Plan for Today (AP Physics 2) Lecture/Notes on Heat Engines, Carnot Engines, and Entropy

Energy Transfer by Conduction Kinetic energy exchange between microscopic particles Collisions take place between particles, energy transfer, and gradually it works through a material

Conduction Rate depends on properties of the substance Metals are good thermal conductors (free electrons to transfer energy)

Conduction Only occurs if there is a difference in temperature Temperature difference drives the flow in energy

Conduction Rate of energy transfer is proportional to the cross sectional area of the slab and the temperature difference H = Q/t And is inversely proportional to the thickness of the slab

Conduction Equation k is proportionality constant, depending on the material

Heat engine A device that takes in heat energy and converts some of it to other forms of energy (like mechanical) Work done by a heat engine through a cyclic process is W = |Qh| - |Qc| Qh is energy absorbed from hot reservoir, Qc is energy expelled to cold

HEAT ENGINES Qhot Wout Qcold A heat engine is any device which through a cyclic process: Cold Res. TC Engine Hot Res. TH Qhot Wout Qcold Absorbs heat Qhot Performs work Wout Rejects heat Qcold

THE SECOND LAW OF THERMODYNAMICS Wout Cold Res. TC Engine Hot Res. TH Qhot Qcold It is impossible to construct an engine that, operating in a cycle, produces no effect other than the extraction of heat from a reservoir and the performance of an equivalent amount of work. Not only can you not win (1st law); you can’t even break even (2nd law)!

THE SECOND LAW OF THERMODYNAMICS Cold Res. TC Engine Hot Res. TH 400 J 300 J 100 J A possible engine. An IMPOSSIBLE engine. Cold Res. TC Engine Hot Res. TH 400 J

EFFICIENCY OF AN ENGINE The efficiency of a heat engine is the ratio of the net work done W to the heat input QH. Cold Res. TC Engine Hot Res. TH QH W QC e = = W QH QH- QC e = 1 - QC QH

EFFICIENCY EXAMPLE 800 J W 600 J An engine absorbs 800 J and wastes 600 J every cycle. What is the efficiency? Cold Res. TC Engine Hot Res. TH 800 J W 600 J e = 1 - QC QH e = 1 - 600 J 800 J e = 25% Question: How many joules of work is done?

Carnot Engine No real engine operating between two reservoirs can be more efficient than a Carnot engine

Carnot Engine Substance whose temperature varies between Tc and Th Ideal gas in a cylinder with a movable piston Cycle consists of 2 adiabatic and 2 isothermal processes

EFFICIENCY OF AN IDEAL ENGINE (Carnot Engine) Cold Res. TC Engine Hot Res. TH QH W QC For a perfect engine, the quantities Q of heat gained and lost are proportional to the absolute temperatures T. e = TH- TC TH e = 1 - TC TH

Example 3: A steam engine absorbs 600 J of heat at 500 K and the exhaust temperature is 300 K. If the actual efficiency is only half of the ideal efficiency, how much work is done during each cycle? Actual e = 0.5ei = 20% e = 1 - TC TH e = W QH e = 1 - 300 K 500 K W = eQH = 0.20 (600 J) e = 40% Work = 120 J

REFRIGERATORS Qhot Win Win + Qcold = Qhot Qcold WIN = Qhot - Qcold A refrigerator is an engine operating in reverse: Work is done on gas extracting heat from cold reservoir and depositing heat into hot reservoir. Cold Res. TC Engine Hot Res. TH Qhot Qcold Win Win + Qcold = Qhot WIN = Qhot - Qcold

THE SECOND LAW FOR REFRIGERATORS It is impossible to construct a refrigerator that absorbs heat from a cold reservoir and deposits equal heat to a hot reservoir with W = 0. Cold Res. TC Engine Hot Res. TH Qhot Qcold If this were possible, we could establish perpetual motion!

Second Law of Thermodynamics Energy will not flow spontaneously by heat from a cold object to a hot object No heat engine operating in a cycle can absorb energy from a reservoir and perform an equal amount of work

Entropy Systems tend toward disorder A disorderly arrangement is more probable than an orderly one Entropy is a measure of the disorder The entropy of the Universe increases in all natural processes (alternate 2nd law)

Entropy The change in entropy is equal to the energy flowing into a system (while the system changes from one state to another) divided by the absolute temperature Change in S = Qr/T

COEFFICIENT OF PERFORMANCE Cold Res. TC Engine Hot Res. TH QH W QC The COP (K) of a heat engine is the ratio of the HEAT Qc extracted to the net WORK done W. QC W K = = QH QH- QC K = TH TH- TC For an IDEAL refrigerator:

COP EXAMPLE A Carnot refrigerator operates between 500 K and 400 K. It extracts 800 J from a cold reservoir during each cycle. What is C.O.P., W and QH ? Cold Res. TC Eng ine Hot Res. TH 800 J W QH 500 K 400 K K = 400 K 500 K - 400 K TC TH- TC = C.O.P. (K) = 4.0

COP EXAMPLE (Cont.) QH W 800 J 500 K 400 K Cold Res. TC Eng ine Hot Res. TH 800 J W QH 500 K 400 K Next we will find QH by assuming same K for actual refrigerator (Carnot). K = QC QH- QC 800 J QH - 800 J = 4.0 QH = 1000 J

COP EXAMPLE (Cont.) 1000 J W 800 J 500 K Cold Res. TC Engine Hot Res. TH 800 J W 1000 J 500 K 400 K Now, can you say how much work is done in each cycle? Work = 1000 J - 800 J Work = 200 J

Q = U + W final - initial) Summary The First Law of Thermodynamics: The net heat taken in by a system is equal to the sum of the change in internal energy and the work done by the system. Q = U + W final - initial) Isochoric Process: V = 0, W = 0 Isobaric Process: P = 0 Isothermal Process: T = 0, U = 0 Adiabatic Process: Q = 0

The following are true for ANY process: Summary (Cont.) The Molar Specific Heat capacity, C: Units are:Joules per mole per Kelvin degree c = Q n T The following are true for ANY process: Q = U + W U = nCv T PV = nRT

Summary (Cont.) Qhot Wout Qcold Cold Res. TC Engine Hot Res. TH Qhot Qcold Wout The Second Law of Thermo: It is impossible to construct an engine that, operating in a cycle, produces no effect other than the extraction of heat from a reservoir and the performance of an equivalent amount of work. Not only can you not win (1st law); you can’t even break even (2nd law)!

Summary (Cont.) The efficiency of a heat engine: e = 1 - QC QH e = 1 - TC TH The coefficient of performance of a refrigerator: