Solved: The electric power output of all the thermal electric power plants in the United

Could you cool the kitchen by leaving the refrigerator open? Explain.

Could you heat the kitchen by leaving the oven open? Explain.

Should a car get better mileage in the summer or the winter? Explain.

Is there a limit to the maximum temperature that can be achievedby focusing sunlight with a lens? If so, what is it?

Name some irreversible processes that occur in a real engine.

Your power company claims that electric heat is 100% efficient.Discuss.

A hydroelectric power plant, using the energy of falling water,can operate with efficiency arbitrarily close to 100%. Why?

A heat-pump manufacturer claims the device will heat your homeusing only energy already available in the ground. Is this true?

Why do refrigerators and heat pumps have different definitionsof COP?

The heat Q added during adiabatic free expansion is zero. Whycant we then argue from Equation 19.6 that the entropy changeis zero?

Energy is conserved, so why cant we recycle it as we do materials?

Why doesnt the evolution of human civilization violate the second law of thermodynamics?

What are the efficiencies of reversible heat engines operating between (a) the normal freezing and boiling points of water,(b) the 25C temperature at the surface of a tropical ocean anddeep water at 4C, and (c) a 1000C flame and room temperature?

A cosmic heat engine might operate between the Suns 5800 Ksurface and the 2.7 K temperature of intergalactic space. Whatwould be its maximum efficiency?

A reversible Carnot engine operating between heliums meltingpoint and its 4.25 K boiling point has an efficiency of 77.7%.Whats the melting point?

A Carnot engine absorbs 900 J of heat each cycle and provides350 J of work. (a) Whats its efficiency? (b) How much heat isrejected each cycle? (c) If the engine rejects heat at 10C, whatsits maximum temperature?

Find the COP of a reversible refrigerator operating between 0Cand 30C.

How much work does a refrigerator with COP = 4.2 require tofreeze 670 g of water already at its freezing point?

The human body can be 25% efficient at converting chemicalenergy of fuel to mechanical work. Can the body be considereda heat engine, operating on the temperature difference between body temperature and the environment?

Calculate the entropy change associated with melting 1.0 kg of ice at 0C.

You metabolize a 650-kcal burger at your 37C body temperature. Whats the associated entropy increase?

You heat 250 g of water from 10C to 95C. By how much does the entropy of the water increase?

Melting a block of lead already at its melting point results in an entropy increase of 900 J/K. Whats the mass of the lead? (Hint: Consult Table 17.1.)

How much energy becomes unavailable for work in an isothermal process at 440 K, if the entropy increase is 25 J/K?

For a gas of six molecules confined to a box, find the probability that (a) all the molecules will be found on one side of the box and (b) half the molecules will be found on each side.

A Carnot engine extracts 745 J from a 592-K reservoir during each cycle and rejects 458 J to a cooler reservoir. It operates at 18.6 cycles per second. Find (a) the work done during each cycle, (b) its efficiency, (c) the temperature of the cool reservoir, and (d) its mechanical power output.

The maximum steam temperature in a nuclear power plant is 570 K. The plant rejects heat to a river whose temperature is 0C in the winter and 25C in the summer. What are the maximum possible efficiencies for the plant during these seasons?

Youre engineering an energy-efficient house that will require an average of 6.85 kW to heat on cold winter days. Youve designed a photovoltaic system for electric power, which will supply on average 2.32 kW. You propose to heat the house with an electrically operated groundwater-based heat pump. What should you specify as the minimum acceptable COP for the pump if the photovoltaic system supplies its energy?

A power plants electrical output is 750 MW. Cooling water at 15C flows through the plant at 2.8*104 kg/s, and its temperature rises by 8.5C. Assuming that the plants only energy loss is to the cooling water, which serves as its low-temperature reservoir, find (a) the rate of energy extraction from the fuel, (b) the plants efficiency, and (c) its highest temperature

A power plant extracts energy from steam at 280C and delivers 880 MW of electric power. It discharges waste heat to a river at 30C. The plants overall efficiency is 29%. (a) How does this efficiency compare with the maximum possible at these temperatures? (b) Find the rate of waste-heat discharge to the river. (c) How many houses, each requiring 23 kW of heating power, could be heated with the waste heat from this plant?

