Physics for Scientists and Engineers with Modern Physics
4th Edition
ISBN: 9780131495081
Author: Douglas C. Giancoli
Publisher: Addison-Wesley
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Textbook Question
Chapter 20, Problem 56P
(II) Calculate the relative probabilities, when you throw two I dice, of obtaining (a) a 7, (b) an 11, (c) a 4.
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(III) Rank the following five-card hands in order ofincreasing probability: (a) four aces and a king; (b) six ofhearts, eight of diamonds, queen of clubs, three of hearts,jack of spades; (c) two jacks, two queens, and an ace; and(d) any hand having no two equal-value cards (no pairs,etc.). Discuss your ranking in terms of microstates andmacrostates
(II) Suppose that you repeatedly shake six coins in your handand drop them on the floor. Construct a table showing thenumber of microstates that correspond to each macrostate.What is the probability of obtaining (a) three heads andthree tails, and (b) six heads?
(4) When variables x, y, z are related by F(x, y, z) = 0, show the following relations, by
referencing any calculus book. For example, the variables x, y, z are p, V, T in thermodynamics:
(a)
(b)
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(с)
:17(2),
дz
y
(x), + ( x), (x)
y
x
() () (), = -1 (Chain relation)
Z
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y
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= 0
Chapter 20 Solutions
Physics for Scientists and Engineers with Modern Physics
Ch. 20.2 - An adiabatic process is defined as one in which no...Ch. 20.3 - A motor is running with an intake temperature TH =...Ch. 20.6 - A 1.00.kg piece of ice at 0C melts very slowly to...Ch. 20.9 - Prob. 1EECh. 20 - Prob. 1QCh. 20 - Can you warm a kitchen in winter by leaving the...Ch. 20 - Would a definition of heat engine efficiency as e...Ch. 20 - What plays the role of high-temperature and...Ch. 20 - Which will give the greater improvement in the...Ch. 20 - The oceans contain a tremendous amount of thermal...
Ch. 20 - Discuss the factors that keep real engines from...Ch. 20 - Prob. 8QCh. 20 - Describe a process in nature that is nearly...Ch. 20 - (a) Describe how heat could be added to a system...Ch. 20 - Suppose a gas expands to twice its original volume...Ch. 20 - Give three examples, other than those mentioned in...Ch. 20 - Which do you think has the greater entropy, 1 kg...Ch. 20 - (a) What happens if you remove the lid of a bottle...Ch. 20 - Prob. 15QCh. 20 - Prob. 16QCh. 20 - Prob. 17QCh. 20 - The first law of thermodynamics is sometimes...Ch. 20 - Powdered milk is very slowly (quasistatically)...Ch. 20 - Two identical systems are taken from state a to...Ch. 20 - It can he said that the total change in entropy...Ch. 20 - Use arguments, other than the principle of entropy...Ch. 20 - (I) A heat engine exhausts 7800 J of heat while...Ch. 20 - (I) A certain power plant puts out 580 MW of...Ch. 20 - (II) A typical compact car experiences a total...Ch. 20 - (II) A four-cylinder gasoline engine has an...Ch. 20 - (II) The burning of gasoline in a car releases...Ch. 20 - (II) Figure 2017 is a PV diagram for a reversible...Ch. 20 - (III) The operation of a diesel engine can be...Ch. 20 - (I) What is the maximum efficiency of a heat...Ch. 20 - (I) It is not necessary that a heat engines hot...Ch. 20 - (II) A heal engine exhausts its heat at 340C and...Ch. 20 - (II) (a) Show that the work done by a Carnot...Ch. 20 - (II) A Carnot engines operating temperatures are...Ch. 20 - (II) A nuclear power plant operates at 65% of its...Ch. 20 - (II) A Carnot engine performs work at the rate of...Ch. 20 - (II) Assume that a 65 kg hiker needs 4.0 103 kcal...Ch. 20 - (II) A particular car does