Heat Engines Quickcheck 19.11

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Chapter 19 Heat Engines QuickCheck 19.11

The efficiency of this Carnot heat engine is

A. Less than 0.5. B. 0.5. C. Between 0.5 and 1.0. D. 2.0. E. Can’t say without

knowing QH.

The efficiency of this Carnot heat engine is

A. Less than 0.5. B. 0.5. C. Between 0.5 and 1.0. D. 2.0. E. Can’t say without

knowing QH.

Qc TTcc andec  1  QTTh h h

Qc Tc Qh Th COPC  COPH  WTThc WTThc Heat Engines . In a steam turbine of a modern power plant, expanding steam does work by spinning the turbine. . The steam is then condensed to liquid water and pumped back to the boiler to start the process again. . First heat is transferred to the water in the boiler to create steam, and later heat is transferred out of the water to an external cold reservoir, in the condenser. . This steam generator is an example of a heat engine. © 2013 Pearson Education, Inc. Slide 19-33 Heat Engine Energy Transfer Diagram

Eint = 0 for the entire cycle

 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

WQQe n g 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 What’s the efficiency of our engine? W QQQ e eng h c 1  c QQQh h h W QQQ e eng h c 1  c QQQ Efficiency h h h Heat Engine Problems Rank in order, from largest to smallest, the work Wout performed by these four heat engines.

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 QuickCheck 19.5

The efficiency of this heat engine is

A. 1.00. B. 0.60. C. 0.50. D. 0.40. E. 0.20.

The efficiency of this heat engine is

A. 1.00. B. 0.60. C. 0.50. D. 0.40. E. 0.20.

How much heat is exhausted to the cold reservoir?

A. 7000 J. B. 5000 J. C. 3000 J. D. 2000 J. E. 0 J.

How much heat is exhausted to the cold reservoir?

A. 7000 J. B. 5000 J. C. 3000 J. D. 2000 J. E. 0 J.

Which heat engine has the larger efficiency?

A. Engine 1. B. Engine 2. C. They have the same efficiency. D. Can’t tell without knowing the number of moles of gas.

Which heat engine has the larger efficiency?

A. Engine 1. B. Engine 2. C. They have the same efficiency. D. Can’t tell without knowing the number of moles of gas.

 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 Refrigerators

. In a sense, a refrigerator or air conditioner is the opposite of a heat engine. . In a heat engine, heat energy flows from a hot reservoir to a cool

reservoir, and work Wout is produced. . In a refrigerator, heat energy is somehow forced to flow from a cool reservoir to a hot reservoir, but it requires

work Win to make this happen.

 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 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. energy transferred at high temp Q COP =  h heating work done by heat pump W

QQhh  0.100 WW Carnot cycle

Q h Th 293 K 0.100  0.100  1.17 WTThc293 K 268 K

1.17 joules of energy enter the room by heat for each joule of work done. Refrigerators 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. Refrigerators

. Shown is the energy- transfer diagram of a refrigerator. . All state variables (pressure, temperature, thermal energy, etc.) return to their initial values once every cycle. . The heat exhausted per cycle by a refrigerator is:

QH = QC +Win

© 2013 Pearson Education, Inc. Slide 19-42 Refrigerators . The purpose of a refrigerator is to remove heat from a cold reservoir, and it requires work input to do this. . We define the coefficient of performance K of a refrigerator to be:

. If a “perfect refrigerator” could be built in which Win = 0, then heat would move spontaneously from cold to hot. . This is expressly forbidden by the second law of thermodynamics:

The coefficient of performance of this refrigerator is

A. 0.40. B. 0.60. C. 1.50. D. 1.67. E. 2.00.

The coefficient of performance of this refrigerator is

A. 0.40. B. 0.60. C. 1.50. D. 1.67. E. 2.00.

Heat Engine: Lab The Brayton Cycle

. Many ideal-gas heat engines, such as jet engines in aircraft, use the Brayton Cycle, as shown. . The cycle involves adiabatic compression (1-2), isobaric heating during combustion (2-3), adiabatic expansion which does work (3-4), and isobaric cooling (4-1). . The efficiency is:

