Questions and Answers of The Physics Energy

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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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,
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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 =
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
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.
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
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
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
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
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
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
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
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
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
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
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
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.
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
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
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
A concern with plans for capture of CO2 directly from ambient air (DAC), is the sheer volume of material that must be processed. One design requires fans to blow air at 2 m/s through 2.8 m thickness
Assume that the linearized analysis of climate leading to (34.46)is correct, and F2× ≅ 3.7 W/m2. Assume also that climate models correctly predict that quadrupling of CO2 levels would give a
Using the simplified model of Earth’s atmosphere as in Example 34.1, with no absorption, no meridional energy transport, and an albedo of 0.16, use the yearly average integrated insolation computed
Assume that ice albedo feedback gives a feedback parameter λ = 0.5 W/m2 ◦C. Estimate the corresponding addition to the change in temperature under adoubling of atmospheric CO2 in the absence of
Earth’s albedo is currently estimated to be a⊕ ≈ 0.30.By what percentage would a⊕ have to increase to offset the estimated increase in forcing eq. (34.36) due to doubling of CO2 since
Show that radiation at a distribution of temperatures decreases the estimate (34.34) of the uniform temperature radiative response λ0 by proving the result in the case where the radiation comes from
Prove that radiative forcing grows logarithmically withCO2 concentration under the circumstances illustrated in Figure 34.13 Specifically, assume that for wavelengths in the vicinity of the 15 ?m
Use the value of atmospheric pressure at sea level to estimate the total mass of the atmosphere. Estimate the number of molecules in the atmosphere and check for agreement with recent numbers for the
The bond energy of the double bond in the O2 molecule is 5.06 eV. Verify that light must have wavelength less than???246 nm in order to break this bond. Assuming sunlight has a blackbody spectrum at
We have described hydrostatic equilibrium in §34.2.1 under the approximation that the atmosphere lies above a planar surface. Compute the pressure in hydrostatic equilibrium as a function of height
Consider a slight improvement on the two-layer toy model of Earth’s atmosphere shown in the figure in Example 34.2. Assume that there are two atmospheric layers, each transparent to incoming solar
Show that an n-layer atmosphere of the type described in Example 34.2 gives a surface temperature? = ( Vn + 1) × 255 K Is 4
Given the following approximations for planetary albedos and given approximate radii of their orbits, estimate the average effective temperature of the planets Mars and Neptune. (The effective
Compare the energy density of oil and geothermal fluid at 250 ◦C pumped from oil/geothermal wells at a rate of 30 L/s. To make a fair comparison, assume that the oil is transformed into useful
Compute and compare the amount of carbon released per GJ of delivered energy by (a) a coal plant operating at 35% efficiency, (b) a natural gas combined cycle plant operating at 60%
Bitumen extracted from tar sands in Athabasca, Canada, has an API gravity of ◦API 8. Compute the mass of one liter of such bitumen and compare to that of a liter of light crude at ◦API 35.
Using an activation energy E = 250 kJ/mol, compute the change in rate of petroleum generation when temperature increases from 130 ◦C to 430 ◦C. If petroleum generation through such a process
Use the Arrhenius equation in Box 33.5 to show that a reaction rate doubles under a temperature shift ofT ≅ (kBT2 ln 2)/E, assuming E ≫ kBT.
An underground mass of salt may form a dome trapping a petroleum reservoir. Compute the gravitational anomaly (deviation of gravitational acceleration) produced by an underground salt mass, where for
Compute the fraction of Carnot efficiency realized by a coal plant operating at 600 ◦C and 45% efficiency (assume ambient temperature of 300 K). If another plant operates at the same fraction of
The deformation in a solid can be described by a vector field u(x) = (u1, u2, u3) describing the displacement of the solid away from the equilibrium point x. This is similar to the displacement
Estimate how many solar panels or wind turbines are needed to produce the same amount of electrical energy as the 10 kt of coal that can be extracted in a long wall mining operation in one year by
When computing efficiencies, European power plants sometimes use the LHV of a fuel, while for US power plants the HHV is standard. Consider a power plant burning bituminous coal with HHV/LHV of
A rough measure of the enthalpy of combustion of a hydrocarbon can be obtained by assuming that all CC bonds contribute the same energy to the combustion process when broken, and that the same is
Estimate the energy content of a coal seam measuring 1 km2 by 1 m deep. Estimate the electrical power output of a coal plant burning this fuel over one year, and the area required for a solar thermal
Estimate the energy extracted from 1 km3 of granite if cooled from 300 ◦C to 200 ◦C. Assume that a power plant runs between the (time-varying) temperature Tg of the granite and an ambient
Compute the (ideal) efficiency of a double-flash plant with the same conditions as the example single-flash plant described in Example 32.5. The cycle is labeled in Figure 32.15 You will need to
Consider the efficiency computed in the example single-flash cycle in Example 32.5. Use thermodynamic data on water to show that running the separator at T = 140 ◦C or T = 160 ◦C will decrease
For a geothermal well that has been running for some time, pressure at the bottom of the well is pw ≅ 15MPa at a depth of 2 km. Assume the fluid is water at 280 ◦C. Estimate the location of the
Given a geothermal reservoir containing water at temperature T = 200 ◦C at a depth of 1.5 km, use steam tables to determine the density and vapor pressure of the water. Assuming that pressure in
Consider a geothermal reservoir (see Figure 32.17)At a depth of 1.5 km, modeled as a cylindrical volume of radius r = 5 km and height h = 500m, with pressure at the periphery of pr ≅ 15 MPa,
Compute the draw down coefficient (32.11)in a simple model where the geothermal reservoir is a large cylindrical volume with height h much smaller than the radius r (see Figure 32.17)Assume that the

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