The electric power output of all the thermal electric power plants in the United States is about 2*1011 W, and these plants operate at an average efficiency of around 33%. Find the rate at which all these plants use cooling water, assuming an average 5C rise in cooling-water temperature. Compare with the 1.8*107 kg/s average flow at the mouth of the Mississippi River.

Consider a Carnot engine operating between temperatures Th and Ti , where Ti is intermediate between Th and the ambient temperature Tc (Fig. 19.21). It should be possible to operate a second engine between Ti and Tc. Show that the maximum overall efficiency of such a two-stage engine is the same as that of a single engine operating between Th and Tc (which is why combinedcycle power plants achieve high efficiencies).

An industrial freezer operates between 0C and 32C, consuming electrical energy at the rate of 12 kW. Assuming the freezer is perfectly reversible, (a) whats its COP? (b) How much water at 0C can it freeze in 1 hour?

Use appropriate energy-flow diagrams to analyze the situation in GOT IT? 19.3; that is, show that using a refrigerator to cool the low-temperature reservoir cant increase the overall efficiency of a Carnot engine when the work input to the refrigerator is included

It costs $230 to heat a house with electricity in a winter month. (Electric heat converts all the incoming electrical energy to heat.) What would the monthly heating bill be after converting to an electrically powered heat pump with COP = 3.4?

A refrigerator maintains an interior temperature of 4C while its exhaust temperature is 30C. The refrigerators insulation is imperfect, and heat leaks in at the rate of 340 W. Assuming the refrigerator is reversible, at what rate must it consume electrical energy to maintain a constant 4C interior?

You operate a store thats heated by an oil furnace supplying 30 kWh of heat from each gallon of oil. Youre considering switching to a heat-pump system. Oil costs $1.75/gallon, and electricity costs 16.5./kWh. Whats the minimum heat-pump COP that will reduce your heating costs?

Use energy-flow diagrams to show that the existence of a perfect heat engine would permit the construction of a perfect refrigerator, thus violating the Clausius statement of the second law.

A heat pump extracts energy from groundwater at 10C and transfers it to water at 70C to heat a building. Find (a) its COP and (b) its electric power consumption if it supplies heat at the rate of 20 kW. (c) Compare the pumps hourly operating cost with that of an oil furnace if electricity costs 15.5./kWh and oil costs $3.60/gallon and releases about 30 kWh/gal when burned.

A reversible engine contains 0.350 mol of ideal monatomic gas, initially at 586 K and confined to a volume of 2.42 L. The gas undergoes the following cycle: Isothermal expansion to 4.84 L Constant-volume cooling to 292 K Isothermal compression to 2.42 L Constant-volume heating back to 586 K Determine the engines efficiency, defined as the ratio of the work done to the heat absorbed during the cycle.

(a) Determine the efficiency for the cycle shown in Fig. 19.22, using the definition given in the preceding problem. (b) Compare with the efficiency of a Carnot engine operating between the same temperature extremes. Why are the two efficiencies different?

A 0.20-mol sample of an ideal gas goes through the Carnot cycle of Fig. 19.23. Calculate (a) the heat Qh absorbed, (b) the heat Qc rejected, and (c) the work done. (d) Use these quantities to determine the efficiency. (e) Find the maximum and minimum temperatures, and show explicitly that the efficiency as defined in Equation 19.1 is equal to the Carnot efficiency of Equation 19.3.

A shallow pond contains 94 Mg of water. In winter, its entirely frozen. By how much does the entropy of the pond increase when the ice, already at 0C, melts and then heats to its summer temperature of 15C?

Estimate the rate of entropy increase associated with your bodysnormal metabolism.

The temperature of n moles of ideal gas is changed from T1 to T2at constant volume. Show that the corresponding entropy changeis S = nCV ln1T2/T12.

The temperature of n moles of ideal gas is changed from T1 to T2with pressure held constant. Show that the corresponding entropychange is S = nCp ln1T2/T12.

A 6.36-mol sample of ideal diatomic gas is at 1.00 atm pressureand 288 K. Find the entropy change as the gas is heated reversiblyto 552 K (a) at constant volume, (b) at constant pressure, and (c) adiabatically.