work at the rate of...Ch. 20 - (II) A heat engine utilizes a heat source at 580C...Ch. 20 - (II) The working substance of a certain Carnot...Ch. 20 - (III) A Carnot cycle, shown in Fig. 20-7, has the...Ch. 20 - (III) One mole of monatomic gas undergoes a Carnot...Ch. 20 - (III) In an engine that approximates the Otto...Ch. 20 - (I) If an ideal refrigerator keeps its contents at...Ch. 20 - (I) The low temperature of a freezer cooling coil...Ch. 20 - (II) An ideal (Carnot) engine has an efficiency of...Ch. 20 - (II) An ideal heal pump is used to maintain the...Ch. 20 - (II) A restaurant refrigerator has a coefficient...Ch. 20 - (II) A heat pump is used to keep a house warm at...Ch. 20 - (II) (a) Given that the coefficient of performance...Ch. 20 - (II) A Carnot refrigerator (reverse of a Carnot...Ch. 20 - (II) A central heat pump updating as an air...Ch. 20 - (II) What volume of water at 0C can a freezer make...Ch. 20 - (I) What is the change in entropy of 250g of steam...Ch. 20 - (I) A 7.5-kg box having an initial speed of 4.0m/s...Ch. 20 - (I) What is the change in entropy of 1.00 m3 of...Ch. 20 - (II) If 1.00m3 of water at 0C is frozen and cooled...Ch. 20 - (II) If 0.45kg f water at 100C is changed by a...Ch. 20 - (II) An aluminum rod conducts 9.50 cal/s from a...Ch. 20 - (II) A 2.8-kg piece of aluminum at 43.0C is placed...Ch. 20 - (II) An ideal gas expands isothermally (T = 410 K)...Ch. 20 - (II) When 2.0 kg of water at 12.0C is mixed with...Ch. 20 - (II) (a) An ice cube of mass m at 0C is placed in...Ch. 20 - (II) The temperature of 2.0mol of an ideal...Ch. 20 - (II) Calculate the change in entropy of 1.00kg of...Ch. 20 - (II) An ideal gas of n moles undergoes the...Ch. 20 - (II) Two samples of an ideal gas are initially at...Ch. 20 - (II) A 150-g insulated aluminum cup at 15C is...Ch. 20 - (II) (a) Why would you expect the total entropy...Ch. 20 - (II) 1.00 mole of nitrogen (N2) gas and 1.00 mole...Ch. 20 - (II) Thermodynamic processes are sometimes...Ch. 20 - (III) The specific heat per mole of potassium at...Ch. 20 - (III) Consider an ideal gas of n moles with molar...Ch. 20 - (III) A general theorem states that the amount of...Ch. 20 - (III) Determine the work available in a 3.5-kg...Ch. 20 - (I) Use Eq. 2014 to determine the entropy of each...Ch. 20 - (II) Suppose that you repeatedly shake six coins...Ch. 20 - (II) Calculate the relative probabilities, when...Ch. 20 - (II) (a) Suppose you have four coins, all with...Ch. 20 - Prob. 58PCh. 20 - (II) Energy may be stored for use during peak...Ch. 20 - (II) Solar cells (Fig. 20-22) can produce about...Ch. 20 - Prob. 61PCh. 20 - It has been suggested that a heat engine could be...Ch. 20 - A heat engine takes a diatomic gas around the...Ch. 20 - A 126.5-g insulated aluminum cup at 18.00C is...Ch. 20 - (a) At a steam power plant, steam engines work in...Ch. 20 - (II) Refrigeration units can be rated in tons. A...Ch. 20 - Prob. 67GPCh. 20 - (a) What is the coefficient of performance of an...Ch. 20 - The operation of a certain heat engine takes an...Ch. 20 - A car engine whose output power is 155 hp operates...Ch. 20 - Suppose a power plant delivers energy at 850 MW...Ch. 20 - 1.00 mole of an ideal monatomic gas at STP first...Ch. 20 - Two 1100-kg cars are traveling 75 km/h in opposite...Ch. 20 - Metabolizing 1.0 kg of fat results in about 3.7 ...Ch. 20 - A cooling unit for a new freezer has an inner...Ch. 20 - Prob. 76GPCh. 20 - The Stirling cycle shown in Fig 20-27, is useful...Ch. 20 - A gas turbine operates under the Brayton cycle,...Ch. 20 - Thermodynamic processes can be represented not...Ch. 20 - An aluminum can, with negligible heat capacity, is...Ch. 20 - Prob. 81GPCh. 20 - A bowl contains a large number of red, orange, and...
