The Physics of Energy 1st edition Robert L. Jaffe, Washington Taylor - Solutions

Why does it take more work to compress a gas adiabatically than isothermally from V1 to V2 ? Why does it take more heat to raise the temperature of a gas isobarically (constant pressure) than isometrically from T1 to T2?
The Iron Age began around 1200 BCE, more than 2000 years after the first appearance of bronze in human history. It may come as a surprise, therefore, that the reaction Fe2O3 +3CO → 2Fe +3CO2 is exothermic (ΔHr = -25 kJ/mol) and has negative reaction free energy (ΔGr = -29 kJ/mol) at NTP. So
H2O has a triple point near 0℃, where all three phases, solid (ice),liquid (water), and gas (water vapor), can coexist. So there are three possible phase transitions, solid → liquid (melting), water → gas(vaporization), and solid → vapor (sublimation). Each has an associated enthalpy of
The heat capacity per molecule of carbon monoxide at constant pressure is shown in Figure? from 175 K to over 5000 K. Explain why c?p ? (7/2)KB for small T and explain its subsequent increase with T. 5.0 4.5 4.0 3.5 200 500 1 000 2000 5 000 temperature [K]
According to the Sackur–Tetrode formula, the entropy of an ideal monatomic gas grows with the mass of the atoms. Thus the entropy of a volume of argon is much greater than the same volume of helium (at the same T and p). Can you explain this in terms of information entropy?
An inventor claims to have constructed a device that removes CO2 from the air. It consists of a box with an opening through which the ambient air wafts. The CO2 is separated out by a complex system of tubes and membranes, and ends up in a cylinder, ready for disposal. The device consumes no
Living systems are highly ordered and therefore relatively low entropy compared to their surroundings; for example, a kilogram of wood from a pine tree has less entropy then the corresponding masses of water and carbon dioxide placed in a container in equilibrium at room temperature. When living
Explain why the statements “No cyclic device can transform heat into work without expelling heat to the environment” and “No device can move thermal energy from a low-temperature reservoir to a high temperature reservoir without doing work” follow from the laws of thermodynamics.
In the game of ScrabbleTM, the letters of the English alphabet are inscribed on tiles and a prescribed number of tiles are provided for each letter. Consider an ensemble of ScrabbleTM tiles with a probability distribution defined by the frequency of tiles in the box. Explain how to calculate
Here is an energy basis state of three electrons in a magnetic field? Are all three of these electrons entangled? What is the probability that a measurement of the first electron?s spin yields +1/2 ?? If the first electron?s spin is measured to be +1/2 ?, what would a measurement of the second and
A suggestion rather than a question: a video recording was made in 1964 of Richard Feynman describing the double slit experiment. It can be found at www.cornell.edu/video/playlist/richard-feynmanmessenger- lectures where it is the main part of Lecture 6: The Quantum Mechanical View of Nature. It is
We make a big deal about the linearity of quantum mechanics. Is classical mechanics linear? Consider, for example, two solutions to Newton’s laws for motion in Earth’s gravitational field, x1(t) and x2(t). Both obey mẍ(t) = - GmM|x|. Show that a linear combination of x1 and x2 is not a
Sketch the magnitude and direction of the heat flux under the ground driven by annual temperature variations as a function of depth for the four times of the year shown in Figure. 25 20E midsummer 15 autumn 10 spring midwinter 2 4 6. 8 10 depth [m] temperature [°C]
A water bed replaces an ordinary mattress with a plastic bag filled with water. If the ambient temperature is below body temperature, water beds must either be heated or covered with a relatively thick layer of insulating foam. Why should this be necessary for a water bed, but not for an ordinary
Although it was not mentioned in the text, Newton’s law of cooling requires that the thermal conductivity k of the object be “high enough,” otherwise the surface of the object will cool below its bulk temperature T. Then the convective heat transfer from the surface would be suppressed and
Look up the effective R-value of wall insulation when the structural support for the wall is either 2 X 4 wood studs or 2 X 4 metal studs. Explain the difference.
