C22 - 2nd Law of Thermodynamics

2nd law of thermodynamics (entropy)

All processes in the Universe increase entropy

2nd law of thermodynamics (Clausius statement)

Heat transfer will not occur from a colder area to a warmer area (w/o some input work)

2nd law of thermodynamics (Kelvin-Planck statement)

No heat engine can output work equivalent to the energy input

• i.e. there must be some leakage

e (engine efficiency)

COP_cooling

COP_heating

reversible process

process which can be returned to its initial state (no change in energy or entropy)

• irreversibilities: real-life processes preventing reversibility (friction, deformation, chemical rxn, etc.)

Carnot engine

Ideal, reversible engine with max efficiency possible

• A: isothermal expansion (T_h)

• B: adiabatic expansion

• C: isothermal compression (T_c)

• D: adiabatic compression

PV diagram (carnot)

Q → T relationship (Carnot cycle)

e (Carnot cycle)

COP_{C, cooling}

COP_{C, heating}

Otto cycle

Idealized cycle for 4-stroke spark-plug piston engine

• Intake: valve opens to let combustion gases in

• Compression: increase in pressure

• Power: after pressurized gases are combusted, piston pushed & work is done

• Exhaust: after release, piston rises to spit out exhaust gases

PV diagram (otto)

e_Otto

Entropy

• The amount of microstates/uncertainty given by any given arrangement of a system

  • Macrostate = overall characteristic

  • Microstate = one of many possibilities within a macrostate

• S = k_Bln(W) = nRln(V/V_m)

∆S

∆S_reversible

hp → watts

1 hp = 746 W