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Energy transfers by heat through the exterior walls and roof of a house at a rate of5.00103J/s=5.00kW5.00103J/s=5.00kWwhen the interior temperature is22.0C22.0Cand the outside temperature is5.00C5.00C.

(a) Calculate the electric power required to maintain the interior temperature at22.0C22.0Cif the power is used in electric resistance heaters that convert all the energy transferred in by electrical transmission into internal energy.

(b) What If? Calculate the electric power required to maintain the interior temperature at22.0C22.0Cif the power is used to drive an electric motor that operates the compressor of a heat pump that has a coefficient of performance equal to 60.0%%of the Carnot-cycle value.

In 1993, the U.S. government instituted a requirement that all room air conditioners sold in the United States must have an energy efficiency ratio (EER) of 10 or higher. The EER is defined as the ratio of the cooling capacity of the air conditioner, measured in British thermal units per hour, or Btu/h, to its electrical power requirement in watts.

(a) Convert the EER of 10.0 to dimensionless form, using the conversion1Btu=1055J1Btu=1055J.

(b) What is the appropriate name for this dimensionless quantity? (c) In the 1970ss, it was common to find room air conditioners with EERs, of 5 or lower. State how the operating costs compare for 10 000 -Btu/h air conditioners with EERs of 5.00 and 10.0 . Assume each air conditioner operates for 1500 h during the summer in a city where electricity costs 17.0perkWhkWh.

In 1816, Robert Stirling, a Scottish clergyman, patented the Stirling engine, which has found a wide variety of applications ever since, including the solar power application discussed on the cover of this textbook. Fuel is burned externally to warm one of the engine's two cylinders. A fixed quantity of inert gas moves cyclically between the cylinders, expanding in the hot one and contracting in the cold one. Figure P22.57 represents a model for its thermodynamic cycle. Consider n moles of an ideal monatomic gas being taken once through the cycle, consisting of two isothermal processes at temperatures 3TiTiandTiTiand two constant- volume processes.

Let us find the efficiency of this engine.

(a) Find the energy transferred by heat into the gas during the isovolumetric process AB.

(b) Find the energy transferred by heat into the gas during the isothermal process BC.

(c) Find the energy transferred by heat into the gas during the isovolumetric process CD.

(d) Find the energy transferred by heat into the gas during the isothermal process DA.

(e) Identify which of the results from parts (a) through (d) are positive and evaluate the energy input to the engine by heat.

(f) From the first law of thermodynamics, find the work done by the engine.

(g) From the results of parts (e) and (f), evaluate the efficiency of the engine. A Stirling engine is easier to manufacture than an internal combustion engine or a turbine. It can run on burning garbage. It can run on the energy transferred by sunlight and produce no material exhaust. Stirling engines are not currently used in automobiles due to long startup times and poor acceleration response.

A firebox is at 750 K, and the ambient temperature is 300KK. The efficiency of a Carnot engine doing 150JofJofwork as it transports cnergy between these constant-temperature baths is 60.0%%. The Carnot engine must take in energy150J/0.600=250J150J/0.600=250Jfrom the hot reservon and must put out 100JJof energy by heat into the environment. To follow Carnot's reasoning, suppose some other heat engine S could have an efficicncy of 70.0%%

(a) Find the cnergy input and exhaust energy output of engineSSas it does 150JJof work. (b) Let engine S operate as in part (a) and run the Carnot engine in reverse between the same reservoirs. The output work of engineSSis the input work for the Carnot refrigerator. Find the total energy transferred to or from the firebox and the total energy transferred to or from the environment as both engines operate together. (c) Explain how the results of parts (a) and

(b) show that the Clausius statement of the second law of thermodynamics is violated. (d) Find the energy input and work output of engine S as it puts out exhaust energy of 100JJJ. Let engine S operate as in part

(c) and contribute 150JJof its work output to running the Carnot engine in reverse. Find (e) the total energy the firebox puts out as both engines operate together, (f) the total work output, and (g) the total energy transferred to the environment.

(h) Explain how the results show that the Kelvin-Planck statement of the second law is violated. Therefore, our assumption about the efficiency of engine S must be false.