People usually discuss their experience of heat and cold in terms of temperature. Closer consideration, however, suggests that it is heat conduction rather than temperature that matters. What do you think? Have you ever taken a sauna? Or touched a metal surface at –30∘C?
The phase diagram for pure iron is shown in Figure 5.13. Iron has three different solid phases, called ?, ?, and ?-iron, with different crystal structures. Discuss the behavior of iron as it is heated at different pressures, at 1 atm or at 10-6atm, for example. Under what conditions can several
CO2 is a colorless gas. Why do you suppose the CO2 vapor in Figure 5.8? streaming away from the dry ice appears white? wit
A mixture of sodium and potassium salts is used for energy storage in certain solar energy plant designs. Such a mixture is used in a temperature range between 300 ∘C and 500∘C where it is a liquid and where its specific heat is approximately 1.5 kJ/kg K. Why would engineers choose a substance
A one liter box containing 0.1 L of liquid water at NTP is lifted from the floor and placed on a table one meter high. How much has the energy of the water changed? How much has its internal energy changed? The water is now heated until it is all converted to vapor. Has all this heat gone into the
Polarized sunglasses are designed to transmit only one polarization of light – the polarization with electric fields vertical – since glare arising from reflections on horizontal snow and water surfaces is preferentially polarized with horizontal electric fields. LCD displays such as the view
Suppose an electromagnetic plane wave propagates in a direction perpendicular to a long straight wire. Can you see why a current develops in the wire with the same frequency as the wave? Qualitatively, how does the current depend on the orientation of the wire and the polarization of the light?
Explain why the strings that play lower frequency notes on a guitar or violin are generally thicker and less tightly strung than the strings playing higher notes.
Currents produce magnetic fields, and magnetic fields exert forces on currents. When a current flows through a wire, does the magnetic field it produces act to make the wire expand or contract? What about the force on the wires in a solenoid? Does it act to make the solenoid expand or contract?
Discuss the statement that Lenz?s law follows from conservation of energy. Consider, for example, the scenario of Figure 3.22(b)? if thesign of eq.? (3.64) were reversed. B = Bot2 B (b)
Most countries provide AC electricity at VRMS ≈ 220–240 V to residential customers. In the US and parts of South America VRMS ≈ 110–120 V is provided. How do resistive losses in household wires compare between the two? Given the result, why do you think even higher voltages are not
Can you identify the largest component of your personal electric power consumption?
Think of some devices that generally are not run on electrical power. Discuss the reasons why other power sources are favored for these devices.
Regenerative brakes in many hybrid cars such as the Toyota Prius are designed to store the vehicle’s kinetic energy in the battery for later use in acceleration. Such brakes currently can absorb roughly 50% of the kinetic energy lost through braking. Most cars get better gas mileage in highway
Using the ideas developed in this chapter, consider the relative energy use of other modes of transport such as airplane or train travel compared to the automobile. Use the internet or other resources to estimate numbers for mass, cross-sectional area, and drag coefficient for a train or a plane,
Is there a minimum energy necessary for transport? Do the laws of physics dictate some minimum energy required to transport, say, 2000 kg of material from Cambridge, Massachusetts to New York? How would you minimize the energy required for transport?
The analysis of a road trip from Cambridge, Massachusetts to New York suggests many ways that the energy cost of transport could be reduced including (a) slower speed; (b) a more efficient engine; (c) keeping tires properly inflated; (d) a more streamlined car; (e)
Compare the global average rate of energy use per person to typical human food energy consumption. What does this say about the viability of biologically produced energy as a principal energy solution for the future?
Discuss some possible answers, depending on the context, to the question posed in the text, “What is the energy of a bucket of water?”
Give examples of each of the types of energy described in §1.2.
Try to describe the flow of energy through various systems before and after you use it in a light bulb in your house. Which of the various forms of energy discussed in the chapter does the energy pass through?
