Heat Engines, Entropy, & the 2nd Law of Thermodynamics Chapter 18 Heat Engines, Entropy, & the 2nd Law of Thermodynamics

Heat Engines A heat engine is a device that converts internal energy to other useful forms, such as kinetic energy . A heat engine carries some working substance through which cyclic processes during which Energy is transferred from a source at a high temperature Work is done by the engine Energy is expelled by the engine to a source at a lower temperature

DEint = Q + W = 0 Qnet = - W = Weng Heat Engines A process that utilizes heat energy input (Qh) to enable a working substance perform work output. Because the working substance goes through a cycle, DEint =0. From the 1st law, DEint = Q + W = 0 Qnet = - W = Weng Qh Weng Qc Heat Engine Hot reservoir at Th Cold reservoir at Tc Qh Weng Qc Heat Engine Hot reservoir at Th Cold reservoir at Tc Weng = |Qh|-|Qc| = Qnet

Heat Engines If the working substance is a gas, the net work done by the engine for a cyclic process is the area enclosed by the curve representing the process on a PV diagram. The thermal efficiency e Efficiency = e = Weng/|Qh| = (|Qh| - |Qc| ) /|Qh| =1 - |Qc|/|Qh| P Area=Weng o V

Heat engines High T, high P gas Low T, low P gas Condenser Hot reservoir

The 2nd Law of Thermodynamics The Kelvin-Planck statement of the 2nd law of thermodynamics: It is impossible to construct a heat engine that, operating in a cycle, produces on effect other than the absorption of energy from a reservoir and the performance of an equal amount of work. impossible to achieve e =100%

The Carnot (“ideal”) engine A reversible process is one for which the system can be return to its initial conditions along the same path and for which every point along the path is an equilibrium state. A process dose not satisfy these requirements is irreversible.

The Carnot (“ideal”) engine A heat engine operating in an ideal, reversible cycle — called a Carnot cycle — between two energy reservoirs is the most efficient engine possible. An “ideal” reversible heat engine (no heat engine can be more efficient than a Carnot engine). Sadi Carnot (1796-1832)

A->B Isothermal expansion A 4 stage engine that operates between 2 temperature reservoirs (Th and Tc) consisting of 2 isothermal phases 2 adiabatic phases D->A Adiabatic compression A->B: isothermal expansion at Th. The gas absorbs Qh from the reservoir and does work WAB in raising the piston. B->C Adiabatic expansion C->D Isothermal compression

A->B Isothermal expansion A 4 stage engine that operates between 2 temperature reservoirs (Th and Tc) consisting of 2 isothermal phases 2 adiabatic phases D->A Adiabatic compression B->C: adiabatic expansion. No energy enters or leaves the system by heat. T falls from Th to Tc and the gas does work WBC in raising the piston. B->C Adiabatic expansion C->D Isothermal compression

A->B Isothermal expansion A 4 stage engine that operates between 2 temperature reservoirs (Th and Tc) consisting of 2 isothermal phases 2 adiabatic phases D->A Adiabatic compression C->D: isothermal compression at Tc. The gas expels Qc to the reservoir and the work done on the gas is WCD. B->C Adiabatic expansion C->D Isothermal compression

A->B Isothermal expansion A 4 stage engine that operates between 2 temperature reservoirs (Th and Tc) consisting of 2 isothermal phases 2 adiabatic phases D->A Adiabatic compression D->A: adiabatic compression. No energy enters or leaves the system by heat. T increases from Tc to Th and the work done on the gas is WDA. B->C Adiabatic expansion C->D Isothermal compression

The Carnot (“ideal”) engine For the Carnot (“ideal”) engine: Efficiency = e Carnot = (|Qh|– |Qc|)/|Qh| since |Qh| / |Qc| = Th/Tc the efficiency can be written as eCarnot = [(Th-Tc)/Th ].100% = 1-Tc/Th

Heat Pumps & Refrigerators How to move energy from the cold reservoir to the hot reservoir? Transfer some energy into a device! Qh W Qc Heat pump Hot reservoir at Th Cold reservoir at Tc

Heat Pumps & Refrigerators The coefficient of performance, COP

Heat Pumps

Refrigerators Evaporator Condenser Low T, low P liquid High T, high P Expansion valve

W W A B D C A B D C Heat engine Heat pump Hot reservoir Hot reservoir Cold reservoir W A B C D

Heat Pumps

The 2nd Law of Thermodynamics 2nd Law: thermodynamic limit of heat engine efficiency Heat only flows spontaneously from high T to cold T A heat engine can never be more efficient that a “Carnot” engine operating between the same hot & cold temperature range The total entropy of the universe never decreases

Entropy Entropy is a measure of the disorder (or randomness) of a system. For a reversible the change in entropy is measured as the ratio of heat gained to temperature dS = dQr/T When heat energy is gained by a system, entropy is gained by the system (and lost by the surrounding environment) When heat is lost by a system, entropy is lost by the system (and gained by the surrounding environment) Entropy is a state function (like energy). Changes in entropy occur independent of path taken by the system.

Entropy Multiplicity = W Entropy = k lnW (k is Boltzmann's constant ) High-probability macrostates are disordered macrostates. Low-probability macrostates are ordered macrostates.

Entropy All physical processes tend toward more probable states for the system andits surroundings. The more probable state is always one of higher disorder.

Entropy & The 2nd Law For the Carnot engine |Qh| / Th= |Qc| /Tc the line integral is path independent For the Carnot engine |Qh| / Th= |Qc| /Tc Qh / Th= -Qc /Tc or Qh / Th + Qc /Tc =0 DS=0 For a system taken through an arbitrary reversible cycle,

Entropy Changes in a Free Expansion This process is neither reversible nor quasi-static. The wall is insulating, Q=0. The work done by gas is W=0. From the 1st Law, DEint = Q + W = 0 Eint,i = Eint,f Ti = Tf Vacuum Vf Vi

Entropy Changes in a Free Expansion Find an equivalent reversible path that share the same initial and final states. An isothermal, reversible expansion, in which the gas pushes slowly against a piston: Vacuum Vf Vi Vf>Vi, DS>0 dQr = -dW = PdV

Entropy Changes in Irreversible Processes The total entropy of an isolated system that undergoes a change cannot decrease. DS≥0 The net entropy change by the universe due to a thermodynamic process: DSuniverse = Sgained - Slost = Qcold/Tcold - Qhot/Thot The total entropy of the universe (Suniverse) will never decrease, it will either Remain unchanged (for a reversible process) Increase (for an irreversible process)

The 2nd Law of Thermodynamics 2nd Law: thermodynamic limit of heat engine efficiency Heat only flows spontaneously from high T to cold T A heat engine can never be more efficient that a “Carnot” engine operating between the same hot & cold temperature range The total entropy of the universe never decreases