(i) Let the engines operate together through one cycle as in part (d). Find the change in entropy of the Universe. (j) Explain how the result of part (i) shows that the entropy statement of the second law is violated.

In the operation of a single cylinder internal combustion piston engine, one charge of fuel explodes to drive the piston outward in the power stroke. Part of its energy output is stored in a turning flywheel. This energy is then used to push the piston inward to compress the next charge of fuel and air. In this compression process, assume an original volume of 0.120 L of a diatomic ideal gas at atmospheric pressure is compressed adiabatically to one-eighth of its original volume.

(a) Find the work input required to compress the gas.

(b) Assume the flywheel is a solid disk of mass 5.10 kg and radius 8.50 cm, turning freely without friction between the power stroke and the compression stroke. How fast must the flywheel turn immediately after the power stroke? This situation represents the minimum angular speed at which the engine can operate without stalling.

(c) When the engine's operation is well above the point of stalling, assume the flywheel puts 5.00% of its maximum energy into compressing the next charge of fuel and air. Find its maximum angular speed in this case.

A system consisting ofnnmoles of an ideal gas with molar specific heat at constant pressureCPCPundergoes two reversible processes. It starts with pressurePiPiand volumeVi,Vi,expands isothermally, and then contracts adiabatically to reach a final state with pressurePiPiand volume 3ViVi(a) Find its change in entropy in the isothermal process. (The entropy does not change in the adiabatic process.) (b) What If? Explain why the answer to part

1. must be the same as the answer to Problem 65 . (You do not need to solve Problem 65 to answer this question.)

A sample of an ideal gas expands isothermally, doubling in volume. (a) Show that the work done on the gas in expanding isW=nRTW=nRTin2.2.(b) Because the internal energyEintEintof an ideal gas depends solely on its temperature, the change in internal energy is zero during the expansion. It follows from the first law that the energy input to the gas by heat during the expansion is equal to the energy output by work. Does this process have 100%%efficiency in converting energy input by heat into work output? (C) Does this conversion violate the second law? Explain.

The compression ratio of an Otto cycle as shown in Active Figure 22.12 isVA/VB=8.00.VA/VB=8.00.At the beginningAAof the compression process, 500cm3cm3of gas is at 100kPakPaand20.0C20.0C. At the beginning of the adiabatic expansion, the temperature isTC=750CTC=750C. Model the working fluid as an ideal gas with=1.40.=1.40.(a) Fill in this table to follow the states of the gas: (c) Identify the energy inputQk,|Qk|,(d) the energy exhaust|Q|,|Q|,and (e) the net output workWcngWcng(f) Calculate the thermal efficiency. (g) Find the number of crankshaft revolutions per minute required for a one-cylinder engine to have an output power of1.00kW=1.34hp.1.00kW=1.34hp.Note: The thermodynamic cycle involves four piston strokes.

An electric power plant that would make use of the temperature gradient in the ocean has been proposed. The system is to operate between20.0C20.0C(surface-water temperature) and5.00C5.00C(water temperature at a depth of about 1kmkm). (a) What is the maximum efficiency of such a system? (b) If the electric power output of the plant is 75.0 MW, how much energy is taken in from the warm reservoir per hour? (c) In view of your answer to part (a), explain whether you think such a system is worthwhile. Note that the "fuel" is free.

A multicylinder gasoline engine in an airplane, operating at2.501032.50103rev/min, takes in energy7.89103J7.89103Jand exhausts4.58103J4.58103Jfor each revolution of the crankshaft. (a) How many liters of fuel does it consume in 1.00hhof operation if the heat of combustion of the fuel is equal to4.03107J/L24.03107J/L2(b) What is the mechanical power output of the engine? Ignore friction and express the answer in horsepower. (c) What is the torque exerted by the crank-shaft on the load? (d) What power must the exhaust and cooling system transfer out of the engine?

Why is the following situation impossible? An inventor comes to a patent office with the claim that her heat engine, which employs water as a working substance, has a thermodynamic efficiency of 0.110 . Although this efficiency is low compared with typical automobile engines, she explains that her engine operates between an energy reservoir at room temperature and a water-ice mixture at atmospheric pressure and therefore requires no fuel other than that to make the ice. The patent is approved, and working prototypes of the engine prove the inventor's efficiency claim.