A 250-g sample of water at 80C is mixed with 250 g of water at10C. Find the entropy changes for (a) the hot water, (b) the coolwater, and (c) the system.

An ideal gas undergoes a process that takes it from pressure p1and volume V1 to p2 and V2, such that p1Vg1 = p2Vg2, where g is the specific heat ratio. Find the entropy change if the process consists of constant-pressure and constant-volume segments.Why does your result make sense?

In an adiabatic free expansion, 6.36 mol of ideal gas at 305 Kexpands 15-fold in volume. How much energy becomes unavailableto do work?

Find the entropy change when a 2.4-kg aluminum pan at 155C is plunged into 3.5 kg of water at 15C.

An engine with mechanical power output 8.5 kW extracts heat from a source at 420 K and rejects it to a 1000-kg block of ice at its melting point. (a) Whats its efficiency? (b) How long can it maintain this efficiency if the ice isnt replenished?

Find the change in entropy as 2.00 kg of H2O at 100C turns to vapor at the same temperature.

Gasoline engines operate approximately on the Otto cycle, consisting of two adiabatic and two constant-volume segments. Figure 19.24 shows the Otto cycle for a particular engine. (a) If the gas in the engine has specific heat ratio g, find the engines efficiency, assuming all processes are reversible. (b) Find the maximum temperature in terms of the minimum temperature Tmin. (c) How does the efficiency compare with that of a Carnot engine operating between the same temperature extremes?

The compression ratio r of an engine is the ratio of maximum to minimum gas volume. (For the gasoline engine of the preceding problem, Fig. 19.24 shows that the compression ratio is 5.) Find a general expression for the engine efficiency of an Otto-cycle engine as a function of compression ratio

In a diesel cycle, gas at volume V1 and pressure p1 undergoes adiabatic compression to a smaller volume V2. It is then heated at constant pressure while it expands to volume V3. The gas then expands adiabatically until its again at volume V1, whereupon it cools, at constant volume, until its back to its initial state of p1 and V1. Show that the work done by the engine over one cycle can be written as W = p1V1 3rg-1 1a - 12g - ag + 14 g - 1 . Here r = V1/V2 is the compression ratio and a = V3/V2 is the so-called cutoff ratio

(a) Show that the heat flowing into the diesel engine of Problem 56 during the cycle (not the net heat flow) is given by Qin = p1V1rg-1 1a - 12g g - 1 . (b) Use this quantity, along with the result of Problem 56, to show that the diesel engines efficiency can be written as ediesel = 1 - r1-g 1ag - 12 1a - 12g .

Youre considering buying a car that comes in either gasoline or diesel versions. The gas engine has compression ratio r = 8.3, while the diesel has compression ratio r = 19 and cutoff ratio a = 2.4. Use the results of Problems 55 and 57 to determine which engine is more efficient. Both engines breathe air, which is diatomic

The 54-MW wood-fired McNeil Generating Station in Burlington, Vermont, produces steam at 950F to drive its turbines, and condensed steam returns to the boiler as 90F water. (Note the temperatures in F, used in U.S. engineering situations.) Find McNeils maximum thermodynamic efficiency, and compare with its actual efficiency of 25%.

A 500-g copper block at 80C is dropped into 1.0 kg of water at 10C. Find (a) the final temperature and (b) the entropy change of the system.

An objects heat capacity is inversely proportional to its absolute temperature: C = C01T0/T2, where C0 and T0 are constants. Find the entropy change when the object is heated from T0 to T1.

A Carnot engine extracts heat from a block of mass m and specific heat c initially at temperature Th0 but without a heat source to maintain that temperature. The engine rejects heat to a reservoir at constant temperature Tc. The engine is operated so its mechanical power output is proportional to the temperature difference Th - Tc: P = P0 Th - Tc Th0 - Tc where Th is the instantaneous temperature of the hot block and P0 is the initial power. (a) Find an expression for Th as a function of time, and (b) determine how long it takes for the engines power output to reach zero.

