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Heat Engines Important Concepts Heat Engines Refrigerators Important Concepts 2Nd Law of Thermo

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Heat Engines Important Concepts Heat Engines Refrigerators Important Concepts 2Nd Law of Thermo Chapter 19 Heat Engines Important Concepts Heat Engines Refrigerators Important Concepts 2nd Law of Thermo • Heat flows spontaneously from a substance at a higher temperature to a substance at a lower temperature and does not flow spontaneously in the reverse direction. • Heat flows from hot to cold. • Alternative: Irreversible processes must have an increase in Entropy; Reversible processes have no change in Entropy. • Entropy is a measure of disorder in a system 2nd Law: Perfect Heat Engine Can NOT exist! No energy is expelled to the cold reservoir It takes in some amount of energy and does an equal amount of work e = 100% It is an impossible engine No Free Lunch! Limit of efficiency is a Carnot Engine Second Law – Clausius Form It is impossible to construct a cyclical machine whose sole effect is to transfer energy continuously by heat from one object to another object at a higher temperature without the input of energy by work. Or – energy does not transfer spontaneously by heat from a cold object to a hot object. Section 22.2 Heat Pumps and Refrigerators Heat engines can run in reverse This is not a natural direction of energy transfer Must put some energy into a device to do this Devices that do this are called heat pumps or refrigerators energy transferred at high temp Q COP = h heating work done by heat pump W energy transferred at low temp Q COP = C cooling work done by heat pump W A heat pump, is essentially an air conditioner installed backward. It extracts energy from colder air outside and deposits it in a warmer room. Suppose that the ratio of the actual energy entering the room to the work done by the device’s motor is 10.0% of the theoretical maximum ratio. Determine the energy entering the room per joule of work done by the motor, given that the inside temperature is 20.0°C and the outside temperature is –5.00°C. QQhh 0.100 WW Carnot cycle energy transferred at high temp Q COP = h heating work done by heat pump W Q h Th 293 K 0.100 0.100 1.17 WTThc293 K 268 K 1.17 joules of energy enter the room by heat for each joule of work done. Heat Pumps Refrigerators Reversible and Irreversible Processes The Arrow of Time! Play the Movie Backwards! Entropy The Maximum Efficiency Qc TTcc andec 1 QTTh h h Qc Tc Qh Th COPC COPH WTThc WTThc Reversible and Irreversible Processes The reversible process is an idealization. All real processes on Earth are irreversible. Example of an approximate reversible process: The gas is compressed isothermally The gas is in contact with an energy reservoir Continually transfer just enough energy to keep the temperature constant The change in entropy is equal to zero for a reversible process and increases for irreversible processes. Section 22.3 Eint = 0 for the entire cycle Heat Engine A heat engine is a device that takes in energy by heat and, operating in a cyclic process, expels a fraction of that energy by means of work A heat engine carries some working substance through a cyclical process The working substance absorbs energy by heat from a high temperature energy reservoir (Qh) Work is done by the engine (Weng) Energy is expelled as heat to a lower temperature reservoir (Qc) Thermal Efficiency of a Heat Engine Eint = 0 for the entire cycle WQQeng hc Thermal efficiency is defined as the ratio of the net work done by the engine during one cycle to the energy input at the higher temperature W QQQ e eng h c 1 c QQQh h h Rank in order, from largest to smallest, the work Wout performed by these four heat engines. W QQQ e eng h c 1 c QQQh h h A. Wb > Wa > Wc > Wd B. Wb > Wa > Wb > Wc C. Wb > Wa > Wb = Wc D. Wd > Wa = Wb > Wc E. Wd > Wa > Wb > Wc Rank in order, from largest to smallest, the work Wout performed by these four heat engines. W QQQ e eng h c 1 c QQQh h h A. Wb > Wa > Wc > Wd B. Wb > Wa > Wb > Wc C. Wb > Wa > Wb = Wc D. Wd > Wa = Wb > Wc E. Wd > Wa > Wb > Wc Analyze this engine to determine (a) the net work done per cycle, (b) the engine’s thermal efficiency and (c) the engine’s power output if it runs at 600 rpm. Assume the gas is monatomic and follows the ideal- gas process above. 