1 Lecture Ch. 2b • Entropy • Second law of thermodynamics • Maxwell’s equations • Heat capacity • “Meteorologist’s entropy” Curry and Webster, Ch. 2 pp. 47-62!Van Ness, Ch. 5-7!Entropy • Is there a way to quantify “useful” energy? • Need a measure that is conserved, exact, unique • While Q is not exact, Qrev is exact – Reversible heat is limit of maximum work done – Since path is specified, cyclic integral is 0 Curry and Webster, Ch. 2 pp. 47-62!Van Ness, Ch. 5-7!Second Law of Thermodynamics • Heat cannot pass of itself from a colder body to a hotter body. • A system left to itself cannot move from a less ordered state to a more ordered state.!• The entropy of an isolated system cannot decrease.!19oC! 21oC!10oC! 30oC!not!possible!room containing air!not!possible!O2!here!N2!here!ΔSsystem≥ 0ΔSsystem=dQrevTsystemstate1state2∫The 2nd Law • Energy spontaneously tends to flow only from being concentrated in one place to becoming diffused or dispersed and spread out.!http://www.secondlaw.com/two.html!2 The 2nd law in practice • All types of energy spread out • A sinking ship loses its potential energy to the water it pushes away from itself as it sinks. • A tire pops. The air never spontaneously fills up the tire. www.creators.com/ 0305/LK/LK0310bg.gif Clausius’ Inequality Maxwell’s Equations Potential Temperature Virtual Potential Temperature • Potential Temperature (for moist air) • Virtual Potential Temperature € θv= T 1+ 0.608qv( )p0p RdcpdVirtual Temperature € Tv≥ T, Tv≈ T + [0 → 3K ]3 Meteorologists’ Entropy € η2−η1cp= lnθ2θ1θ2θ1= expη2−η1cp = expΔηcp Meteorologists’ Entropy € η2−η1cp= lnθ2θ1θ2θ1= expη2−η1cp = expΔηcp Example: NOAA HYSPLIT Model • Trajectories!• * Single or multiple (space or time) simultaneous trajectories!• * Optional grid of initial starting locations!• * Computations forward or backward in time!• * Default vertical motion using omega field!• * Other motion options: isentropic, isosigma, isobaric, isopycnic!• * Trajectory ensemble option using meteorological variations!• * Output of meteorological variables along a trajectory !http://www.arl.noaa.gov/ready/hysplit4.html "Example: NOAA HYSPLIT http://www.arl.noaa.gov/ready/hysplit4.html
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