In an alternative universe, youve got the impossible: an infinite heat reservoir, containing infinite energy at temperature Th. But youve only got a finite cool reservoir, with initial temperature Tc0 and heat capacity C. Find an expression for the maximum work you can extract if you operate an engine between these two reservoirs

Youre the environmental protection officer for a 35% efficient nuclear power plant that produces 750 MW of electric power, situated on a river whose minimum flow rate is 110m3 /s. State environmental regulations limit the rise in river temperature from your plants cooling system to 5C. Can you achieve this standard if you use river water for all your cooling, or will you need to install cooling towers that transfer some of your waste heat to the atmosphere?

Find an expression for the entropy gain when hot and cold water are irreversibly mixed. A corresponding reversible process you can use to calculate this change is to bring each water sample slowly to their common final temperature Tf and then mix them. Express your answer in terms of the initial temperatures Th and Tc. Assume equal masses of hot and cold water, with constant specific heat c. Whats the sign of your answer?

Problem 74 of Chapter 16 provided an approximate expression for the specific heat of copper at low absolute temperatures: c = 311T/343 K23 J/kg # K. Use this to find the entropy change when 40 g of copper are cooled from 25 K to 10 K. Why is the change negative?

The molar specific heat at constant pressure for a certain gas is given by Cp = a + bT + cT2 , where a = 33.6 J/mol # K, b = 2.93*10-3 J/mol # K2 , and c = 2.13*10-5 J/mol # K3 . Find the entropy change when 2.00 moles of this gas are heated from 20.0C to 200C

Consider a gas containing an even number N of molecules, distributed among the two halves of a closed box. Find expressions for (a) the total number of microstates and (b) the number of microstates with half the molecules on each side of the box. (You can either work out a formula, or explore the term combinations in a math reference source.) (c) Use these results to find the ratio of the probability that all the molecules will be found on one side of the box to the probability that there will be equal numbers on both sides. (d) Evaluate for N = 4 and N = 100.

Energy-efficiency specialists measure the heat Qh delivered by a heat pump and the corresponding electrical energy W needed to run the pump, and they compute the pumps COP as the ratio Qh/W. They also measure the outdoor temperature, and they know that the pump produces hot water at Th = 52C. The table below shows their results for Q and T. (a) Determine a quantity that, when you plot the COP against it, should give a straight line. (b) Make your plot, fit a straight line, and from it determine how the heat pumps COP compares with the theoretical maximum COP.

Refrigerators remain among the greatest consumers of electrical energy in most homes, although mandated efficiency standards have decreased their energy consumption by some 80% in the past four decades. In the course of a day, one kitchen refrigerator removes 30 MJ of energy from its contents, in the process consuming 10 MJ of electrical energy. The electricity comes from a 40% efficient coal-fired power plant The electrical energy a. is used to run the light bulb inside the refrigerator. b. wouldnt be necessary if the refrigerator had enough insulation. c. retains its high-quality status after the refrigerator has used it. d. ends up as waste heat rejected to the kitchen environment.

Refrigerators remain among the greatest consumers of electrical energy in most homes, although mandated efficiency standards have decreased their energy consumption by some 80% in the past four decades. In the course of a day, one kitchen refrigerator removes 30 MJ of energy from its contents, in the process consuming 10 MJ of electrical energy. The electricity comes from a 40% efficient coal-fired power plant The refrigerators COP is a. 1 3. b. 2. c. 3. d. 4.

Refrigerators remain among the greatest consumers of electrical energy in most homes, although mandated efficiency standards have decreased their energy consumption by some 80% in the past four decades. In the course of a day, one kitchen refrigerator removes 30 MJ of energy from its contents, in the process consuming 10 MJ of electrical energy. The electricity comes from a 40% efficient coal-fired power plant The fuel energy consumed at the power plant to run this refrigerator for the day is a. 12 MJ. b. 25 MJ. c. 40 MJ. d. 75 MJ.

Refrigerators remain among the greatest consumers of electrical energy in most homes, although mandated efficiency standards have decreased their energy consumption by some 80% in the past four decades. In the course of a day, one kitchen refrigerator removes 30 MJ of energy from its contents, in the process consuming 10 MJ of electrical energy. The electricity comes from a 40% efficient coal-fired power plant The total energy rejected to the surrounding kitchen during the course of the day is a. 10 MJ. b. 30 MJ. c. 40 MJ. d. 75 MJ.