A residential photo voltaic installation is described as producing “5000 kilowatt hours per year.” What is a kilowatt hour per year in SI units? What might be the purpose of using kWh/y rather than the equivalent SI unit?
Given that energy is everywhere, and cannot be destroyed, try to articulate some reasons why it is so hard to get useful energy from natural systems in a clean and affordable way.
Fluorescent light bulbs have significant impedance. Measurements on a compact fluorescent bulb with luminosity equivalent to a 40 W incandescent indicate that it consumes 9 W real power. Measurements of RMS current and voltage, however, indicated that it drew an apparent power of 14 VA. What is the
Suppose a small resistance R is added in series to the LC circuit of Problem 38.3. Assume that Q(t) has the form Q(t) = Q? (t) cos ?t, where Q?(t) is a slowly changing function that would be constant if there were no resistance and was determined in Problem 38.3. Compute the energy stored in this
A homeowner is trying to decide whether to heat with a furnace rated at 95% efficiency or by an electrically powered heat pump. She lives in a town where electricity is produced by a coal-fired power plant that claims to operate with 1st law efficiency that is 55% of the Carnot limit. The heat
A 345 kV transmission line consisting of three conductors has a resistance per unit length of R′ =R/l = 0.0351/km, and an inductive reactance per unit length of ωL′ = ωL/l = 0.371 Ω/km, as described in §38.4.1. Assess the utility of this line for transmission of three-phase power over a
A 200 kV transmission line is being designed to carry power 400 km from one power plant to another as part of a transmission network. The line has inductive reactance per unit length ωL′ = 0.44 Ω/km. Assuming that the maximum phase difference that can be to lerated between the sending and
Suppose, as in Figure 38.28 , a generator is supplying(time-averaged) power PL to a purely resistive load R. The voltage at the generator is V1(t) = ?2V1 cos ?t.The power is carried to the load along a single conductor with inductance L and negligible resistance. V2(t)is the voltage at the end of
Suppose a synchronous generator is supplying power at (RMS) voltage V to a load characterized by impedance Z0 = R0 + iX0 = z0eiφ0, when an inductive load with negligible resistance Z1 = iωL is added in parallel with the original load. Show that the real power delivered by the generator does not
The rating of each generator at the Three Gorges Dam(TGD) in China is quoted as 778 MVA of apparent power (see ?38.2.3) produced at 20 kV and 50 Hz. Given that the quoted real power is 700 MW, what power factor has been assumed? The TGD generator rotors turn at 75 rpm. Assuming a three-phase stator
A three-phase generator delivers voltages VA(t) = V0 cosωt, VB(t) = V0 cos(ωt + 2π/3), and VC(t) = V0 cos (ωt − 2π/3). First, assume that all three phases are connected to identical, purely resistive loads. Show that the total power delivered is 3V20 /2R, independent of time. Next, assume
A 150 kV (RMS) power supply is providing 300 MW of (real) power at 60 Hz to a load with power factor cos φ = 0.8.What capacitance would you have to install in parallel with the load to restore the power factor to one? Given a large number of individual 310 μF capacitors rated to a maximum of,
Consider an AC circuit with only a capacitor of capacitance C, driven by an AC voltage V(t) = V0 cosωt. Compute the average 〈|P|〉 of the absolute value of the rate of energy transfer back and forth from the power source to the capacitor. Compare to the apparent (= reactive) power for this
Suppose a capacitor C, initially charged to a voltage V, is connected to an inductor L. Show that the current in the resulting LC circuit oscillates, I(t) = I0 sin ?t.Find I0 and show Sketch the current in the circuit and the voltage across the capacitor as functions of time. An (idealized)
Suppose amass m is connected to a rigid support by a spring with spring constant k. A frictional force −bẋ is applied by a damper that provides viscous friction, and an external force F(t) may also be applied (see Figure 38.27)Show that Newton’s laws give an equation of motion for the mass
Thomas Edison’s first DC power plant on Pearl St.in New York City produced roughly 100 kW at 110 V(DC), which was distributed over two copper wires spanning distances of order 1 km. Suppose resistive transmission losses were limited to 5%. Estimate the diameter of the copper wires necessary to
A geothermal resource outputs saturated (liquid) water at 250 ◦C (as in Example 32.5). Consider two alternative ways to use this resource to deliver space heating at T = 20 ◦C. First, the hot water is circulated through a heat exchanger that transfers its thermal energy with 90% (1st law)
A heating system uses thermal energy from a reservoir at temperature T+ to run a heat engine that in turn powers a mechanical heat pump that takes thermal energy from an environment at temperature T− and delivers it for space heating at temperature T. Define a suitable 1st law efficiency for this
In §13.3.5 we specified a realistic Rankine cycle working between T+ = 600 ◦C and T− = 36 ◦C. We found its efficiency to be 38%.What is its 2nd law efficiency?