The Otto cycle approximates the processes occurring in an internal combustion engine

If the air-fuel mixture is assumed to be an ideal gas, then the efficiency of the Otto cycle is 1 e 1  1 VV12  is the ratio of the molar specific heats

V1 / V2 is called the compression ratio Typical values: Compression ratio of 8  = 1.4 e = 56%

Efficiencies of real engines are 15% to 20% Mainly due to friction, energy transfer by conduction, incomplete combustion of the air-fuel mixture 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 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 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. Sadi Carnot The Limits of Efficiency A perfectly reversible engine must use only two types of processes: 1. Frictionless mechanical interactions with no heat transfer (Q = 0) 2. Thermal interactions in which heat is transferred in

an isothermal process (ΔEth = 0).

Any engine that uses only these two types of processes is called a Carnot engine.

A Carnot engine is a perfectly reversible engine; it has the maximum possible thermal efficiency and, if operated as a refrigerator, the maximum possible coefficient of performance. 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 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. QuickCheck 19.11

The efficiency of this Carnot heat engine is

A. Less than 0.5. B. 0.5. C. Between 0.5 and 1.0. D. 2.0. E. Can’t say without

knowing QH.

The efficiency of this Carnot heat engine is

A. Less than 0.5. B. 0.5. C. Between 0.5 and 1.0. D. 2.0. E. Can’t say without

knowing QH.

 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 QuickCheck 19.11

The efficiency of this Carnot heat engine is

A. Less than 0.5. B. 0.5. C. Between 0.5 and 1.0. D. 2.0. E. Can’t say without

knowing QH.

The efficiency of this Carnot heat engine is

A. Less than 0.5. B. 0.5. C. Between 0.5 and 1.0. D. 2.0. E. Can’t say without

knowing QH.

Qc TTcc andec  1  QTTh h h

Qc Tc Qh Th COPC  COPH  WTThc WTThc Limits of Heat Efficiency

This heat engine is

A. A reversible Carnot engine. B. An irreversible engine. C. An impossible engine.

This heat engine is

A. A reversible Carnot engine. B. An irreversible engine. C. An impossible engine.

• 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 Entropy Reversible and Irreversible Processes The Arrow of Time! Play the Movie Backwards! https://www.youtube.com/watc h?v=yKbJ9leUNDE

https://www.youtube.com/watch?v=GdTMuivYF30 Entropy on a Microscopic Scale We can treat entropy from a microscopic viewpoint through statistical analysis of molecular motions. A connection between entropy and the number of microstates (W) for a given macrostate is

S = kB ln W . The more microstates that correspond to a given macrostate, the greater the entropy of that macrostate. This shows that entropy is a measure of disorder.

Section 22.8 Entropy

https://www.youtube.com/watch?v=yKbJ9leUNDE Heat Death of the Universe

Ultimately, the entropy of the Universe should reach a maximum value. At this value, the Universe will be in a state of uniform temperature and density. All physical, chemical, and biological processes will cease. The state of perfect disorder implies that no energy is available for doing work. This state is called the heat death of the Universe.

Big Bang Cosmogenesis The Stellar Age Stars Rule for a Trillion Years In about 5 billion years,

Our Sun will swell into a cool Red Giant, engulfing Mercury, Venus and possibly Earth! The Degenerate Age After about 100 trillion, years, the stars are dead. By 1037 years, the material in the "Local Galaxy" consists of isolated stellar remnants and black holes. Everything is cold and dark. The Black Hole Age

All the stars turn into black holes. After about 10100 years, all the black holes are gone. The Dark Era

The remaining black holes evaporate: first the small ones, and then the supermassive black holes. All matter that used to make up the stars and galaxies has now degenerated into photons and leptons.

Boltzmann was subject to rapid alternation of depressed moods with elevated, expansive or irritable moods, likely the symptoms of undiagnosed bipolar disorder. On September 5, 1906, while on a summer vacation in Duino, near Trieste, Boltzmann hanged himself during an attack of depression. He is buried in the Viennese Zentralfriedhof; his tombstone bears the inscription.