heat transfer by...Ch. 14 - Find the net rate of heat transfer by radiation...Ch. 14 - Suppose you walk into a sauna that has an ambient...Ch. 14 - Thermography is a technique for measuring radiant...Ch. 14 - The Sun radiates like a perfect black body with an...Ch. 14 - A large body of lava from a volcano has stopped...Ch. 14 - Calculate the temperature the entire sky would...Ch. 14 - (a) A shirtless rider under a circus tent feels...Ch. 14 - Integrated Concepts One 30.0C day the relative...Ch. 14 - Integrated Concepts Large meteors sometimes strike...Ch. 14 - Integrated Concepts Frozen waste from airplane...Ch. 14 - €69. Integrated Concepts (a) A large electrical...Ch. 14 - Integrated Concepts (a) Suppose you start a...Ch. 14 - Integrated Concepts A 76.0-kg person suffering...Ch. 14 - Integrated Concepts In certain large geographic...Ch. 14 - Integrated Concepts Heat transfers from your lungs...Ch. 14 - Integrated Concepts (a) What is the temperature...Ch. 14 - Integrated Concepts Hot air rises because it has...Ch. 14 - Unreasonable Results (a) What is the temperature...Ch. 14 - Unreasonable Results A slightly deranged Arctic...Ch. 14 - Unreasonable Results (a) Calculate the rate of...Ch. 14 - Unreasonable Results A meteorite 1.20 cm in...Ch. 14 - Construct Your Own Problem Consider a new model of...Ch. 14 - Construct Your Own Problem Consider a person...
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