Estimate the contribution to global sea level rise over a century if Greenland’s glaciers continue to melt at a rate of 290 Gt/y.
Assume that the rate of carbon emission at 10 Gt/year increases at a constant rate to a maximum of 20 Gt/year in 2050, and then decreases at the same rate. Assume that ocean and land biomass together absorb excess CO2 at a constant rate of −5 Gt/year.In what year will atmospheric CO2 levels peak?
Assume that 1% of a net radiative forcing of 3.7 W/m2 world wide goes to melting ice over land. Estimate the rate of sea level rise from this melting.
Compute the time for the oceanic mixed layer (350 Mkm2 × 200 m) to warm by 3.2 K, using 50% of the energy coming from a change in radiative forcing of 3.7 W/m2. Advanced version: assume that radiative forcing is proportional to T − Teq as the surface warm sand describe the time-history of the
Compute the time to melt 3000 m thickness of ice if there is an extra 5% of 200 W/m2 average daily insolation for four months out of the year beyond the insolation that would give an ablation rate matching the accumulation rate from fresh snowfall.
In another billion years solar luminosity will increase by roughly another 10%. Estimate the resulting radiative forcing and change in terrestrial surface temperature.
Since the formation of the solar system 4.6 billion years ago, the net solar luminosity has increased roughly 40% from its initial value. Assuming that luminosity has increased at a constant rate, estimate the solar constant 100 million years ago, during the Cretaceous period. Assuming current
Variation in sunspot activity leads to variation in the solar constant by roughly 1–2 W/m2 with a roughly 11 year cycle. Assuming an albedo of a = 0.3, estimate the radiative forcing arising from an increase in the solar constant by 2 W/m2. Using the IPCC mean result for feedback, what increase
Compute the insolation at 65◦ latitude on the summer solstice for tilt of 22.05◦ and compare to the value at 24.5◦.
A load consists of a large number N of identical resistors R (e.g. incandescent lights, toasters,. . . ) in parallel.Suppose they are powered by an AC generator with RMS voltage V. Compare the line losses if (a) The load is connected to the generator by single-phase power(b) The load is
Suppose a power plant is supplying 300 MW of real power over a 150 kV (RMS) transmission line to a load that has an impedance characterized by a phase φ = 26◦(corresponding to a power factor of cos φ = 0.9 lagging).The (three-phase) power is supplied over lines with inductive reactance and
Suppose that the Maxwell BCAP0310 ultra capacitor described in Example 37.5 used “conventional” capacitor technology. Specifically, assume that it can be described essentially as a parallel plate capacitor of area A, plate separation d, and dielectric constant ε =kε0 rolled into a spiral to
For the Maxwell BCAP0310 ultra capacitor described in Example 37.5, the capacitance is 310 F, mass is 0.06 kg, maximum voltage is 2.85 V, and internal resistance is r = 2.2 mΩ. Consider connecting the ultra capacitor to an external load with resistance RL. Compute the maximum possible
For the conditions described in Example 37.4 compute the moment of inertia of the flywheel, its angular momentum, and kinetic energy of rotation. Assuming that the car loses kinetic energy only to wind resistance(with a drag coefficient of cd = 1/3) and that the flywheel’s energy can be converted
Compute the speed of a fragment of metal released from the rim of the example flywheel described in the box in Example 37.4. Compare to the speed of a bullet fired by a handgun.