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- vii) Consider a case of a particles and two compartments, if m is the number of particles in one compartment and remaining n=-) particles in other compartment, then the mumber of microstates in the macrostate (n. -m) or thermodynamie probability is a) W(4.a- 4) = b) H(2, n-n)=. (s -, 4' (1 + 1, )!arrow_forwardIt's a thermodynamics question.arrow_forwardExplain, in your own words, how entropy is used in statistical physics.arrow_forward
- (3)arrow_forwardASAPPPParrow_forward(a) A 5.0-kg rock at a temperature of 20 °C is dropped into a shallow lake also at 20 °C from a height of 1.0 × 103 m . What is the resulting change in entropy of the universe? (b) If the temperature of the rock is 100 °C when it is dropped, what is the change of entropy of the universe? Assume that air friction is negligible (not a good assumption) and that c = 860 J/kg · K is the specific heat of the rock.arrow_forward
- (2) [ Describe briefly why the following statements are wrong. (i) "Hot cup of coffee becoming cold spontaneously is an entropy-decreasing process. So the law of entropy increase is violated in this situation." (ii) "Air conditioners require bulky external unit, exhausting heat to outside. With the technology constantly advancing, external unit will be eliminated in the future."arrow_forward1) (a) Assuming that the total number of microstates accessible to a given statistical system is 2, show that the entropy of the system, as given by S = -kB Er P, InPr, is maximum when all 2, states are equally likely to occur. (b) If, on the other hand, we have an ensemble of systems sharing energy (with mean value E), then show that the entropy, as given by the same formal expression, is maximum when Pr x exp(-BEr), ß being a constant to be determined by the given value of E,. (c) Further, if we have an ensemble of systems sharing energy (with mean value E) and also sharing particles (with mean value N), then show that the entropy, given by a similar expression, is maximum when Pr,s x exp(-aNr – BEs), a and B being constants to be determined by the given values of N and E. Note you may use the method of Lagrange's multipliers.arrow_forward(iii) Show that the entropy of xenon would be reduced if the xenon was confined to two dimensions at a surface, i.e., a two-dimensional gas. +RIn + R h-6.626 x 1034 J s k-1.38 x 10JK I atm 101325 Nm2 NA 6.022 x 102 molarrow_forward
- (1) When the energy of the system (simple harmonic oscillator) is given by E = (n+) ħw in a heat bath of temperature T, (a) Derive the partition function Z. (b) For high temperature kT » ħw, derive the approximate form of Z. (c) Calculate F (Helmholtz free energy), U (internal energy), and S (entropy) of the system.arrow_forward(II) Determine the energy content of 100 g of Karen’s fudgecookies from the following measurements. A 10-g sampleof a cookie is allowed to dry before putting it in a bombcalorimeter (page 396). The aluminum bomb has a mass of0.615 kg and is placed in 2.00 kg of water contained in analuminum calorimeter cup of mass 0.524 kg. The initialtemperature of the system is 15.0°C, and its temperatureafter ignition is 36.0°Carrow_forwardConsider a case of n particles and two compartments, if n1 is the number of particles in one compartment and remaining n2=n-n1 particles in other compartment, then the number of microstates in the macrostate (n1, n-n1) or thermodynamic probability isarrow_forward
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