Lecture Ch 2a Internal Energy vs Enthalpy Energy and its properties State functions or exact differentials Internal energy vs enthalpy First law of thermodynamics Heat work cycles Difference b w U and H U depends on v H depends on p Energy vs heat work Adiabatic processes Reversible P V work Homework problem Ch 2 Prob 2 Specific heats a k a heat capacity cv is constant v cp is constant p Curry and Webster Ch 2 pp 35 47 Van Ness Ch 2 Heat Capacity For an ideal gas Simplify to Types of processes Constant pressure Constant volume Lord Kelvin a k a William Thomson Other Kinds of Energy In addition to changes in internal energy a system may change James P Joule Potential energy for height change z Kinetic energy for velocity change v Nuclear energy for mass change m The First Law of Thermodynamics 1 E U p V T mg z m v 2 c 2 m Q W 2 Consequences Wrev pdv Uniqueness of work values Definition of energy Conservation of energy Q 0 E W Q 0 W 0 E 0 E2 E1 Impossibility of perpetual motion machine Relativity Q 0 E 0 W 0 E mc 2 Reversible Adiabatic State function See also 2nd law Proof follows if E U p V T then U p V T Q W Van Ness p 13 1 Work Expansion work W pdV or w pdv Lifting rising Mixing Convergence Other kinds of work Electrochemical e g batteries Cycles Work and heat are path dependent transfers Exact Differentials State functions are exact differentials W work Q heat State functions are unique states U internal energy H enthalpy also S entropy A Helmholtz free energy 2 Heat Work Cycles Carnot was an engineer in Napoleon s defeated army with an interest in engines The efficiency with which work is accomplished in a reversible cyclic process depends only on the temperature of the reservoirs to which heat is transferred THE CARNOT CYCLE T1 Q1 STEP 1 Expand isothermally and reversibly at T1 W1 Q1 RT1 ln PA PB STEP 2 Expand adiabatically and reversibly FLUID Q2 W W Cv T2 T1 STEP 3 Compress isothermally and reversibly at T2 W2 Q2 RT2 ln PC PD STEP 4 Compress adiabatically and reversibly T2 W Cv T1 T2 Efficiency 1 TCold THot Nikolaus Otto developed the Otto cycle in 1876 P V diagrams of work Rudolf Diesel developed the Diesel cycle in 1892 Other Work Cycles Work is determined by pathway The Otto Cycle works by compressing a mixture of air and fuel in a piston and then igniting the mixture with a spark Efficiency 1 TB TC T A TD The Diesel Cycle works by compressing air and then adding fuel directly to the piston The compressed air then combusts the mixture The compression ratio of the Diesel Cycle ranges from 14 1 to 25 1 while the Otto Cycle range is significantly lower from 8 1 to 12 1 The defining feature of the Diesel engine is the use of compression ignition to burn the fuel which is injected into the combustion chamber during the final stage of compression This is in contrast to a gasoline engine which utilizes the Otto cycle in which ignition is initiated by a spark plug following the aspiration and compression of a fuel air mixture Efficiency 1 T TC 1 B T A TD 5 4 Steps of Carnot Engine 3 for monatomic ideal gas Hurricane as Carnot Cycle 3 Lose Heat isothermally 2 Adiabatic 4 Adiabatic 1 Add Heat isothermally 1 Add Heat 3 Lose Heat 2 Adiabatic 4 Adiabatic isothermally isothermally 3 Ideal Gases W pdv Reversible mass is conserved Frictionless Low P High T Ideal Gas Adiabatic p1v1 pv R 2 2 T1 T2 Q 0 thick walls h dh h cp T p dT T v First Law u Q W Internal Energy u c vdT Reversible Adiabatic T2 P2 T1 P1 R cp grain of sand Reversible W pdv Ideal Gas p1v1 pv R 2 2 T1 T2 Q 0 mass is conserved Frictionless Low P High T Adiabatic W rev pdv Reversible mass is conserved Frictionless thick walls First Law u Q W Internal Energy u c vdT Reversible Adiabatic T2 P2 T1 P1 pdv c v dT RT dv c v dT v 2 R R cp 1 dv v 2 c 1 v dT T Always at or infinitesimally close to equilibrium Infinitesimally small steps Infinite number of steps Each step can be reversed with infinitesimal force Quiz Ch 2 Answer briefly and clearly with appropriate equations or diagrams 1 What is the first law of thermodynamics 2 What is a state function What property makes it useful and why 3 What is an energy cycle Give an example 4 What is reversible work Give an equation in terms of p and v Curry and Webster Ch 2 4 Homework Ch 2 Problem 2 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 The 2nd Law Heat cannot pass of itself from a colder body to a hotter body 19oC 21oC 10oC not possible 30oC A system left to itself cannot move from a less ordered state to a more ordered state room containing air not possible O2 here Energy spontaneously tends to flow only from being concentrated in one place to becoming diffused or dispersed and spread out N2 here The entropy of an isolated system cannot decrease Ssystem 0 Ssystem state 2 state 1 dQrev Tsystem http www secondlaw com two html 5 Clausius Inequality Maxwell s Equations Potential Temperature Virtual Potential Temperature Potential Temperature for moist air Virtual Potential Temperature p v T 1 0 608qv 0 p Rd c pd Virtual Temperature Meteorologists Entropy 2 1 ln 2 cp 1 Tv T Tv T 0 3K 2 exp 2 1 exp 1 cp cp 6 Example NOAA HYSPLIT Model Meteorologists Entropy 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 2 1 ln 2 cp 1 2 exp 2 1 exp 1 cp cp http www arl noaa gov ready hysplit4 html Example NOAA HYSPLIT http www arl noaa gov ready hysplit4 html 7
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