According to Figure 37.7, the energy density of hydrogen compressed to 700 atm is approximately 5.6 MJ/L.Assuming hydrogen behaves as an ideal gas throughout,estimate the energy density of hydrogen compressed to 700 atm by adding the enthalpy of combustion and the energy required to compress the
Compute the 2nd law bound on the efficiency of a methanol fuel cell.
Confirm the 2nd law bound η = 83% quoted in the texton the efficiency of a hydrogen fuel cell.
Compute an upper bound on the energy density of a lead-acid battery in which the overall chemical process is ? and for each such reaction two electrons pass around the external circuit, assuming that the only material needed is that involved in the reaction. The standard energy density is
Compute the free energy of reaction ??G0, ideal cell voltage ?0, maximum possible effective energy density ?effective, and thermodynamic efficiency limit ? = ?G0/?H0 for an alkaline dry-cell battery (37.11) ? given the enthalpies and free energies of formation in Table 37.2. ? Zn(s)+ 2MNO2(s) →
In a lithium-iodine (LiI) battery, a solid lithium anode is surrounded by a polymer impregnated with iodine. The net reaction, Li + ½ I2→LiI, has a standard reaction free energy of ΔG0 = −266.9 kJ/mol and a standard reaction enthalpy of ΔH0 = −270.08 kJ/mol. Estimate the cell voltage ℰ0,
Estimate the specifications for a solar thermal energy plant and storage system. The plant should output a steady 100 MW, 24/7. Assume that the plant is builtin a desert area with an average 250 W/m2 insolation. Assume a gross conversion efficiency of 3%.Tanks of molten salt at 450 ◦C (specific
Verify the computations in Example 37.2 describing the McIntosh CAES plant. In particular, use eq. (37.2) to compute the energy stored through isothermal compression; verify that 1.4 TJ of work would be done if the stored air were allowed to expand adiabatically as described in Example 37.2 and
Confirm explicitly that the work (37.2)done in isothermal compression of a CAES system with volume V, and low, high, and ambient atmospheric pressures pL, pH, p0 is equivalent to the energy (36.25)of the system. wisothermal PH PL - (рн - PL) PO V In PL In Po PH |
Consider using the McIntosh salt mine described in Example 37.2 for adiabatic storage. Compute the energy stored if a volume of air initially at p0 = 1 atm is compressed to pH = 75 atm, and compare to the energy stored if the air were compressed isothermally. Takeγ = 1.4 for air. Compute the
Show that the energy stored when air is compressed adiabatically from pressure p0 to pressure pH in a final volume VH = V is given byafter the work done by/on the atmosphere is subtracted.Here r = pH/p0 and γ = 1.4 is the adiabatic index of air. „(adiabatic) ´stored (H1/r)r-H)}{1-1/1) РнV
A company is proposing to build an advanced rail energy storage system: excess electric energy willpower engines that will transport a heavy mass up a slope. During periods of peak demand, the process will be reversed, converting the gravitational potential energy of the mass back into electric
The world’s largest pumped hydro storage facility,located in Bath County, Virginia, has a generating capacity of about 3 GW. When generating power, the turbine flow rate is roughly 850 m3/s. Estimate the difference in elevation between the upper reservoir and the turbines. The area of the upper
Consider the scope of pumped hydro storage needed to store and release 12 PJ of energy per day. Compare to the total US hydro power output. If the full 12 PJ were stored using local modest-sized UPH reservoirs of volume 20000 m3 at a depth of 100 m, how many such reservoirs would be needed?
A typical lithium-ion battery for a laptop has a storage capacity of 200 kJ and a mass of 0.5 kg. Compute the number of such batteries required and total mass in order to store 30% of US daily electric energy consumption of 12 PJ.