2nd Law: Carnot’s Theorem No real heat engine operating between two energy reservoirs can be more efficient than a Carnot engine operating between the same two reservoirs All real engines are less efficient than a Carnot engine because they do not operate through a 1796 – 1832 reversible cycle French engineer The efficiency of a real engine is further reduced by friction, energy losses through conduction, etc. The Carnot cycle is an ideal-gas cycle that consists of the two adiabatic processes (Q = 0) and the two isothermal processes (ΔEth = 0) shown. These are the two types of processes allowed in a perfectly reversible gas engine. Section 22.4 The Carnot cycle is an ideal-gas cycle that consists of the two adiabatic processes (Q = 0) and the two isothermal processes (ΔEth = 0) shown. These are the two types of processes allowed in a perfectly reversible gas engine. Section 22.4 Carnot Cycle, A to B A → B is an isothermal expansion. The gas is placed in contact with the high temperature reservoir, Th. The gas absorbs heat |Qh|. The gas does work WAB in raising the piston. Section 22.4 Carnot Cycle, B to C B → C is an adiabatic expansion. The base of the cylinder is replaced by a thermally nonconducting wall. No energy enters or leaves the system by heat. The temperature falls from Th to Tc. The gas does work WBC. Section 22.4 Carnot Cycle, C to D The gas is placed in thermal contact with the cold temperature reservoir. C → D is an isothermal compression. The gas expels energy |Qc|. Work WCD is done on the gas. Section 22.4 Carnot Cycle, D to A D → A is an adiabatic compression. The base is replaced by a thermally nonconducting wall. So no heat is exchanged with the surroundings. The temperature of the gas increases from Tc to Th. The work done on the gas is WDA. Section 22.4 Carnot Engine – Carnot Cycle A heat engine operating in an ideal, reversible cycle (now called a Carnot cycle) between two reservoirs is the most efficient engine possible. This sets an upper limit on the efficiencies of all other engines Qc TTcc andec 1 QTTh h h Temperatures must be in Kelvins Carnot Cycle Problem An ideal gas is taken through a Carnot cycle. The isothermal expansion occurs at 250°C, and the isothermal compression takes place at 50.0°C. The gas takes in 1 200 J of energy from the hot reservoir during the isothermal expansion. Find (a) the energy expelled to the cold reservoir in each cycle and (b) (b) the net work done by the gas in each cycle. Refrigerators • Understanding a refrigerator is a little harder than understanding a heat engine. • Heat is always transferred from a hotter object to a colder object. • The gas in a refrigerator can extract heat QC from the cold reservoir only if the gas temperature is lower than the cold-reservoir temperature TC. Heat energy is then transferred from the cold reservoir into the colder gas. • The gas in a refrigerator can exhaust heat QH to the hot reservoir only if the gas temperature is higher than the hot-reservoir temperature TH. Heat energy is then transferred from the warmer gas into the hot reservoir. Coefficient of Performance The effectiveness of a heat pump is described by a number called the coefficient of performance (COP) In heating mode, the COP is the ratio of the heat transferred in to the work required energy transferred at high temp Q COP = h work done by heat pump W COP, Heating Mode COP is similar to efficiency Qh is typically higher than W Values of COP are generally greater than 1 It is possible for them to be less than 1 We would like the COP to be as high as possible COP, Cooling Mode In cooling mode, you “gain” energy from a cold temperature reservoir Q COP c W A good refrigerator should have a high COP Typical values are 5 or 6 Carnot Cycle in Reverse Theoretically, a Carnot-cycle heat engine can run in reverse This would constitute the most effective heat pump available This would determine the maximum possible COPs for a given combination of hot and cold reservoirs Can this refrigerator be built? WQQHC Q COP c W Qc Tc COPC WTThc Free Expansion Consider an adiabatic free expansion. This process is irreversible since the gas would not spontaneously crowd into half the volume after filling the entire volume . The change in entropy is greater than zero for a irreversible processes. Section 22.7 The Limits of Efficiency Everyone knows that heat can produce motion. That it possesses vast motive power no one can doubt, in these days when the steam engine is everywhere so well known. Notwithstanding the satisfactory condition to which they have been brought today, their theory is very little understood. The question has often been raised whether the motive power of heat is unbounded, or whether the possible improvements in steam engines have an assignable limit.
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