Lithium is the source of tritium, which is the primary ?fuel? for a dt fusion reactor. (The deuterium, which his abundant and relatively cheap, can be considered as analogous to the air required for combustion of a fossil fuel.) Compute the energy density (J/kg) of lithium with respect to dt
The cottage described in the previous problem sits in a location with average mean temperature T = 8 ◦C, and maximum average annual variation, T = 16 ◦C. Estimate the number of heating degree days at this location. If you solved the previous problem, calculate the annual heating energy
Verify the claim that the yearly heating requirement of the dwelling described in §36.5.3 drops from ≈ 40 GJ/y to ≈ 28 GJ/y when the 15 m2 of windows are changed from single to double glazing.
A rural cottage sits on pilings with a breezeway underneath. It has insulated wooden walls (Awalls = 50 m2,Rwalls = 3 m2 K/W), a plywood floor (Afloor = 35 m2)2.5 cm thick, and a simple peaked slate roof (slope 30◦) covering the floor area. The slates are roughly 2 cm thick, laid over plywood
A homeowner turns down the thermostat from Ts =18.3 ◦C to T′s = 16.3 ◦C for ttotal = 8 h every night. Including the effects of reheating, compute the fraction of heating energy saved compared with leaving the other most at set at 18.3 ◦C throughout. Assume that the outside temperature
Show that ≈ 1000 L of home heating oil with energy density of about 40 MJ/L are required to provide heat for our typical dwelling (AH = 100 m2, CH = 10 MJ/K,RH = 0.7 m2 K/W) in Boston. Assume that the (1st law) efficiency of the oil furnace is 95%.
Given T̅ and ΔT for Boston, show that the heating season is on average ≈ 260 days long and evaluate eq. (36.44)to obtain the average number of heating degree days in Boston. Then choose a city for which monthly average temperature data are available, compute T̅, ΔT, and Dcity. Compare your
According to the US EIA, 1350 Mt(CO2) were emitted from combustion of coal and 530 Mt(CO2) we re emitted from combustion of natural gas for electricity production in 2015. Using the data in §36.5.1 show that improving the efficiency of coal and natural gas power plants to 45% and 60% respectively
Look up the molar enthalpy of combustion ΔHc(T0)and Gibbs free energy of combustion ΔGc(T0) for hydrogen under standard conditions. Notice that |ΔHc(T0)| > |ΔGc(T0)|, suggesting that one might be able to extract more than |ΔGc| from combustion of hydrogen at high temperature, contradicting
Consider an isothermal and isobaric combustion system that operates as follows: a stream of fuel and air originally at T0 and p0 absorbs thermal energy reversibly from a regenerator reaching temperature T. It then enters a combustion chamber at temperature T and pressure p0, where the fuel is
A colloquial measure of power used in the air conditioning industry is the ton of air conditioning =3.517 kW(see §9, Problem 9.5). It is the average power required to melt one ton of ice in one day. Check this number. If melting ice was actually used to provide cooling, it would not only be
Suppose a quantity of gas, held in a fixed volume V and initially at the ambient temperature T0, is heated by a resistor to temperature T. Let Q be the heat delivered by the resistor and let CV be the (assumed constant) heat capacity of the gas at constant volume. How much energy is destroyed in
What is the internal energy and the energy of a one ton block of stone (c = 0.8 kJ/kg K) at 100 ◦C relative to an environment at 20 ◦C? What would be the mass and internal energy of a block of stone with the same energy at 60 ◦C? This problem illustrates energy as a measure of the quality of
Reproduce the results in Example 36.4 using eq. (36.25) rather than by the direct calculation of available work that was used in the example. you can use the Sackur?Tetrode formula (8.65) for the entropy of an ideal gas, expressed as a function of temperature and pressure. B = Max {Wuseful} =

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The Physics of Energy 1st edition Robert L. Jaffe, Washington Taylor - Solutions

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